diff --git a/Main Code 64bits/Affichage.cpp b/Main Code 64bits/Affichage.cpp new file mode 100644 index 0000000..381b553 --- /dev/null +++ b/Main Code 64bits/Affichage.cpp @@ -0,0 +1,366 @@ + +/* + Name: + Copyright: + Author: + Date: 23/10/06 10:01 + Description: Affichage de particules + + +Les N particules sont des Vecteur3D et sont regroupées dans une + classe Body quelconque (pour plus de fléxibilité) (bod[i] est la particule i). + La classe Body qui doit contenir les fonctions: + + bod.get_pos pour avoir la position + couleur_bod[N] donne la couleur + + +Utilise OPEN_GL +Voici ce que j'ai compris d'OPENGL voir les autres références dans readMe_graphique.txt + +glMatrixMode(GL_MODELVIEW); //la pile des transformations "point de vue" est selectionnee +glLoadIdentity(); // initialisation de la transformation. Evite que les rotations, translations, .. s’ajoutent à la transformation courante. +glRotate, glTranslatef, ... // Crée chaque fois une matrice 4*4 qui tient compte de chaque transformation et qui s'empile dans la pile de "point de vue" +fonction de dessin1 Vertex, sphère etc... +fonction de dessin2 Vertex, sphère etc... + // Effectue les dessins, puis effectue l'ensemble des matrices puis la projection + +Si on veut dépiller par exemple que dessin 2 soit sans la dernière translation. Il faut faire +glPushMatrix(); + fonction de dessin2 Vertex, sphère etc... +glPopMatrix(); +fonction de dessin1 Vertex, sphère etc... + +Pour la spécification d’une projection perspective : +glMatrixMode(GL_PROJECTION); +glLoadIdentity(); +glFrustum(left, right, bas, haut, proche, loin); + +L'unité de base est donc SIZE_real = SIZE_affichage; +*/ + + + +#include "Affichage.h" + + +/************************************************************************/ +/************************** Programme *************************/ +/************************************************************************/ + + +// Cette fonction trace un repère de taille longueur, +// centré sur le repère objet avec +// une flêche rouge le long de l'axe des x, +// une flêche verte le long de l'axe des y +// et une flêche bleue le long de l'axe des z. + +// http://www.irit.fr/~Loic.Barthe/Enseignements/TPs_OpenGL/M1_IO5/TP8/tp8.html +void traceRepere (float longueur) +{ + + float DIAMETRECYLINDRE = 1.0/30.0; + float DIAMETRECONE = 1.0/15.0; + + GLUquadricObj *quad; + quad = gluNewQuadric(); + + + /* Axe X */ + glColor3d(1.0,0.0,0.0); + glPushMatrix(); + glRotatef(90.,0.0,1.0,0.0); + gluCylinder(quad, longueur*DIAMETRECYLINDRE, longueur*DIAMETRECYLINDRE, 0.8*longueur, 10, 10); + glTranslatef(0.0,0.0,0.8*longueur); + gluCylinder(quad, longueur*DIAMETRECONE, 0.0, 0.2*longueur, 10, 10); + glPopMatrix(); + /* Axe Y */ + glColor3d(0.0,1.0,0.0); + glPushMatrix(); + glRotatef(-90.,1.0,0.0,0.0); + gluCylinder(quad, longueur*DIAMETRECYLINDRE, longueur*DIAMETRECYLINDRE, 0.8*longueur, 10, 10); + glTranslatef(0.0,0.0,0.8*longueur); + gluCylinder(quad, longueur*DIAMETRECONE, 0.0, 0.2*longueur, 10, 10); + glPopMatrix(); + /* Axe Z */ + glColor3d(0.0,0.0,1.0); + glPushMatrix(); + glRotatef(180.,1.0,0.0,0.0); + gluCylinder(quad, longueur*DIAMETRECYLINDRE, longueur*DIAMETRECYLINDRE, 0.8*longueur, 10, 10); + glTranslatef(0.0,0.0,0.8*longueur); + gluCylinder(quad, longueur*DIAMETRECONE, 0.0, 0.2*longueur, 10, 10); + glPopMatrix(); + + + gluDeleteQuadric(quad); + +} + + +// Fonction pour recadrer l'image lors de sa première apparition ou si on la bouge avec la souris +void reshape(int w,int h) +{ + glViewport(0,0,w,h); + glMatrixMode(GL_PROJECTION); + glLoadIdentity(); + gluOrtho2D(0,w,0,h); + glScalef(1,-1,1); + glTranslatef(0,-h,0); + glMatrixMode(GL_MODELVIEW); +} + + +// Permet d'afficher du texte avec GLUT en x,y +// essayer ModuleFont.h +// http://raphaello.univ-fcomte.fr/IG/Modules/Modules.htm +void bitmap_output(int x,int y,char *string,void *font) +{ + int len,i; + glRasterPos2f(x,y); + len = (int) strlen(string); + for (i = 0; i < len; i++) + { + glutBitmapCharacter(font,string[i]); + } +} + +// Procedure simplifiant l'écriture +void texte_output(const double nombre, string text_string,const int x, const int y) +{ + char nb[16]; + sprintf(nb,"%d",(int) nombre); + string snb = nb ; + text_string += snb; + char texte[256]; // Doit être assez long + strcpy(texte, text_string.c_str()); + bitmap_output(x,y,texte,GLUT_BITMAP_HELVETICA_18); +} + +// Affiche une ellipse de taille Radius3D +// couleur par défault blanc +// nb de polygônes 20 par défault pour simuler la sphère +void affichage_ellipse(const Vecteur3D Radius3D, const Vecteur3D color, const int nb_polygone, const double SIZE_real) +{ + glPushMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit + glScalef(Radius3D.x()/SIZE_real,Radius3D.y()/SIZE_real,Radius3D.z()/SIZE_real); + // Donne la bonne forme elliptique + + GLUquadricObj *q = gluNewQuadric(); + gluQuadricDrawStyle(q, GLU_LINE); + glColor3d(color.x(), color.y(), color.z()); // Blanc + double rayon=Radius3D.mag()/SIZE_real; // Dessine le rayon + gluSphere(q, rayon, nb_polygone, nb_polygone); // divisée en nb_polygone polygones des 2 axes + gluDeleteQuadric(q); + glPopMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit +} + +/************ +// Affiche un hyperboloide de révolution +// D'après http://www-math.edu.kagoshima-u.ac.jp/~fractaro/AnschaulicheGeometrie/Hyperboloid.c + +// int mode = 0; +// int sign = 1; +// GLfloat blue[4], cyan[4], orange[4], yellow[4]; +**************/ + + + +double length(double v[]) +{ + return sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]); +} + +void exterior(double v1[], double v2[], double v3[]) +{ + v3[0] = v1[1] * v2[2] - v1[2] * v2[1]; + v3[1] = v1[2] * v2[0] - v1[0] * v2[2]; + v3[2] = v1[0] * v2[1] - v1[1] * v2[0]; +} + +void cylinder(double a[], double b[], double r, int slices, GLfloat color[]) +{ + double e1[3], e2[3], e3[3], va[40][3], vb[40][3], n[40][3], e4[3]; + double h, sinbeta, cosalpha, sinalpha, t, c, s; + int m, i, m1; + double epsilon = 0.00000001; + + for (i = 0; i < 3; i++) + { + e3[i] = b[i] - a[i]; + } + h = length(e3); + for (i = 0; i < 3; i++) + { + e3[i] /= h; + } + + sinbeta = sqrt(e3[0] * e3[0] + e3[1] * e3[1]); + if (sinbeta > epsilon) + { + cosalpha = e3[0] / sinbeta; + sinalpha = e3[1] / sinbeta; + e1[0] = -sinalpha; + e1[1] = cosalpha; + e1[2] = 0; + } + else + { + e1[0] = 1; + e1[1] = e1[2] = 0; + } + exterior(e3, e1, e2); + + for (m = 0; m < slices; m++) + { + t = 2.0 * pi / slices * m; + c = cos(t); + s = sin(t); + for (i = 0; i < 3; i++) + { + va[m][i] = a[i] + r * (c * e1[i] + s * e2[i]); + vb[m][i] = va[m][i] + h * e3[i]; + } + } + + for (m = 0; m < slices; m++) + { + t = 2.0 * pi / slices * (m + 0.5); + c = cos(t); + s = sin(t); + for (i = 0; i < 3; i++) + { + n[m][i] = c * e1[i] + s * e2[i]; + } + } + + for (i = 0; i < 3; i++) e4[i] = -e3[i]; + + glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, color); + + for (m = 0; m < slices; m++) + { + m1 = m + 1; + if (m1 == slices) m1 = 0; + glBegin(GL_POLYGON); + glNormal3dv(&n[m][0]); + glVertex3dv(&vb[m][0]); + glVertex3dv(&va[m][0]); + glVertex3dv(&va[m1][0]); + glVertex3dv(&vb[m1][0]); + glEnd(); + } + + for (m = 0; m < slices; m++) + { + m1 = m + 1; + if (m1 == slices) m1 = 0; + glBegin(GL_POLYGON); + glNormal3dv(&e4[0]); + glVertex3dv(&a[0]); + glVertex3dv(&va[m1][0]); + glVertex3dv(&va[m][0]); + glEnd(); + } + + for (m = 0; m < slices; m++) + { + m1 = m + 1; + if (m1 == slices) m1 = 0; + glBegin(GL_POLYGON); + glNormal3dv(&e3[0]); + glVertex3dv(&b[0]); + glVertex3dv(&vb[m][0]); + glVertex3dv(&vb[m1][0]); + glEnd(); + } +} + + +// Affiche un hyperboloide de révolution +// D'après http://www-math.edu.kagoshima-u.ac.jp/~fractaro/AnschaulicheGeometrie/Hyperboloid.c +// hyperboloid of one sheet is expressed by an equation +// x^2/a^2 + y^2/b^2 − z^2/c^2 = 1. I.E. taille a selon x, b selon y et c selon z +// n = nb de ligne le formant +// h = ? +// r = rayon des cylindre le formant +void Hyperboloid(double a, double b, double c, int n, double h, double r) +{ + + + double phi, dphi, cosphi, sinphi, w, t, P[3], e1[3], e2[3], A1[3], B1[3], A2[3], B2[3]; + int i, m; + + dphi = 2.0 * pi / n; + + for (m = 0; m < n; m++) + { + phi = dphi * m; + cosphi = cos(phi); + sinphi = sin(phi); + w = 1.0 / sqrt(c * c + b * b * cosphi * cosphi + a * a * sinphi * sinphi); + t = h / (c * w); + P[0] = a * cosphi; + P[1] = b * sinphi; + P[2] = 0; + e1[0] = -a * sinphi * w; + e1[1] = b * cosphi * w; + e1[2] = c * w; + e2[0] = -e1[0]; + e2[1] = -e1[1]; + e2[2] = e1[2]; + for (i = 0; i < 3; i++) + { + A1[i] = P[i] - t * e1[i]; + B1[i] = P[i] + t * e1[i]; + A2[i] = P[i] - t * e2[i]; + B2[i] = P[i] + t * e2[i]; + } + +GLfloat blue[4], cyan[4], orange[4], yellow[4]; + + cylinder(A1, B1, r, 10, yellow); + cylinder(A2, B2, r, 10, blue); + } +} + +// Affichage des lasers +void affichage_laser(const Laser my_laser, const double SIZE_real, int /* n */, double /* h */, double /* r */) +{ + +// glPushMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit +// glLoadIdentity(); // initialisation de la transformation. Evite que les rotations, translations, .. s’ajoutent à la transformation courante. +// // glScalef(1./SIZE_real,1./SIZE_real,1./SIZE_real); // Donne la bonne taille +// +// +// Vecteur3D waist_position= my_laser.get_waist_pos(); +// Vecteur3D waist=my_laser.waist_size(waist_position); // wx,wy,zone de Rayleigh moyenne +// Vecteur3D direction= my_laser.get_direction(); +// +// Vecteur3D rot=direction.cross(Vecteur3D(0.,0.,1.)); // rotation Euler pour amener OZ sur k +// double angle_rot= direction.angle(Vecteur3D(0.,0.,1.)); +// +// glTranslatef(waist_position.x(),waist_position.y(),waist_position.z()); // centre le laser sur son waist +// glRotated(angle_rot ,rot.x(), rot.y(), rot.z()); // glRotated(angle ,rot_axe_x, rot_axe_y, rot_axe_z); +// +// Hyperboloid(waist.x(), waist.y(), waist.z(), n, h, r); +// +// glPopMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit + + + Vecteur3D waist_position= my_laser.get_waist_pos(); + Vecteur3D waist=my_laser.waist_size(waist_position); // wx,wy,zone de Rayleigh moyenne + + glPushMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit + glLoadIdentity(); // initialisation de la transformation. Evite que les rotations, translations, .. s’ajoutent à la transformation courante. + + glScalef(10,10,10); // Donne la bonne taille + glRotated(45,1,1,1); // glRotated(angle ,rot_axe_x, rot_axe_y, rot_axe_z); + Hyperboloid(waist.x(), waist.y(), waist.z(), 10, 10, 0.01); + glPopMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit +} + + + + + + diff --git a/Main Code 64bits/Affichage.h b/Main Code 64bits/Affichage.h new file mode 100644 index 0000000..422c38b --- /dev/null +++ b/Main Code 64bits/Affichage.h @@ -0,0 +1,140 @@ +/* + Name: + Copyright: + Author: + Date: 23/10/06 10:01 + Description: Affichage de particules + + +Les N particules sont des Vecteur3D et sont regroupées dans une + classe Body quelconque (pour plus de flexibilité) (bod[i] est la particule i). + La classe Body qui doit contenir les fonctions: + + bod.get_pos pour avoir la position + couleur_bod[N] donne la couleur + + +Utilise OPEN_GL +Voici ce que j'ai compris d'OPENGL voir les autres références dans readMe_graphique.txt + +glMatrixMode(GL_MODELVIEW); //la pile des transformations "point de vue" est selectionnee +glLoadIdentity(); // initialisation de la transformation. Evite que les rotations, translations, .. s’ajoutent à la transformation courante. +glRotate, glTranslatef, ... // Crée chaque fois une matrice 4*4 qui tient compte de chaque transformation et qui s'empile dans la pile de "point de vue" +fonction de dessin1 Vertex, sphère etc... +fonction de dessin2 Vertex, sphère etc... + // Effectue les dessins, puis effectue l'ensemble des matrices puis la projection + +Si on veut dépiller par exemple que dessin 2 soit sans la dernière translation. Il faut faire +glPushMatrix(); + fonction de dessin2 Vertex, sphère etc... +glPopMatrix(); +fonction de dessin1 Vertex, sphère etc... + +Pour la spécification d’une projection perspective : +glMatrixMode(GL_PROJECTION); +glLoadIdentity(); +glFrustum(left, right, bas, haut, proche, loin); + +L'unité de base est donc SIZE_real = SIZE_affichage +*/ + + + + + + +#ifndef Affichage_SEEN +#define Affichage_SEEN + + + +#include + + +#include // For clock() + +#include +#ifdef __APPLE__ +#include +#else +#include +#endif + +#include // OPENGL +#include // OPENGL (GLU) +#include // glut bibliotheque +// #include // glut bibliotheque +#include + +#include "Vecteur3D.h" +#include "Laser.h" // Classe Laser + +using namespace std; + +const double SIZE_SCREEN = 2.; // L'écran est en X -1,1 en Y -1,1 et en Z -1,-3 donc SIZE_SCREEN = 2 +const double Z0 = 2.; // dans OPEN_GL il faut Z >0 donc je translate de Z0; + + +/************************************************************************/ +/************************** Programme *************************/ +/************************************************************************/ + + +// Cette fonction trace un repère de taille longueur, +// centré sur le repère objet avec +// une flêche rouge le long de l'axe des x, +// une flêche verte le long de l'axe des y +// et une flêche bleue le long de l'axe des z. + +// http://www.irit.fr/~Loic.Barthe/Enseignements/TPs_OpenGL/M1_IO5/TP8/tp8.html +void traceRepere (float longueur); + +// Fonction pour recadrer l'image lors de sa première apparition ou si on la bouge avec la souris +void reshape(int w,int h); + +// Permet d'afficher du texte avec glut en x,y +// essayer ModuleFont.h +// http://raphaello.univ-fcomte.fr/IG/Modules/Modules.htm +void bitmap_output(int x,int y,char *string,void *font); + +// Procedure simplifiant l'écriture +void texte_output(const double nombre, string text_string,const int x, const int y); + +// Affiche une ellipse de taille Radius3D +// couleur par défault blanc +// nb de polygônes 20 par défault pour simuler la sphère +void affichage_ellipse(const Vecteur3D Radius3D, const Vecteur3D color=Vecteur3D(1.,0.,1.), const int nb_polygone=20, const double SIZE_real = 0.005); + +/************ +// Pour pouvoir afficher des faisceaux lasers comme des hyperboloides de révolution +// D'après http://www-math.edu.kagoshima-u.ac.jp/~fractaro/AnschaulicheGeometrie/Hyperboloid.c +**************/ + +// +//int mode = 0; +//int sign = 1; +// +//GLfloat blue[4], cyan[4], orange[4], yellow[4]; + +double length(double v[]); +void exterior(double v1[], double v2[], double v3[]); +void cylinder(double a[], double b[], double r, int slices, GLfloat color[]); + +// Affiche un hyperboloide de révolution +// D'après http://www-math.edu.kagoshima-u.ac.jp/~fractaro/AnschaulicheGeometrie/Hyperboloid.c +// hyperboloid of one sheet is expressed by an equation +// x^2/a^2 + y^2/b^2 − z^2/c^2 = 1. I.E. taille a selon x, b selon y et c selon z +// n = nb de ligne le formant +// h = ? +// r = rayon des cylindre le formant +void Hyperboloid(double a, double b, double c, int n, double h, double r); + +// Affichage des lasers +void affichage_laser(const Laser my_laser, const double SIZE_real, int n, double h, double r); + + +#endif + + + + diff --git a/Main Code 64bits/Affichage_Mol.h b/Main Code 64bits/Affichage_Mol.h new file mode 100644 index 0000000..9941d76 --- /dev/null +++ b/Main Code 64bits/Affichage_Mol.h @@ -0,0 +1,454 @@ +/* + Name: + Copyright: + Author: + Date: 23/10/06 10:01 + Description: Paramètre pour l'affichage des molécules avec OPEN_GL (voir aussi Affichage.h) + + A priori tout est dans le dessin d'une particule unique +affichage_one_bod + +*/ + + + +#ifndef Affichage_Mol_SEEN +#define Affichage_Mol_SEEN + +#include +using namespace std; + +#include "constantes_SI.h" +#include "Vecteur3D.h" +#include "Molecule.h" +#include "Field.h" +#include "Affichage.h" + +/************************************************************************/ +/************************** Programme *************************/ +/************************************************************************/ + + +// Choix des couleurs + +//Vecteur3D(0,1,0); // vert +//Vecteur3D(1,1,0); // jaune +//Vecteur3D(1,0,0); // rouge +//Vecteur3D(0,0,1); // bleu +//Vecteur3D(1,1,1); // blanc +//Vecteur3D(1,0,1); // violet + + + +void init_couleurs(Vecteur3D *couleur, const int Nmax); + +// initialisation des tailles affichées sur l'écran +void init_tailles(double *taille, const int Nmax); + +// dessin d'une particule unique +// Pour nous la taille est proportionnelle à la vibration +// L'angle de rotation est donné par la rotation J (selon Ox), MJ (selon 0y) +template +void affichage_one_bod(const Body my_bod, FitParams ¶ms); // Affichage des points + +template +void affichage_legend(const vector &bod, const vector &Level, const double t, const int Nb_body, const int Nb_state, FitParams ¶ms); + +// Affiche la légende pour l'état des particules +template +void affichage_stat_color(Body my_bod, const int Nb_state, FitParams ¶ms); + +// Affichage des particules +template +void affichage_zone(const vector &bod, const int Nb_body, const double SIZE_real, FitParams ¶ms); // Affichage des points + +// Affichage du système +template +void Draw(const vector &bod, const vector &Level, const Field &fieldB, const Field &fieldE, const vector &lasers, const double t, const int Nb_body, const int Nb_of_different_type_body, FitParams ¶ms); + + + + +/************************************** +JE MET ICI L'equivalent du .cpp car "On peut pas séparer un .h et .cpp pour les template". + +En effet si un symbole template est utilisé uniquement dans un .cpp (fichier source), il peut être implémenté dans ce .cpp +Sinon, il doit être implémenté dans un .hpp (header). + +cf http://www.commentcamarche.net/faq/11194-les-templates-en-c +***************************************/ + + +/************************************************************************/ +/******** PARAMETER TO DRAW MOLECULES (color, size, ...) ***************/ +/************************************************************************/ + + +// List of Basic color in RGB code, but divided by 255 to fit for OPENGL +const Vecteur3D Black = Vecteur3D (0,0,0) / 255 ; +const Vecteur3D White = Vecteur3D (255,255,255) / 255 ; +const Vecteur3D Red = Vecteur3D (255,0,0) / 255 ; +const Vecteur3D Lime = Vecteur3D (0,255,0) / 255 ; +const Vecteur3D Blue = Vecteur3D (0,0,255) / 255 ; +const Vecteur3D Yellow = Vecteur3D (255,255,0) / 255 ; +const Vecteur3D Cyan_Aqua = Vecteur3D (0,255,255) / 255 ; +const Vecteur3D Magenta_Fuchsia = Vecteur3D (255,0,255) / 255 ; +const Vecteur3D Silver = Vecteur3D (192,192,192) / 255 ; +const Vecteur3D Gray = Vecteur3D (128,128,128) / 255 ; +const Vecteur3D Maroon = Vecteur3D (128,0,0) / 255 ; +const Vecteur3D Olive = Vecteur3D (128,128,0) / 255 ; +const Vecteur3D Green = Vecteur3D (0,128,0) / 255 ; +const Vecteur3D Purple = Vecteur3D (128,0,128) / 255 ; +const Vecteur3D Teal = Vecteur3D (0,128,128) / 255 ; +const Vecteur3D Navy = Vecteur3D (0,0,128) / 255 ; + + +/*** Class Param_Draw_Mol to decide how to draw a molecule ***/ + +/*********** + +class Param_Draw_Mol +{ +protected: + string name; + double mass; + map color_electronical_state; + map size_electronical_state; + double scale_vibrational_state; // v + double angle_rotational_state; // J + double angle_angular_state; // M + +public: + Param_Draw_Mol(); //constructor + virtual ~Param_Draw_Mol(); // Destructor + + virtual void read(istream & flux) + { + flux >> name; + flux >> mass; + // flux >> color_electronical_state; + // flux >> size_electronical_state; + flux >> scale_vibrational_state; + flux >> angle_rotational_state; + flux >> angle_angular_state; + } +}; + +istream& operator >> (istream &flux,Param_Draw_Mol & at) +{ + at.read(flux); + return(flux); +} + +// Default Constructor +Param_Draw_Mol::Param_Draw_Mol() +{ + name = "Cs"; + mass = MCs; + // color_electronical_state = map < int,Vecteur3D > (); +// color_electronical_state[fond] = Green; // +// color_electronical_state = ; +// size_electronical_state; +// scale_vibrational_state; // v +// angle_rotational_state; // J +// angle_angular_state; // M +}; + +**********/ + +void init_couleurs(Vecteur3D *couleur, const int Nmax) +{ + couleur[fond] = Green; + couleur[excite] = Yellow; + couleur[excite2] = Blue; + couleur[excite3] = Olive; + for (int i = excite3; i < Nmax; i++) + couleur[i] = Vecteur3D (50+2*i,50+2*i,0) / 255; +} + +// initialisation des tailles affichées sur l'écran +void init_tailles(double *taille, const int Nmax) +{ + taille[fond] = 0.01; + taille[excite] = 0.015; + taille[excite2] = 0.02; + taille[excite3] = 0.03; + for (int i = excite3; i < Nmax; i++) + taille[i] = 0.005*i; +} + + + +// dessin d'une particule unique +// Pour nous la taille est proportionnelle à la vibration +// L'angle de rotation est donné par la rotation J (selon Ox), MJ (selon 0y) +template +void affichage_one_bod(const Body my_bod, FitParams ¶ms) // Affichage des points +{ + + int etat = my_bod.exc; + if (etat < 0) etat = excite3; // choose the color for the lost (or ionized) particules to plot them + if (my_bod.get_name() == "P_bar") etat = excite3; // Then P_bar are red + + + int v = my_bod.v; + int two_J = my_bod.two_J; + int two_M = my_bod.two_M; + + int Nb_max = 100; // Pour etre conservatif + if (etat >= Nb_max) etat = excite2; // To avoid to call array[etat] outside of its broder + + Vecteur3D couleur_bod[Nb_max]; + double tailles_bod[Nb_max]; + init_couleurs(couleur_bod,Nb_max); + init_tailles(tailles_bod,Nb_max); // On met 100 et pas Nb_max car cela buggait ????? + + + int two_J_maX= params.LocateParam("N_Two_JX_out_max")->val + params.LocateParam("N_Two_JA_out_max")->val; // J_max pour l'affichage + int v_maX=params.LocateParam("NX_out")->val; // v_max pour l'affichage + + + // glRotate produces a rotation of angle degrees around the vector (x,y,z) for all object + glRotated(90.*two_J/(two_J_maX+1.1),0.,0.,1.); + glRotated(90.*two_M/(two_J+1.1),0.,1.,0.); // +1.1 pour éviter le J=0 et convertir le int en double + + double DIAM = (1.0/50.0); + double longueur = 0.2*(v+1.2)/(v_maX+1.1); // ou 1.1*v/(v_maX+1.1) si on veut l'état v=0 petit + + + // glColor3d((MJ+J)/(2.*J)+couleur_bod[etat].x(),(MJ+2.*J)/(2.*J)*couleur_bod[etat].y(),couleur_bod[etat].z()); + // Pour l'état fondamental M=-J vert sombre M=+J jaune clair + + glColor3d(couleur_bod[etat].x(),couleur_bod[etat].y(),couleur_bod[etat].z()); + + glutSolidSphere(tailles_bod[etat],10,10); + + glPushMatrix(); + + GLUquadricObj *quad; + quad = gluNewQuadric(); +// Je ne comprend pas pourquoi il faut cela + glRotatef(90.,0.0,1.0,0.0); + + + gluCylinder(quad, longueur*DIAM, longueur*DIAM, 0.8*longueur, 10, 10); + glPopMatrix(); + + gluDeleteQuadric(quad); + + glTranslatef(longueur,0.,0.); //position du 2ème atome + glColor3d (1,1,1); + glutSolidSphere(tailles_bod[etat],10,10); +} + + + +template +void affichage_legend(const vector &bod, const vector &Level, const Field &fieldB, const Field &fieldE, const double t, const int Nb_body, const int Nb_state, FitParams ¶ms) +{ + + int Nb_max=100; + Vecteur3D couleur_bod [Nb_max]; // For safety because the last color is excite3 3; + double tailles_bod [Nb_max]; + + init_couleurs(couleur_bod,Nb_max); + init_tailles(tailles_bod,Nb_max); + + + int size_screen =600; // Cela correspond à la taille dans main + glViewport(0,0,size_screen,size_screen); + glMatrixMode(GL_PROJECTION); + glLoadIdentity(); + gluOrtho2D(0,size_screen,0,size_screen); + glScalef(1,-1,1); + glTranslatef(0,-size_screen,0); + glMatrixMode(GL_MODELVIEW); + glLoadIdentity(); + + Body bod_avg, bod_var; + // vector stat_Mol; + // stat_molecule(bod, stat_Mol, Level, fieldB, fieldE, Nb_body, Nb_state, params); + + + // Affiche le nombre d'molecules excités dans chaque état exc + int taille_police = 18; + int position_y =70; + int step_y = 1; + + + position_y -= taille_police+2; + + + + int i=1; + glColor3d ( couleur_bod[i].x(),couleur_bod[i].y(),couleur_bod[i].z()); + bitmap_output(25,position_y,const_cast(" excité "),GLUT_BITMAP_TIMES_ROMAN_24); // Le const_cast est là pour éviter le warning: deprecated conversion from string constant to 'char*' + position_y -= taille_police+step_y; + i=0; + glColor3d (couleur_bod[i].x(),couleur_bod[i].y(),couleur_bod[i].z()); + bitmap_output(25,position_y,const_cast(" fond "),GLUT_BITMAP_TIMES_ROMAN_24); + + Stat stat_Mol; + stat_molecule_un_niveau(bod, stat_Mol, Level, fieldB, fieldE, all, Nb_body, params); + + int nb_fond = stat_Mol.population; + + glColor3d(1, 1, 1); // Blanc + position_y += taille_police+360; + + texte_output(t/nanosecond," t (ns) = ",5, position_y); + position_y += taille_police+step_y; + + texte_output(stat_Mol.mean_v.x()/cm," vx (cm/s) = ",5, position_y); + texte_output(stat_Mol.Temp_1D_50.x()/muK," Tx (mu K) = ",5, position_y); // Calcul la température kB T=m v^2 sur chaque axe + + position_y += taille_police+step_y; + texte_output(stat_Mol.mean_v.y()/cm," vy (cm/s) = ",5, position_y); + texte_output(stat_Mol.Temp_1D_50.y()/muK," Ty (mu K) = ",5, position_y); // On suppose que toutes les particules ont la même masse + + position_y += taille_police+step_y; + texte_output(stat_Mol.mean_v.z()/cm," vz (cm/s) = ",5, position_y); + texte_output(stat_Mol.Temp_1D_50.z()/muK," Tz (mu K) = ",5, position_y); + + position_y += taille_police+step_y; + texte_output((stat_Mol.E_pot/kB)/mK/1.5/nb_fond," E_pot(mK) ",5, position_y); + texte_output((stat_Mol.E_cin/kB)/mK/1.5/nb_fond," E_cin(mK) ",5, position_y); + + position_y += taille_police+step_y; + texte_output(stat_Mol.mean_pos.x()/MICRON," x (mu m) = ",5, position_y); + texte_output(stat_Mol.sigma_pos.x()/MICRON," Dx (mu m) = ",5, position_y); + + position_y += taille_police+step_y; + texte_output(stat_Mol.mean_pos.y()/MICRON," y (mu m) = ",5, position_y); + texte_output(stat_Mol.sigma_pos.y()/MICRON," Dy (mu m) = ",5, position_y); + + position_y += taille_police+step_y; + texte_output(stat_Mol.mean_pos.z()/MICRON," z (mu m) = ",5, position_y); + texte_output(stat_Mol.sigma_pos.z()/MICRON," Dz (mu m) = ",5, position_y); + + /****** Stats of all molecules, of N_Mol[0] and others ******/ + position_y += taille_police+step_y; + texte_output(((stat_Mol.E_pot+stat_Mol.E_cin)/kB)/mK/3./nb_fond," E_tot(mK) ",5, position_y); + texte_output(stat_Mol.Temp_3D_50/mK," T_all (mK)= ",3, position_y); +// Attention relative à la température E_pot = 3/2 k T, E_cin =3/2 kT; E tot=3 kT + + int N_Mol_0 = params.LocateParam("N_Mol[0]")->val ; + vector liste_Adresses_Mol_dans_niveau; //List of Molecule of first type + for (int i=0; i!= N_Mol_0; i++) + liste_Adresses_Mol_dans_niveau.push_back(bod[i]); + stat_molecule_form_list(bod, liste_Adresses_Mol_dans_niveau, stat_Mol, Level, fieldB, fieldE, Nb_body, params); + texte_output(stat_Mol.Temp_3D_50/mK," T[0]= ",3, position_y); + + liste_Adresses_Mol_dans_niveau.clear(); + for (int i=N_Mol_0; i!= Nb_body; i++) + liste_Adresses_Mol_dans_niveau.push_back(bod[i]); + stat_molecule_form_list(bod, liste_Adresses_Mol_dans_niveau, stat_Mol, Level, fieldB, fieldE, Nb_body, params); + texte_output(stat_Mol.Temp_3D_50/mK," T[1]= ",3, position_y); + + + +} + +// Affiche la légende pour l'état des particules +template +void affichage_stat_color(Body my_bod, const int Nb_state, FitParams ¶ms) +{ + glMatrixMode(GL_PROJECTION); + glLoadIdentity(); + + glMatrixMode(GL_MODELVIEW); //la pile des transformations "point de vue" est selectionnee + glLoadIdentity(); // initialisation de la transformation. Evite que les rotations, translations, .. s’ajoutent à la transformation courante. + + + glTranslatef(-0.95,0.95,0); + + for (int i=0; i!= Nb_state; i++) + { + glPushMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit + my_bod.set_pos(Vecteur3D(0,-(i+2)/10.,0)); + + affichage_one_bod(my_bod, params); + glPopMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit + + } +} + + + +// Affichage des particules +template +void affichage_zone(const vector &bod, const int Nb_body, const double SIZE_real, FitParams ¶ms) // Affichage des points +{ + + for (int i = 0; i < Nb_body; i++) + { + Vecteur3D position ( (bod[i].get_pos())/SIZE_real); // Ramène la position + + glPushMatrix(); // Empile la matrice courante dans la pile de matrices. Permet d'effectuer la transformation uniquement sur ce qui suit + // glTranslatef(0,0,0); + glTranslatef(position.x(),position.y(),-position.z()); + + affichage_one_bod(bod[i], params); + + glPopMatrix(); // Dépile la matrice en haut de pile et remplace la matrice courante par celle-ci. + } + // glFlush(); // Vide la matrice de transformation de point de vue +} + +// Affichage du système +template +void Draw(const vector &bod, const vector &Level, const Field &fieldB, const Field &fieldE, const vector &lasers, const double SIZE_real, const double t, const int Nb_body, const int Nb_of_different_type_body, FitParams ¶ms) +{ + + glClear(GL_DEPTH_BUFFER_BIT|GL_COLOR_BUFFER_BIT|GL_ACCUM_BUFFER_BIT); + + int Nb_state = Level.size(); + + glMatrixMode(GL_PROJECTION); + glLoadIdentity(); + glFrustum (-1.0, 1.0, -1.0, 1.0, 1, 3); // glFrustum(left, right, bas, haut, proche, loin); + // Ici la caméra est à l'origine et l'écran va de X -1,1 en Y -1,1 (Attention Z<0 mais les coeef sont >0 !) + + + glMatrixMode(GL_MODELVIEW); //la pile des transformations "point de vue" est selectionnee + glLoadIdentity(); // initialisation de la transformation. Evite que les rotations, translations, .. s’ajoutent à la transformation courante. + //glViewport(100,200,300,300); // glViewport(GLint x,GLint y,GLSizei largeur,GLSizei hauteur) 'x' et 'y' sont les coordonnées du coin supérieur left + glTranslatef(0,0,-Z0); + double angle = 90; // 90 pour avoir la gravité vers le bas (Oz vers le haut), 180 (0) pour avoir Oy vers le bas (haut) + + double rot_axe_x = params.LocateParam("rot_axe_x")->val; + double rot_axe_y = params.LocateParam("rot_axe_y")->val; + double rot_axe_z = params.LocateParam("rot_axe_z")->val; + glRotated(angle,rot_axe_x,rot_axe_y,rot_axe_z); // glRotated(angle ,rot_axe_x, rot_axe_y, rot_axe_z); + + // glScalef(1.,1.,1.); // multiplie la taille de l'image par zoom (effectue un zoom) +// On pourrait faire le zoom avec la souris et le fichier zpr.c + + affichage_zone(bod, Nb_body, SIZE_real, params); // Affiche les particules + + traceRepere (0.5); // // Cette fonction trace un repère de taille longueur, +// centré sur le repère objet avec +// une flêche rouge le long de l'axe des x, +// une flêche verte le long de l'axe des y +// et une flêche bleue le long de l'axe des z. + + affichage_legend(bod, Level, fieldB, fieldE, t, Nb_body,Nb_state, params) ; // Affiche les statistiques sur les molecules + + // affichage_stat_color(bod[0],Nb_state, params); // Affiche les statistiques sur les molecules + + glutSwapBuffers(); // A TESTER permet d'eviter un "blincking" lors de l'affichage + + // wait(1.5); // Permet de ne pas avoir un affichage trop rapide + + +} + + + + + +#endif + + + + diff --git a/Main Code 64bits/BicubicInterpolation_module.cpp b/Main Code 64bits/BicubicInterpolation_module.cpp new file mode 100644 index 0000000..9dec726 --- /dev/null +++ b/Main Code 64bits/BicubicInterpolation_module.cpp @@ -0,0 +1,364 @@ +#include "BicubicInterpolation_module.h" +#include "LekienMarsdenMatrix.h" +#include +#include // to read the data and put them in files +// #include + + +using namespace std; + + +// Create equidistant points with offset X0 -and Y0) and spaced delta_x (or delta y) +// Initialize the value of the matrix by the Xvalues[i]=X0 + i*delta_x and same for Y +void Bicubic_Interpolator::Init(int NewXDimension, int NewYDimension, double delta_x, double delta_y, double X0, double Y0) +{ + + m_xdimension = NewXDimension; + m_ydimension = NewYDimension; + //Prepare X positions array + + // vector m_xvalues(m_xdimension); // m_xvalues = new double[m_xdimension]; + m_xvalues.clear(); + for(int i = 0; i< m_xdimension; i++) + { + m_xvalues.push_back(X0 + i*delta_x); // m_xvalues[i] = X0 + i*delta_x; + } + //Prepare Y positions array + + // vector m_yvalues(m_ydimension); // m_yvalues = new double[m_ydimension]; + m_yvalues.clear(); + for(int i = 0; i< m_ydimension; i++) + { + m_yvalues.push_back(Y0 + i*delta_y);// m_yvalues[i] = Y0 + i*delta_y; + } + //Prepare array for coefficients + //Assume that points are equipartitioned + m_delta_x = delta_x; + m_delta_y = delta_y; + //Allocate nonzero indices + PrepareMatrixIndicesArray(); +}; + + +//Constructor +Bicubic_Interpolator::Bicubic_Interpolator(int NewXDimension, int NewYDimension, double delta_x, double delta_y, double X0, double Y0) +{ + Init(NewXDimension, NewYDimension, delta_x, delta_y, X0, Y0); +}; + +//Prepare nonzero matrix indices from the 16*16 BicubicMatrix +// The indices are calculated using i*100+j -this is useful because we can easily recognize i and j even if the matrix is only 16*16 and i*16+j would have worked but would be less easy to read! +void Bicubic_Interpolator::PrepareMatrixIndicesArray() +{ + m_nonzero_counter = 0; + for(int i=0; i< 16; i++) + { + for(int j=0; j<16; j++) + { + if(Global::BicubicMatrix[i][j] != 0) m_nonzero_counter++; + } + } + int index = 0; + // m_nonzero_indices = new int[m_nonzero_counter]; + m_nonzero_indices.clear(); + for(int i=0; i< 16; i++) + { + for(int j=0; j<16; j++) + { + if(Global::BicubicMatrix[i][j] != 0) + { + m_nonzero_indices.push_back(i*100+j); // m_nonzero_indices[index] = i*100+j; + index++; + } + } + } +} + +//Transform nonzero indices in a duplet i,j +void Bicubic_Interpolator::GetMatrixIndices(int index, int& i, int& j) const +{ + i = index / 100; + j = index - 100*i; +}; + +//Get index of the point (just before) of the grid close to the X,Y point +// return the index near x,y, or (0,0) if one is out of the grid range +void Bicubic_Interpolator::GetIndex(const double& X, const double& Y, int &m_xindex, int &m_yindex) const +{ + //cout<(floor((X-m_xvalues[0])/m_delta_x)); + m_yindex = static_cast(floor((Y-m_yvalues[0])/m_delta_y)); + EvaluateIndices(m_xindex, m_yindex); + +}; + + +//Show indices of the point of the grid close to the X,Y point +void Bicubic_Interpolator::ShowIndex(const double& X, const double& Y) const +{ + cout<<"Xindex = "<(floor((X-m_xvalues[0])/m_delta_x))< > &matrix, int IndexX, int IndexY, int j) const +{ + if(IndexX == 0) return 0; + if(IndexX >= m_xdimension - 1) return 0; + double DeltaF = matrix[j][(IndexX + 1)*m_ydimension + IndexY] - matrix[j][(IndexX - 1)*m_ydimension + IndexY]; + return (DeltaF / (2*m_delta_x)); +}; + +double Bicubic_Interpolator::PartialYDerivative(const vector > &matrix, int IndexX, int IndexY, int j) const +{ + if(IndexY == 0) return 0; + if(IndexY >= m_ydimension - 1) return 0; + double DeltaF = matrix[j][IndexX *m_ydimension + IndexY+1] - matrix[j][IndexX * m_ydimension + IndexY-1]; + return (DeltaF / (2*m_delta_y)); +}; + + +double Bicubic_Interpolator::PartialXYDerivative(const vector > &matrix, int IndexX, int IndexY, int j) const +{ + if(IndexY == 0 || IndexX == 0) return 0; + if(IndexY >= m_ydimension - 1 || IndexX >= m_xdimension - 1) return 0; + double DeltaF = matrix[j][(IndexX + 1)*m_ydimension + IndexY + 1] + matrix[j][(IndexX - 1)*m_ydimension + IndexY - 1] - matrix[j][(IndexX + 1)*m_ydimension + IndexY - 1] - matrix[j][(IndexX - 1)*m_ydimension + IndexY + 1]; + return (DeltaF / (4*m_delta_x*m_delta_y)); +}; + + + +// Same but directly write from the matrix m[j][i]. Recall matrix[m_x][m_y] is transformed in m[j][m_x*m_ydimension + my]. So i = m_x*m_ydimension + my + +double Bicubic_Interpolator::XDerivative(const vector > &matrix, int i, int j) const +{ + int IndexX = i/m_ydimension; + if(IndexX == 0) return 0; + if(IndexX == m_xdimension - 1) return 0; + double DeltaF = matrix[j][i+m_ydimension] - matrix[j][i-m_ydimension]; + return (DeltaF / (2.*m_delta_x)); +}; + +double Bicubic_Interpolator::YDerivative(const vector > &matrix, int i, int j) const +{ + int IndexY = i- m_ydimension*(i/m_ydimension); + if(IndexY == 0) return 0; + if(IndexY >= m_ydimension - 1) return 0; + double DeltaF = matrix[j][i+1] - matrix[j][i-1]; + return (DeltaF / (2.*m_delta_y)); +}; + + +double Bicubic_Interpolator::XYDerivative(const vector > &matrix, int i, int j) const +{ + int IndexX = i/m_ydimension; + int IndexY = i- m_ydimension*(i/m_ydimension); + if(IndexY == 0 || IndexX == 0) return 0; + if(IndexY >= m_ydimension - 1 || IndexX >= m_xdimension - 1) return 0; + double DeltaF = matrix[j][i+m_ydimension + 1] + matrix[j][i-m_ydimension - 1] - matrix[j][i+m_ydimension - 1] - matrix[j][i-m_ydimension+ 1]; + return (DeltaF / (4*m_delta_x*m_delta_y)); +}; + + + + + + + +/* PROTECTED MAIN FUNCTIONS */ + +/** cf discussion in +LekienMarsdenMatrix.h +http://en.wikipedia.org/wiki/Bicubic_interpolation + +Grouping the unknown parameters a_{ij} in a vector a, values of f, df/dx, df/dy, d2f/dxdy at 4 corner point in a vector F +the interpolation +f(x,y) = \sum_{i=0}^3 \sum_{j=0}^3 a_{ij} x^i y^j. + can be reformulated into a matrix for the linear equation: BicubicMatrix a = F. + + Be CAREFUL The order of point is not the same than in Wikipedia + in wikipedia it is (0,0) (1,0) (0,1) (1,1) + Here it "seems" to be (0,0) (1,0) (1,1) (0,1) + because this comes from Numerical Recipies +cf http://www.it.uom.gr/teaching/linearalgebra/NumericalRecipiesInC/c3-6.pdf +**/ + + +void Bicubic_Interpolator::Prepare_Coefficients(const vector > &matrix, int m_xindex, int m_yindex, vector &m_coefficients, int j, int type_field_read) const +{ +// assuming that m_xindex, m_yindex have been already calculated + double f[4]; + double dfdx[4], dfdy[4]; + double d2fdxdy[4]; + double x[16]; + int index_to_points_x[4] = {0, 1, 1, 0}; + int index_to_points_y[4] = {0, 0, 1, 1}; +//std::cout<< +// filling arrays + std::cout.setf(ios::fixed, ios::floatfield); + + for(int i = 0; i< 4; i++) + { + //cout< > &matrix, const double &x, const double &y,double &ans, double &dervx, double &dervy, int column_number, int type_field_read) const +{ + ans = 0.; // answer ! that is f(x,y) + dervx = 0.; // derivation along x that is f_x(x,y) + dervy = 0.; // derivation along y that is f_y(x,y) + // calculate LL indices basing on the point + int m_xindex, m_yindex; + GetIndex(x,y,m_xindex, m_yindex); + if(m_xindex >= m_xdimension || m_xindex < 0 || m_yindex >= m_ydimension || m_yindex < 0) + { + cout< m_coefficients(16,0.); + Prepare_Coefficients(matrix,m_xindex, m_yindex,m_coefficients,column_number,type_field_read); + double xd = (x - m_xvalues[m_xindex])/m_delta_x; + double yd = (y - m_yvalues[m_yindex])/m_delta_y; + + // obtain values + // COMPACT PROCEDURE: 1 cycle only (saves 12 operation per interpolation) - see commented lines for the explicit version + for (int i=3; i>=0; i--) + { + ans = xd*(ans)+((m_coefficients[ij_to_index(3,i)]*yd + m_coefficients[ij_to_index(2,i)])*yd + m_coefficients[ij_to_index(1,i)])*yd + m_coefficients[ij_to_index(0,i)]; + dervy = xd*(dervy)+(3.0*m_coefficients[ij_to_index(3,i)]*yd + 2.0*m_coefficients[ij_to_index(2,i)])*yd + m_coefficients[ij_to_index(1,i)]; + dervx = yd*(dervx)+(3.0*m_coefficients[ij_to_index(i,3)]*xd + 2.0*m_coefficients[ij_to_index(i,2)])*xd + m_coefficients[ij_to_index(i, 1)]; + } + dervx /= m_delta_x; + dervy /= m_delta_y; + + /* + //EXPLICIT VERSION: clearer, helds the same result but proves slower + double arrayX[5] = {0, 1, xd, xd*xd, xd*xd*xd}; + double arrayY[5] = {0, 1, yd, yd*yd, yd*yd*yd}; + for(int j = 0;j < 4;j++) { + for(int i = 0;i < 4;i++) { + double coeff = m_coefficients[ij_to_index(j,i)]; + //cout< > &matrix, const double &x, const double &y, int column_number, int type_field_read) const +{ + double ans = 0; // answer ! that is f(x,y) + // calculate LL indices basing on the point + int m_xindex, m_yindex; + GetIndex(x,y,m_xindex, m_yindex); + // prepare coefficients for the selected matrix + vector m_coefficients(16,0.); + Prepare_Coefficients(matrix,m_xindex, m_yindex,m_coefficients,column_number,type_field_read); + double xd = (x - m_xvalues[m_xindex])/m_delta_x; + double yd = (y - m_yvalues[m_yindex])/m_delta_y; + + // obtain values + // COMPACT PROCEDURE: 1 cycle only (saves 12 operation per interpolation) - see commented lines for the explicit version + for (int i=3; i>=0; i--) + { + ans = xd*(ans)+((m_coefficients[ij_to_index(3,i)]*yd + m_coefficients[ij_to_index(2,i)])*yd + m_coefficients[ij_to_index(1,i)])*yd + m_coefficients[ij_to_index(0,i)]; + } + return ans; +}; + + +// same but faster if only f(x,y) is needed +// Version following http://en.wikipedia.org/wiki/Bicubic_interpolation +double Bicubic_Interpolator::GetValueInterpolated(const vector > &matrix, const double &x, const double &y, int column_number) const +{ + double ans = 0; // answer ! that is f(x,y) + // calculate LL indices basing on the point + int m_xindex, m_yindex; + GetIndex(x,y,m_xindex, m_yindex); + double xd = (x - m_xvalues[m_xindex])/m_delta_x; // TO be betwwen + double yd = (y - m_yvalues[m_yindex])/m_delta_y; + + // obtain values + // COMPACT PROCEDURE: 1 cycle only (saves 12 operation per interpolation) - see commented lines for the explicit version + for (int i=3; i>=0; i--) + { +// ans = xd*(ans)+((m_coefficients[ij_to_index(3,i)]*yd + m_coefficients[ij_to_index(2,i)])*yd + m_coefficients[ij_to_index(1,i)])*yd + m_coefficients[ij_to_index(0,i)]; + } + return ans; +}; + + diff --git a/Main Code 64bits/BicubicInterpolation_module.h b/Main Code 64bits/BicubicInterpolation_module.h new file mode 100644 index 0000000..98f0249 --- /dev/null +++ b/Main Code 64bits/BicubicInterpolation_module.h @@ -0,0 +1,85 @@ +/** +Program for interpolating data points on a two dimensional regular grid. +http://en.wikipedia.org/wiki/Bicubic_interpolation + +coming from +Andrea Demetrio +and modified by Daniel Comparat (and change double **matrix, by vector > &matrix) +change dynamical allocation by vectors + +Here noted x,y but used as r,z in the program + +The initial program was based on matrix m[x][y] that was matrix[m_xindex][m_yindex] +I have modified it for matrix_field[j] (j design a column with a given field such as Br, Bz, Bx, By or else) +which is a column containing m[x,y] so with index m_index*m_ydimension + m_yindex +For this the old matrix[m_x][m_y] is transformed in matrix_field[j][m_x*m_ydimension + my]. + +I also add some const declaration and put m_xindex, m_yindex as non member because they are non const and are more local variable that something that shoudl be memenr of the class +Similarly local variable such as m_coefficients, m_nonzero_indices, m_nonzero_counter are now local variable not member of the class (this was easy to have some functions that are const, even if such parameters are modified) +Finally I put all array as vectors because the dynamical array causes problems when constructed and destructed many times +**/ + + +#ifndef BICUBIC_INTERPOLATION +#define BICUBIC_INTERPOLATION + +#include +#include +#include +#include + +using namespace std; + +class Bicubic_Interpolator +{ +public: + Bicubic_Interpolator() {}; + + Bicubic_Interpolator(int NewXDimension, int NewYDimension, double delta_x, double delta_y, double X0 = 0, double Y0 = 0); // Create equidistant points with offset X0 -and Y0) and spacinf delta_x (or delta y). Initialize the value of the matrix by the Xvalues[i]=X0 + i*delta_x and same for + + void Init(int NewXDimension, int NewYDimension, double delta_x, double delta_y, double X0 = 0, double Y0 = 0); + + +// Cannot be const because called other function like Get_index that modify the m_index + bool GetValue(const vector > &matrix, const double &x, const double &y, double &ans, double &dervx, double &dervy, int column_number=0, int type_field_read = 0) const; // Gives ans=f(x,y), df/dx(x,y), df/dy(x,y) + double GetValue(const vector > &matrix, const double &x, const double &y, int column_number=0, int type_field_read = 0) const; //Return evaluation of f(x,y) + +// same but faster if only f(x,y) is needed + double GetValueInterpolated(const vector > &matrix, const double &x, const double &y, int column_number) const; + + bool EvaluateIndices( int &m_xindex, int &m_yindex) const; //Return false if indices OUT OF RANGE and thus put BOTH them at zero + void ShowIndex(const double &x, const double &y) const; //Print index of the point of the grid close to the X,Y point + const char* GetInterpolationType(); //Get interpolator name + + /* PARTIAL DISCRETE DERIVATIVES using f'(x) = (f(x+eps)-f(x-eps) )/2 eps between 2 grid points */ + // same as bellow but with matrix + double XDerivative(const vector > &matrix, int line_number, int column_number=0) const; + double YDerivative(const vector > &matrix, int line_number, int column_number=0) const; + double XYDerivative(const vector > &matrix, int line_number, int column_number=0) const; + +protected: + int ij_to_index(int i, int j) const; //Transform matrix index into vector index + void PrepareMatrixIndicesArray(); // //Prepare nonzero matrix index from the 16*16 BicubicMatrix + void GetMatrixIndices(int index, int& i, int& j) const; + // void GetIndex(const double &x, const double &y); + void GetIndex(const double &x, const double &y, int &m_xindex, int &m_yindex) const; // return the index near x,y, or (0,0) if one is out of the grid range + + void Prepare_Coefficients(const vector > &matrix, int m_xindex, int m_yindex, vector &m_coefficients, int column_number=0, int type_field_read = 0) const ; + + /* PARTIAL DISCRETE DERIVATIVES using f'(x) = (f(x+eps)-f(x-eps) )/2 eps between 2 grid points */ + double PartialXDerivative(const vector > &matrix, int IndexX, int IndexY, int column_number=0) const; + double PartialYDerivative(const vector > &matrix, int IndexX, int IndexY, int column_number=0) const; + double PartialXYDerivative(const vector > &matrix, int IndexX, int IndexY, int column_number=0) const; + + + +private: // m_ stands for Matrix_ + vector m_xvalues, m_yvalues; // Values + int m_xdimension, m_ydimension; // size of the Box (in number of indices) + // int m_xindex, m_yindex; // Index of the point in the box + double m_delta_x, m_delta_y; // spacing ion the box (Assume that points are equipartitioned) + vector m_nonzero_indices; // use only non zero of the matrix to be faster + int m_nonzero_counter; +}; + +#endif diff --git a/Main Code 64bits/Data/Liste_Param.h b/Main Code 64bits/Data/Liste_Param.h new file mode 100644 index 0000000..12270f5 --- /dev/null +++ b/Main Code 64bits/Data/Liste_Param.h @@ -0,0 +1,473 @@ +/************************* File datacard *************************** + +Can be used in the program by creating a variable such as +double Name_Parameter = params.LocateParam("Name_Parameter")->val + +# 0 = false ; 1 = true + +***********************************************************************/ +########## Particles ############################### +# +// Nb of different particles. For now only the first one is laser cooled (Level and Lines correspond to it) +@Nb_type_of_Mol 1 + +// Le choix du nom (BaF, Cs2, NH, Cs, CO, Li6Cs,Laminus, Li7Cs, Rb85Cs, Rb87Cs, Ps, C2minus, Ps_minus,P_bar,Osminus) ne donne que la masse mais pas le nom des fichiers qu'il faut changer ensuite" +#1st type of particle +// so Mol[0] to Mol[Nom_Mol[0]-1] +@Nom_Mol[0] Ps +// It is the number of molecules that are laser cooled. +@N_Mol[0] 21 +@Temp_ini_x[0] 1e-10 +@Temp_ini_y[0] 1e-10 +@Temp_ini_z[0] 1e-10 + + +// Choice in position: fixed size (sigma_pos) or from density +// -1 fixed size and orders the positions at the start (according to an axis put the other axes randomly) +// 0 fixed size given by size (Gaussian) +// 1 a pot. magn. linear --> Laplace (the coefficient comes from F1) +// 2 pot. magn. quadratic for neutral particle --> Gaussian +// 3 pot. magn. quadratic for charged particle --> Gaussian +// 3 for pot. elec. quadratic (electric field linear) but for CHARGED particles (for instance in a Paul trap)--> Gaussian +// 4 perfect ordered gaussian in velocity (random in position) +// 5 effusive beam. Meaning as in 0 but we keep only the positive velocities + +# +@Procedure_init_x[0] 0 +@Procedure_init_y[0] 0 +@Procedure_init_z[0] 0 +// Taille (x,y,z) si on choisit taille fixe +@size_x[0] 0.1e-6 +@size_y[0] 0.1e-6 +@size_z[0] 0.1e-6 +// Initial position added to the random one +@offset_x[0] 0 +@offset_y[0] 0 +@offset_z[0] 0 +// Initial velocity added to the random one +@v0_x[0] 0. +@v0_y[0] 0. +@v0_z[0] 0. +# +#2nd type of particle +# +// so Mol[Nom_Mol[0]] to Mol[Nom_Mol[0]+Nom_Mol[1]-1] +@Nom_Mol[1] P_bar +@N_Mol[1] 10 +@Temp_ini_x[1] 4 +@Temp_ini_y[1] 4 +@Temp_ini_z[1] 4 +@Procedure_init_x[1] 0 +@Procedure_init_y[1] 0 +@Procedure_init_z[1] 0 +@size_x[1] 1e-4 +@size_y[1] 1e-4 +@size_z[1] 6e-4 +@offset_x[1] 0. +@offset_y[1] 0. +@offset_z[1] 0. +@v0_x[1] 0. +@v0_y[1] 0. +@v0_z[1] 0. +# +########## Temps KMC, paramètres de sortie #################### +# +// For control parameter to determine the dynamical time step size in second to check convergence +// typical is 0.001*waist/velocity (or 0.001*lambda/velocity for lattices) +// or near 0.001 cyclotron period 2pi m/(q B) for Leapfrog (in magnetic field case) +// 0.1 m/(q B) for Boris (10^-8 at 0.0001T for 3me mass; 2 e-8 for C2- 1Telsa). * +// A good test is to remove lasers and check Energy conservation + +//for t< t_scaling_max +@dt_dyn_epsilon_param 1e-10 +//for t> t_scaling_max +// fin du temps. +//@t_fin 10e-9 +@t_fin 0.1e-9 +// time interval between diagnostics (in cout) output +@dt_dia 5e-9 +// time interval between output of snapshots (draw particles) +@dt_out 2e-9 +# +###################### GRAPHICS and OUTPUT ############################### +# +@SIZE_affichage 7e-3 +// Temps d'attende entre 2 affichages. Permet de ne pas avoir un affichage trop rapide +@t_wait_affichage 1e-1 +// 0 = false ; 1 = true +@Graphics 1 +// rotate 90 degree along the vector (rot_axe_x, rot_axe_y, rot_axe_z) +// if no rotation we would have x (red arrow) toward the right, y (green arrow) up and z (blue arrow) toward the screen. +// DEFAULT IS (1,0,0) = x right, y in screen, z up (gravity down) +// (0,1,0) = x out screen, y up, z left +// (0,0,1) = x up, y left, z out of screen +@rot_axe_x 1 +@rot_axe_y 0 +@rot_axe_z 0 + + + +##### VELOCITY SCALING (needs >1 particle) #### + +@is_velocity_scaling false +// velocity scaling ON ou OFF +@time_max_vel_scaling 2e-7 +// temps pendant lequel on procède au time scaling. (temps max) +//@step_vel_scaling 1000 +//nombre de pas +@dt_scal 1e-7 +@coupling_efficiency 0.2 +// in percentage (max 1) 0.1=10% + +// coupling parameter of the BERENDSEN THERMOSTAT Algorithm + + +# +# OUTPUT +# +// gives the number of the manifold that we do not want to take into account for stats +// (can be dead level or photoionized (-1) one or ..) +// To take all manifold into account just put a number that is not used such as -10 +@num_manifold_not_studied -3 +// numéro du niveau étudié pour faire des stats. +// c'est ne numéro (ordre das la lecture du fichier en commençant par 0) du niveau pas de la manifold +// -1 pour toutes les molécules +@num_niveau_etudie -1 +# +######### Diagonalization ################################ +# +// Are the energy levels diagonalized or simple calculed using the simple analytical formula used in the code (linear, quadratic or two level case) +// 0 = false (we use the standard simple formulas) ; 1 = true (we diagonalized) +@is_Levels_Lines_Diagonalized 1 +# +######### CHAMPS EXTERNES SI units (T, T/m, T/m^2 ...) ################################ +# +// We cannot for now have both electric and magnetic field easilly (just because we have only one parameter in the Level file +// Thus we have to choose if this parameter is Zeeman or Stak shift +// But both fields will be used of the Lorentz force between charged particles +// So here +// 0: magnetic (Zeeman shift) +// 1: electric (Stark shift) +@type_of_default_field 0 +# +## MAGNETIC FIELD ## +# +// We cannot for now have both electric and magnetic field easily (just because we have only one parameter in the Level file + + /******** FOR MORE COMPLEX CASE see is_Levels_Lines_Diagonalized ***************/ + +// Thus we have to choose if this parameter is Zeeman (0) or Stark shift (10) +@type_of_field_for_internal_state_shift 0 + +// But both fields will be used of the Lorentz force between charged particles +// For instance in Penning trap --> There is a magnetic and electric. But the magnetic is fully treated (Zeeman + Lorentz force). +// But the electric is only for the Lorentz FOrce not for the Stark effect. +// Or for Paul trap with (not implemented) or without micro-motion. +@type_field_read_E 0 +@type_field_read_B 0 +// THIS is only for the "field_for_internal_state_shift" the other one will be by default at zero so in 2nd +nth order +// DEFAULT +// 0: 2nd order plus a nth order + +// (anti-)Helmotlz coils +// 1: Field in Helmoltz coils (so usualy goes with @type_of_default_field 0) + +// File grids + Electric 2nd order: EQUIPARTITIONED POINTS (at least per axis, the spacing can be different for each axis). Ordered by column (1st increasing then second then third etc ..) +// 2: Field map 3D from 2D cylindrical symmetry: 4 columns r,z, F_r(r,z); F_z(r,z) +// 3: Field map 3D from 2D cylindrical symmetry: F_r(r,z); F_z(r,z)+ derivative d/dr; d/dz and d^2/drdz +// 4: Field map 3D: 6x,y,z, Bx, By, Bz (TO BE DONE) +// For speed. WE SUGGEST TO CALCULATE THE DERIVATIVES IF TYPE 2 USING Field::Calculate_Derivative_Matrix + + +# +# +// Dans le cas 1: Nombre de bobines. Axe z positions (N-1/2) * z_gap auquel on ajoute r si (anti-)Helmotz +@Nb_bobines 1 +// Si is_Helmholtz oui (1) les bobines sont doublées (on an ajoute une décalée de +r) +// Si -1 c'est anti-is_Helmholtz +// si autre (comme 0) on n'ajoute pas de bobine on ne crée que les bobines prévues +@is_Helmholtz -1 +// Ecart entre les bobines +@gap_bobines 25e-3 + // Courant dans les bobines --> Champ au centre µ0 I/ (2 r) --> 0.63 mT for 1A and r=1mm +@courant_bobines 1 +// rayon des bobines +@rayon_bobines 25e-3 +# +// Champ magn selon x,y et z. se décompose par composante: Example selon Ox: B_x + grad_B_x x + grad_grad_B_x x^2 + Bn x^n +// NEVER put 0 but something small like 1e-10 +@B_x 0.0000000001 +@B_y 0. +@B_z 0. +//1.1 +@grad_B_x 0. +@grad_B_y 0. +@grad_B_z 0. +//210 +@grad_grad_B_x 0. +@grad_grad_B_y 0. +@grad_grad_B_z 0. +@n_value_B 3 +@Bn_x 0. +@Bn_y 0. +@Bn_z 0 +# +## ELECTRIC FIELD ## +// Electric Field along x,y and z. example Ox: E_x + grad_E_x x + grad_grad_E_x x^2 + En x^n +// NEVER put 0 but something small like 1e-10 +@E_x 0. +@E_y 0. +@E_z 0. +//@grad_E_x 0 +//@grad_E_y 0 +// V(z) = -0.1 V *(z/1cm)^50 --> E(z) = 0.1 * 50 z^49/(0.01)^50 +//@grad_E_z 0 +@grad_E_x 0. +@grad_E_y 0. +// V(z) = -0.1 V *(z/1cm)^50 --> E(z) = 0.1 * 50 z^49/(0.01)^50 +@grad_E_z 0. + +@grad_grad_E_x 0. +@grad_grad_E_y 0. +@grad_grad_E_z 0. +@n_value_E 3 +@En_x 0. +@En_y 0. +@En_z 0 +# +######### LASERS ######################################## +# +// Parametre multiplicatif de la puissance des lasers +@scale_Power 1 +// Paramètre additif de la fréquence de tous les lasers +// Si Offset_Detuning_cm est >0 le laser est plus bleu (*1K detunning*) +@Offset_Detuning_cm 0 + +// Parametre multiplivatif de la largeur spectrale laser +@scale_Gamma 1 + +// Nb de laser utilisés (pas forcément le nombre ci-après que peut être plus grand) +@Nb_laser 0 + +// We can swhich between lasers +// IF t is between 0 and T1 (modulo T1+T2) THEN the lasers on are the one with number between 0 and N_laser/2 +// IF t is between T1, T1+T2 (modulo T1+T2) THEN the lasers on are between N_laser/2+1 and N_laser. + +@Is_Laser_Switched 0 +@dt_switch_1 3e-8 +@dt_switch_2 1e-8 + +# Premier laser. Laser n°1 (called number 0 in the C++ program) +@waist_pos_x[0] 0. +@waist_pos_y[0] 0. +@waist_pos_z[0] 0 +@direction_x[0] 0. +@direction_y[0] 1. +@direction_z[0] 0. +// @waist_x[0] 5e-3 +// @waist_y[0] 5e-3 +// Mettre si on veux un seul waist +@waist[0] 5e-3 +//cooling: 2T X,v=0, j=1/2, Mj=1/2 -> A, v=0,j=1/2 +//@Energie_cm[0] 3943.504844 + +//normal penning trap 1T (Zeeman shifted) +//X,v=0, j=1/2, Mj=1/2 -> A, v=0,j=1/2 +//@Energie_cm[0] 41155.3604450767 // for 4.5 T and 500 K +@Energie_cm[0] 41148.3848 +//for 1T and 500K + +@Gamma_L_MHz[0] 1e-3 +@Power[0] 200 +// Vector laser polarization (in the laser propagation frame) +// For linear polarization at 54.7356 degree it is sp= -0.707107 sm= 0.707107 and angle 54.7356 +// by the way this creates 1/3 sigma+, 1/3 sigma- and 1/3 pi polarization (for a Y laser beam and quantization axes along z) +@Pol_circulaire_left_sp[0] 1 +@Pol_circulaire_right_sm[0] 0. +@polar_angle_degree[0] 0. +// façonné ---> Energie_cm+2*Gamma > EnergiE_trans_cm > Energie_cm (OBSOLETTE) + // gaussien = 5, lorentzien = 6. (En fait Gaussien ne marche que si le laser est à résonnance et large spectralement) +@type_laser[0] 5 +@nu_offset_MHz[0] 0 +@nu_repetition_MHz[0] 80 +@nu_individual_comb_line_MHz[0] 80 + +// Interférence de tous les lasers qui ont le numéro coherent_avec_laser_num[0] +// si coherent_avec_laser_num[0] = -1 ce laser est seul et n'interfère avec personne. +// Attention bien mettre dans l'ordre un laser j interfère TOUJOURS avec un laser i<=j. S'il y a interférence entre i et j alors le plus petit i interfère avec i aussi +@coherent_avec_laser_num[0] -1 +// est t'il utilisé pour le (re)pompage (i.e. sa fréquence varie avec scale_temp_pompage? False par défaut. +// Si oui on ajoute scale*Temp_initial à son énergie +@is_pompage[0] 0 +@is_rep[0] 0 +// CW = 0, femto =1, multi_mode=2, pulse=3, faconne = 4, gaussien = 5, lorentzien = 6 + +#Deuxieme laser. Laser n°2 +@waist_pos_x[1] 0. +@waist_pos_y[1] 0. +@waist_pos_z[1] 0 +@direction_x[1] 0. +@direction_y[1] 0. +@direction_z[1] -1. + +@waist[1] 10e-3 +//repump 0.2T, X,v=0,j=1/2,Mj=-1/2 -> A,v=0,j=1/2 +//@Energie_cm[1] 3944.511096 +//repump 1T, X,v=0,j=1/2,Mj=-1/2 -> A,v=0,j=1/2 +@Energie_cm[1] 41148.3848 + +@Gamma_L_MHz[1] 1e5 +@Power[1] 1 +// Polarization can be purely circular (sigma+ or sigma -). Example: sigma + --> Pol_circulaire_left_sp = 1 and @Pol_circulaire_right_sm =-1 +// Can also be linear example eX = eX=(e-1-e+1)/sqrt(2). SoPol_circulaire_left_sp = -0.7071 and Pol_circulaire_right_sm[ = 0.7071; +// Then the angle_psi_degree is (for linear polarization) the angle (so 90° if we want eY polarisation) +@Pol_circulaire_left_sp[1] 0.7071067812 +@Pol_circulaire_right_sm[1] -0.7071067812 +@polar_angle_degree[1] 45 + +@type_laser[1] 5 + +@coherent_avec_laser_num[1] -1 + +@is_pompage[1] 0 +@is_rep[1] 0 + + +# +######### PARAMETRES POMPAGE OPTIQUE + SISYPHE #################### +# +// +@num_niveau_first 1 + // numéro du niveau de moindre pente pour le Sisyphe +@num_niveau_second 6 +// numéro du niveau excité +@num_niveau_exc 3 +# +// Repompage ou pompage forcé oui ou non (1 true or 0 false) +@repompage_force 0 +@Pompage_optique_force 0 +# +@rate_repompe 1e7 +@E0_coupure_repompe_cm 33.37 +// scale en temp (pompage Sisyphe à scale_temp * k_B T) +@scale_temp_pompage 3 +// scale en temp (repompage à scale_temp_rep * k_B T) +@scale_temp_rep 0.4 +// Nb de répétition (0 = aucune) du processus Sisyphe. A t_repet on recommence, on garde les molécules mais on remet à t=0 les paramètres +@nb_repet 0 +@t_repet 1000000 +# +# +########## PARAMETRES DE SORTIE FICHIER #################### +# +// sortie de la datacard? +@is_DataCard_out 2 +// # 0 = false ; 1 = true ; 2 = 2 file (one with only datacard, one with data but without datacard) +@is_param_scanned_out 1 +# +# +######### FICHIERS FC ################################ +# +// Lecture du ficher Franck-COndon. Si oui cela crée un autre fichier "nom_file_Levels" et "nom_file_Lines" utilisant l'existant +// (supposé être entre v''=0 et v'=0) et multiplié par le fichier F.C. et avec les énergies et Bv donnés +// Si is_File_FC=true on crée ces fichiers avec noms + "new_v_2Jmax" +@is_File_FC false +// Fichier contenant les facteurs FC entre vA (lignes) et vX (colonnes) +@nom_file_FC_vAvX Data/BaF/FC_vA_0_15Lignes_vX_0_14Colonnes.dat +// Fichier contenant les facteurs niveaux vibrationels, les énergies et les Bv (en cm^-1) +@nom_file_E_vA Data/Ps/Ps_Levels_0B_photo.dat +@nom_file_E_vX Data/Ps/Ps_Lines_0B_photo.dat +// Nb of vibrational levels in X state; 0,1,...,NXmax-1 in the FC file +@NXmax 15 +// Nb of vibrational levels in A state; 0,1,...,NAmax-1 +@NAmax 16 +// Nb of vibrational levels used to calculate the new file for X state; 0,1,...,NX-1 +// Used also to give (for the J,v output) the NX used in the current file if @is_File_FC false) +// This is also used for the drawing of the molecules if the graphic is on +@NX_out 8 +// Nb of vibrational levels used to calculate A; 0,1,...,NA-1 +@NA_out 4 +// Max +1 of rotational levels à mettre dans le fichier de sortie. Si on veux 2J=0,1,2 mettre 3. +// Used also to give (for the J,v output) the 2JX_max used in the current file if @is_File_FC false) +// This is also used for the drawing of the molecules if the graphic is on +@N_Two_JX_out_max 10; +@N_Two_JA_out_max 10; +# +// true pour fixer la durée de vie à duree_vie sinon calculées à partir des forces de transition # 0 = false ; 1 = true +// EN FAIT EST UTILSE JUSTE pour les largeur, car la durée de vie des transitions vient du dipole dans rates_molecule_spon +@if_fixed_lifetime 0 +// en force la durée de vie de l'état excité d'avoir une durée de vie de 15 ns +@duree_vie 15e9 +# +######### NOM_FICHIERS ################################ +# +// Fichier contenant les Niveaux (état, énergie, ...) + +//@nom_file_Levels Data/H/LevelsH_circular_1_60_lmax50.dat +//@nom_file_Lines Data/H/LinesH_circular_1_60_lmax50.dat + +@nom_file_Levels Data/Ps/Ps_Levels_21.dat +@nom_file_Lines Data/Ps/Ps_Lines_21.dat + +// Fichier contenant les spectres laser doit finir en .dat +// Les dichiers contenant les transitions lasers seront donc ce nom +"[numero laser]" où numéro=0 pour le premier laser +@nom_file_Laser_Spectrum Data/Ps/Laser_Spectrum.dat +# +@nom_sortie_donnees Data/donnee_Mol.dat +@nom_sortie_pulse Data/sortie_pulse.dat +@nom_sortie_rate Data/sortie_rate.dat +@nom_sortie_donnees_Data Data/data_card.dat +@nom_sortie_temp Data/sortie_temp.dat +@nom_sortie_scal Data/sortie_scal.dat +# +@nom_fichier_random_gen Data/random_gen.txt +# +# +############# Choix des algorithmes Monte Carlo, N-corps; aléatoire ############## +# +// Vérifier lesquels marchent avant -1, 0, are O.K. !!! +// Aucun_MC = -1 (does not even calculate the rates), Kinetic_Monte_Carlo = 0, Random_Selection_Method = 1, First_Reaction_Method = 2, +// Fast_Rough_Method = 3 is a new one evolving every ~0.1/rate_max time so typically N_Mol/10 evolve during one time step +@Choix_algorithme_Monte_Carlo 0 +// Aucun_N_corps = -1 (mais photon recoil), Verlet_acc = 1 (sans force dipolaire), Verlet_pot (avec potentiel dipolaire) = 2, +// si = 6(c'est Verlet_pot_gradient_high_order avec potentiel dipolaire et calcul du gradient dans one_body à l'ordre supérieur) +// Yoshida6_acc = 3, // 6 th order symplectic algorithm based on Verlet_acc +// Yoshida6_pot = 4, // 6 th order symplectic algorithm based on Verlet_pot +// Boris_Buneman (with Magnetic field for charged particles) = 7 +@Choix_algorithme_N_corps 1 +// Choix du epsilon en position (en metre) pour calculer la dérivée du potentiel. +// Une variation de 1/100 du potentiel selon epsilon semble bien +// So 1e-6 for standard lasers or 1e-9 when interferences are present +// Ne pas hésiter à tester aussi epsilon <0. Et a vérifier avec le epsilon_param +@choix_epsilon 1e-8 +// La même valeur permet d'avoir toujours la même séquence. Une valeur négative utilise le fichier pour renouveler la séquence. If 0 the standard seed from the original implementation +@Seed_Init_Random_Number_Generator 2 +# +# +############# lists of SCAN or time-varying VARIABLE VARIABLES ############# + +// The list starts with BEGIN_OF... and ends with END_OF... +// You have to put exactly the same name preceded by SCAN and followed by the following values (at least until nb_steps) separated by TAB: +// name_scanned, minvalue, maxvalue, nombrestep, bool_is_scanned, bool_is_time_dependent, tau_var +// Nb_steps = nb_intervall --> so 1 means that we will take 2 values min and max. nb_step=2 we take 3 values: min, half and max ... + // val_t0 = minv + steps * (maxv - minv )/nbstep + // tau = time rate of change --> val = val_t0 exp^(-t/tau). +// If true is given then the parameters will thus be changed in exp^(-t/tau). If we don't specify tau and it's time dependent the value will be Tau_Modif +// If there are several values, the table number is set [number]. +# +# Tau_Modif is the default time if no other is marked +// Modification of parameters over time if no other value is specified. +@Tau_Modif 1e-3 +# +# +// To find out if we scan randomly or orderly +@is_Scan_Random false +# name minv maxv nbstep is_scanned is_time tau +BEGIN_OF_FITPARAMS +@SCAN_scale_Power 5 40 4 false false +@SCAN_Offset_Detuning_cm -2.5 -1 5 false false +@SCAN_scale_Gamma 0.3 0.6 3 false false +@SCAN_Tau_Modif 0.5e-3 2e-3 2 false false +@SCAN_B_x 0.0000000001 5 1000 true false +END_OF_FITPARAMS + diff --git a/Main Code 64bits/Data/Liste_Param.h.save-failed b/Main Code 64bits/Data/Liste_Param.h.save-failed new file mode 100644 index 0000000..7f97260 --- /dev/null +++ b/Main Code 64bits/Data/Liste_Param.h.save-failed @@ -0,0 +1,469 @@ +/************************* File datacard *************************** + +Can be used in the program by creating a variable such as +double Name_Parameter = params.LocateParam("Name_Parameter")->val + +# 0 = false ; 1 = true + +***********************************************************************/ +########## Particles ############################### +# +// Nb of different particles. For now only the first one is laser cooled (Level and Lines correspond to it) +@Nb_type_of_Mol 1 + +// Le choix du nom (BaF, Cs2, NH, Cs, CO, Li6Cs,Laminus, Li7Cs, Rb85Cs, Rb87Cs, Ps, C2minus, Ps_minus,P_bar,Osminus) ne donne que la masse mais pas le nom des fichiers qu'il faut changer ensuite" +#1st type of particle +// so Mol[0] to Mol[Nom_Mol[0]-1] +@Nom_Mol[0] Ps +// It is the number of molecules that are laser cooled. +@N_Mol[0] 1 +@Temp_ini_x[0] 1e-10 +@Temp_ini_y[0] 1e-10 +@Temp_ini_z[0] 1e-10 + + +// Choice in position: fixed size (sigma_pos) or from density +// -1 fixed size and orders the positions at the start (according to an axis put the other axes randomly) +// 0 fixed size given by size (Gaussian) +// 1 a pot. magn. linear --> Laplace (the coefficient comes from F1) +// 2 pot. magn. quadratic for neutral particle --> Gaussian +// 3 pot. magn. quadratic for charged particle --> Gaussian +// 3 for pot. elec. quadratic (electric field linear) but for CHARGED particles (for instance in a Paul trap)--> Gaussian +// 4 perfect ordered gaussian in velocity (random in position) +// 5 effusive beam. Meaning as in 0 but we keep only the positive velocities + +# +@Procedure_init_x[0] 5 +@Procedure_init_y[0] 0 +@Procedure_init_z[0] 0 +// Taille (x,y,z) si on choisit taille fixe +@size_x[0] 0.1e-3 +@size_y[0] 2e-3 +@size_z[0] 2e-3 +// Initial position added to the random one +@offset_x[0] 0 +@offset_y[0] 0 +@offset_z[0] 0 +// Initial velocity added to the random one +@v0_x[0] 0. +@v0_y[0] 0. +@v0_z[0] 0. +# +#2nd type of particle +# +// so Mol[Nom_Mol[0]] to Mol[Nom_Mol[0]+Nom_Mol[1]-1] +@Nom_Mol[1] P_bar +@N_Mol[1] 10 +@Temp_ini_x[1] 4 +@Temp_ini_y[1] 4 +@Temp_ini_z[1] 4 +@Procedure_init_x[1] 0 +@Procedure_init_y[1] 0 +@Procedure_init_z[1] 0 +@size_x[1] 1e-4 +@size_y[1] 1e-4 +@size_z[1] 6e-4 +@offset_x[1] 0. +@offset_y[1] 0. +@offset_z[1] 0. +@v0_x[1] 0. +@v0_y[1] 0. +@v0_z[1] 0. +# +########## Temps KMC, paramètres de sortie #################### +# +// For control parameter to determine the dynamical time step size in second to check convergence +// typical is 0.001*waist/velocity (or 0.001*lambda/velocity for lattices) +// or near 0.001 cyclotron period 2pi m/(q B) for Leapfrog (in magnetic field case) +// 0.1 m/(q B) for Boris (10^-8 at 0.0001T for 3me mass; 2 e-8 for C2- 1Telsa). * +// A good test is to remove lasers and check Energy conservation + +//for t< t_scaling_max +@dt_dyn_epsilon_param 1e-9 +//for t> t_scaling_max +// fin du temps. +//@t_fin 10e-9 +@t_fin 0.1e-9 +// time interval between diagnostics (in cout) output +@dt_dia 5e-9 +// time interval between output of snapshots (draw particles) +@dt_out 2e-9 +# +###################### GRAPHICS and OUTPUT ############################### +# +@SIZE_affichage 7e-3 +// Temps d'attende entre 2 affichages. Permet de ne pas avoir un affichage trop rapide +@t_wait_affichage 1e-1 +// 0 = false ; 1 = true +@Graphics 1 +// rotate 90 degree along the vector (rot_axe_x, rot_axe_y, rot_axe_z) +// if no rotation we would have x (red arrow) toward the right, y (green arrow) up and z (blue arrow) toward the screen. +// DEFAULT IS (1,0,0) = x right, y in screen, z up (gravity down) +// (0,1,0) = x out screen, y up, z left +// (0,0,1) = x up, y left, z out of screen +@rot_axe_x 1 +@rot_axe_y 0 +@rot_axe_z 0 + + + +##### VELOCITY SCALING (needs >1 particle) #### + +@is_velocity_scaling false +// velocity scaling ON ou OFF +@time_max_vel_scaling 2e-7 +// temps pendant lequel on procède au time scaling. (temps max) +//@step_vel_scaling 1000 +//nombre de pas +@dt_scal 1e-7 +@coupling_efficiency 0.2 +// in percentage (max 1) 0.1=10% + +// coupling parameter of the BERENDSEN THERMOSTAT Algorithm + + +# +# OUTPUT +# +// gives the number of the manifold that we do not want to take into account for stats +// (can be dead level or photoionized (-1) one or ..) +// To take all manifold into account just put a number that is not used such as -10 +@num_manifold_not_studied -3 +// numéro du niveau étudié pour faire des stats. +// c'est ne numéro (ordre das la lecture du fichier en commençant par 0) du niveau pas de la manifold +// -1 pour toutes les molécules +@num_niveau_etudie -1 +# +######### Diagonalization ################################ +# +// Are the energy levels diagonalized or simple calculed using the simple analytical formula used in the code (linear, quadratic or two level case) +// 0 = false (we use the standard simple formulas) ; 1 = true (we diagonalized) +@is_Levels_Lines_Diagonalized 1 +# +######### CHAMPS EXTERNES SI units (T, T/m, T/m^2 ...) ################################ +# +// We cannot for now have both electric and magnetic field easilly (just because we have only one parameter in the Level file +// Thus we have to choose if this parameter is Zeeman or Stak shift +// But both fields will be used of the Lorentz force between charged particles +// So here +// 0: magnetic (Zeeman shift) +// 1: electric (Stark shift) +@type_of_default_field 0 +# +## MAGNETIC FIELD ## +# +// We cannot for now have both electric and magnetic field easily (just because we have only one parameter in the Level file + + /******** FOR MORE COMPLEX CASE see is_Levels_Lines_Diagonalized ***************/ + +// Thus we have to choose if this parameter is Zeeman (0) or Stark shift (10) +@type_of_field_for_internal_state_shift 0 + +// But both fields will be used of the Lorentz force between charged particles +// For instance in Penning trap --> There is a magnetic and electric. But the magnetic is fully treated (Zeeman + Lorentz force). +// But the electric is only for the Lorentz FOrce not for the Stark effect. +// Or for Paul trap with (not implemented) or without micro-motion. +@type_field_read_E 0 +@type_field_read_B 0 +// THIS is only for the "field_for_internal_state_shift" the other one will be by default at zero so in 2nd +nth order +// DEFAULT +// 0: 2nd order plus a nth order + +// (anti-)Helmotlz coils +// 1: Field in Helmoltz coils (so usualy goes with @type_of_default_field 0) + +// File grids + Electric 2nd order: EQUIPARTITIONED POINTS (at least per axis, the spacing can be different for each axis). Ordered by column (1st increasing then second then third etc ..) +// 2: Field map 3D from 2D cylindrical symmetry: 4 columns r,z, F_r(r,z); F_z(r,z) +// 3: Field map 3D from 2D cylindrical symmetry: F_r(r,z); F_z(r,z)+ derivative d/dr; d/dz and d^2/drdz +// 4: Field map 3D: 6x,y,z, Bx, By, Bz (TO BE DONE) +// For speed. WE SUGGEST TO CALCULATE THE DERIVATIVES IF TYPE 2 USING Field::Calculate_Derivative_Matrix + + +# +# +// Dans le cas 1: Nombre de bobines. Axe z positions (N-1/2) * z_gap auquel on ajoute r si (anti-)Helmotz +@Nb_bobines 1 +// Si is_Helmholtz oui (1) les bobines sont doublées (on an ajoute une décalée de +r) +// Si -1 c'est anti-is_Helmholtz +// si autre (comme 0) on n'ajoute pas de bobine on ne crée que les bobines prévues +@is_Helmholtz -1 +// Ecart entre les bobines +@gap_bobines 25e-3 + // Courant dans les bobines --> Champ au centre µ0 I/ (2 r) --> 0.63 mT for 1A and r=1mm +@courant_bobines 1 +// rayon des bobines +@rayon_bobines 25e-3 +# +// Champ magn selon x,y et z. se décompose par composante: Example selon Ox: B_x + grad_B_x x + grad_grad_B_x x^2 + Bn x^n +// NEVER put 0 but something small like 1e-10 +@B_x 0.1 +@B_y 0. +@B_z 0. +//1.1 +@grad_B_x 0. +@grad_B_y 0. +@grad_B_z 0. +//210 +@grad_grad_B_x 0. +@grad_grad_B_y 0. +@grad_grad_B_z 0. +@n_value_B 3 +@Bn_x 0. +@Bn_y 0. +@Bn_z 0 +# +## ELECTRIC FIELD ## +// Electric Field along x,y and z. example Ox: E_x + grad_E_x x + grad_grad_E_x x^2 + En x^n +// NEVER put 0 but something small like 1e-10 +@E_x 0. +@E_y 0. +@E_z 0. +//@grad_E_x 0 +//@grad_E_y 0 +// V(z) = -0.1 V *(z/1cm)^50 --> E(z) = 0.1 * 50 z^49/(0.01)^50 +//@grad_E_z 0 +@grad_E_x 0. +@grad_E_y 0. +// V(z) = -0.1 V *(z/1cm)^50 --> E(z) = 0.1 * 50 z^49/(0.01)^50 +@grad_E_z 0. + +@grad_grad_E_x 0. +@grad_grad_E_y 0. +@grad_grad_E_z 0. +@n_value_E 3 +@En_x 0. +@En_y 0. +@En_z 0 +# +######### LASERS ######################################## +# +// Parametre multiplicatif de la puissance des lasers +@scale_Power 1 +// Paramètre additif de la fréquence de tous les lasers +// Si Offset_Detuning_cm est >0 le laser est plus bleu (*1K detunning*) +@Offset_Detuning_cm -2 + +// Parametre multiplivatif de la largeur spectrale laser +@scale_Gamma 1 + +// Nb de laser utilisés (pas forcément le nombre ci-après que peut être plus grand) +@Nb_laser 0 + +@Is_Laser_Switched 0 +@dt_switch_1 3e-8 +@dt_switch_2 1e-8 + +# Premier laser. Laser n°1 (called number 0 in the C++ program) +@waist_pos_x[0] 0. +@waist_pos_y[0] 0. +@waist_pos_z[0] 0 +@direction_x[0] 0. +@direction_y[0] 1. +@direction_z[0] 0. +// @waist_x[0] 5e-3 +// @waist_y[0] 5e-3 +// Mettre si on veux un seul waist +@waist[0] 10e-3 +//cooling: 2T X,v=0, j=1/2, Mj=1/2 -> A, v=0,j=1/2 +//@Energie_cm[0] 3943.504844 + +//normal penning trap 1T (Zeeman shifted) +//X,v=0, j=1/2, Mj=1/2 -> A, v=0,j=1/2 +//@Energie_cm[0] 41155.3604450767 // for 4.5 T and 500 K +@Energie_cm[0] 41148.3848 +//for 1T and 500K + +@Gamma_L_MHz[0] 5e4 +@Power[0] 1000 +// Vector laser polarization (in the laser propagation frame) +// For linear polarization at 54.7356 degree it is sp= -0.707107 sm= 0.707107 and angle 54.7356 +// by the way this creates 1/3 sigma+, 1/3 sigma- and 1/3 pi polarization (for a Y laser beam and quantization axes along z) +@Pol_circulaire_left_sp[0] 1 +@Pol_circulaire_right_sm[0] 0. +@polar_angle_degree[0] 0. +// façonné ---> Energie_cm+2*Gamma > EnergiE_trans_cm > Energie_cm (OBSOLETTE) + // gaussien = 5, lorentzien = 6. (En fait Gaussien ne marche que si le laser est à résonnance et large spectralement) +@type_laser[0] 6 +@nu_offset_MHz[0] 0 +@nu_repetition_MHz[0] 80 +@nu_individual_comb_line_MHz[0] 80 + +// Interférence de tous les lasers qui ont le numéro coherent_avec_laser_num[0] +// si coherent_avec_laser_num[0] = -1 ce laser est seul et n'interfère avec personne. +// Attention bien mettre dans l'ordre un laser j interfère TOUJOURS avec un laser i<=j. S'il y a interférence entre i et j alors le plus petit i interfère avec i aussi +@coherent_avec_laser_num[0] -1 +// est t'il utilisé pour le (re)pompage (i.e. sa fréquence varie avec scale_temp_pompage? False par défaut. +// Si oui on ajoute scale*Temp_initial à son énergie +@is_pompage[0] 0 +@is_rep[0] 0 +// CW = 0, femto =1, multi_mode=2, pulse=3, faconne = 4, gaussien = 5, lorentzien = 6 + +#Deuxieme laser. Laser n°2 +@waist_pos_x[1] 0. +@waist_pos_y[1] 0. +@waist_pos_z[1] 0 +@direction_x[1] 0. +@direction_y[1] 0. +@direction_z[1] -1. + +@waist[1] 10e-3 +//repump 0.2T, X,v=0,j=1/2,Mj=-1/2 -> A,v=0,j=1/2 +//@Energie_cm[1] 3944.511096 +//repump 1T, X,v=0,j=1/2,Mj=-1/2 -> A,v=0,j=1/2 +@Energie_cm[1] 41148.3848 + +@Gamma_L_MHz[1] 1e5 +@Power[1] 1 +// Polarization can be purely circular (sigma+ or sigma -). Example: sigma + --> Pol_circulaire_left_sp = 1 and @Pol_circulaire_right_sm =-1 +// Can also be linear example eX = eX=(e-1-e+1)/sqrt(2). SoPol_circulaire_left_sp = -0.7071 and Pol_circulaire_right_sm[ = 0.7071; +// Then the angle_psi_degree is (for linear polarization) the angle (so 90° if we want eY polarisation) +@Pol_circulaire_left_sp[1] 0.7071067812 +@Pol_circulaire_right_sm[1] -0.7071067812 +@polar_angle_degree[1] 45 + +@type_laser[1] 5 + +@coherent_avec_laser_num[1] -1 + +@is_pompage[1] 0 +@is_rep[1] 0 + + +# +######### PARAMETRES POMPAGE OPTIQUE + SISYPHE #################### +# +// +@num_niveau_first 1 + // numéro du niveau de moindre pente pour le Sisyphe +@num_niveau_second 6 +// numéro du niveau excité +@num_niveau_exc 3 +# +// Repompage ou pompage forcé oui ou non (1 true or 0 false) +@repompage_force 0 +@Pompage_optique_force 0 +# +@rate_repompe 1e7 +@E0_coupure_repompe_cm 33.37 +// scale en temp (pompage Sisyphe à scale_temp * k_B T) +@scale_temp_pompage 3 +// scale en temp (repompage à scale_temp_rep * k_B T) +@scale_temp_rep 0.4 +// Nb de répétition (0 = aucune) du processus Sisyphe. A t_repet on recommence, on garde les molécules mais on remet à t=0 les paramètres +@nb_repet 0 +@t_repet 1000000 +# +# +########## PARAMETRES DE SORTIE FICHIER #################### +# +// sortie de la datacard? +@is_DataCard_out 2 +// # 0 = false ; 1 = true ; 2 = 2 file (one with only datacard, one with data but without datacard) +@is_param_scanned_out 1 +# +# +######### FICHIERS FC ################################ +# +// Lecture du ficher Franck-COndon. Si oui cela crée un autre fichier "nom_file_Levels" et "nom_file_Lines" utilisant l'existant +// (supposé être entre v''=0 et v'=0) et multiplié par le fichier F.C. et avec les énergies et Bv donnés +// Si is_File_FC=true on crée ces fichiers avec noms + "new_v_2Jmax" +@is_File_FC false +// Fichier contenant les facteurs FC entre vA (lignes) et vX (colonnes) +@nom_file_FC_vAvX Data/BaF/FC_vA_0_15Lignes_vX_0_14Colonnes.dat +// Fichier contenant les facteurs niveaux vibrationels, les énergies et les Bv (en cm^-1) +@nom_file_E_vA Data/Ps/Ps_Levels_0B_photo.dat +@nom_file_E_vX Data/Ps/Ps_Lines_0B_photo.dat +// Nb of vibrational levels in X state; 0,1,...,NXmax-1 in the FC file +@NXmax 15 +// Nb of vibrational levels in A state; 0,1,...,NAmax-1 +@NAmax 16 +// Nb of vibrational levels used to calculate the new file for X state; 0,1,...,NX-1 +// Used also to give (for the J,v output) the NX used in the current file if @is_File_FC false) +// This is also used for the drawing of the molecules if the graphic is on +@NX_out 8 +// Nb of vibrational levels used to calculate A; 0,1,...,NA-1 +@NA_out 4 +// Max +1 of rotational levels à mettre dans le fichier de sortie. Si on veux 2J=0,1,2 mettre 3. +// Used also to give (for the J,v output) the 2JX_max used in the current file if @is_File_FC false) +// This is also used for the drawing of the molecules if the graphic is on +@N_Two_JX_out_max 10; +@N_Two_JA_out_max 10; +# +// true pour fixer la durée de vie à duree_vie sinon calculées à partir des forces de transition # 0 = false ; 1 = true +// EN FAIT EST UTILSE JUSTE pour les largeur, car la durée de vie des transitions vient du dipole dans rates_molecule_spon +@if_fixed_lifetime 0 +// en force la durée de vie de l'état excité d'avoir une durée de vie de 15 ns +@duree_vie 15e9 +# +######### NOM_FICHIERS ################################ +# +// Fichier contenant les Niveaux (état, énergie, ...) + +//@nom_file_Levels Data/H/LevelsH_circular_1_60_lmax50.dat +//@nom_file_Lines Data/H/LinesH_circular_1_60_lmax50.dat + +@nom_file_Levels Data/Ps/Ps_Levels_21.dat +@nom_file_Lines Data/Ps/Ps_Lines_21.dat + +// Fichier contenant les spectres laser doit finir en .dat +// Les dichiers contenant les transitions lasers seront donc ce nom +"[numero laser]" où numéro=0 pour le premier laser +@nom_file_Laser_Spectrum Data/Ps/Laser_Spectrum.dat +# +@nom_sortie_donnees Data/donnee_Mol.dat +@nom_sortie_pulse Data/sortie_pulse.dat +@nom_sortie_rate Data/sortie_rate.dat +@nom_sortie_donnees_Data Data/data_card.dat +@nom_sortie_temp Data/sortie_temp.dat +@nom_sortie_scal Data/sortie_scal.dat +# +@nom_fichier_random_gen Data/random_gen.txt +# +# +############# Choix des algorithmes Monte Carlo, N-corps; aléatoire ############## +# +// Vérifier lesquels marchent avant -1, 0, are O.K. !!! +// Aucun_MC = -1 (does not even calculate the rates), Kinetic_Monte_Carlo = 0, Random_Selection_Method = 1, First_Reaction_Method = 2, +// Fast_Rough_Method = 3 is a new one evolving every ~0.1/rate_max time so typically N_Mol/10 evolve during one time step +@Choix_algorithme_Monte_Carlo 0 +// Aucun_N_corps = -1 (mais photon recoil), Verlet_acc = 1 (sans force dipolaire), Verlet_pot (avec potentiel dipolaire) = 2, +// si = 6(c'est Verlet_pot_gradient_high_order avec potentiel dipolaire et calcul du gradient dans one_body à l'ordre supérieur) +// Yoshida6_acc = 3, // 6 th order symplectic algorithm based on Verlet_acc +// Yoshida6_pot = 4, // 6 th order symplectic algorithm based on Verlet_pot +// Boris_Buneman (with Magnetic field for charged particles) = 7 +@Choix_algorithme_N_corps 1 +// Choix du epsilon en position (en metre) pour calculer la dérivée du potentiel. +// Une variation de 1/100 du potentiel selon epsilon semble bien +// So 1e-6 for standard lasers or 1e-9 when interferences are present +// Ne pas hésiter à tester aussi epsilon <0. Et a vérifier avec le epsilon_param +@choix_epsilon 1e-8 +// La même valeur permet d'avoir toujours la même séquence. Une valeur négative utilise le fichier pour renouveler la séquence. If 0 the standard seed from the original implementation +@Seed_Init_Random_Number_Generator 2 +# +# +############# listes des VARIABLES SCANNEES ou variées temporellement ############# + +// La liste commence par BEGIN_OF... et finie par END_OF... +// Il faut mettre exactement le même nom précédé de SCAN et suivit des valeurs suivantes (au moins jusqu'a nb_steps) séparée par TAB: +// name_scanned, minvalue, maxvalue, nombrestep, bool_is_scanned, bool_is_time_dependent, tau_var +// Nb_steps =ntervall --> 1 signifie que l'on va prendre 2 valeurs min et max. nb_step=2 on prend 3 valeurs: min, moitié et max ... + // val_t0 = minv + steps * (maxv - minv )/nbstep + // tau = taux de variation temporelle --> val = val_t0 exp^(-t/tau). +// Les paramètres seront modifiés en exp^(-t/tau). Si on ne précise pas tau et que c'est time dependent la valeur sera Tau_Modif +// Si il y a plusieurs valeur on met le numéro du tableau [numéro] +# +# Tau_Modif est le temps par défaut si aucun autre n'est marqué +// Modification des paramètres au cours du temps si aucune autre valeur n'est précisée. +@Tau_Modif 1e-3 +# +# +// Pour savoir si on scan de façon aléatoire ou ordonnée +@is_Scan_Random false +# name minv maxv nbstep is_scanned is_time tau +BEGIN_OF_FITPARAMS +@SCAN_scale_Power 5 40 4 false false +@SCAN_Offset_Detuning_cm -2.5 -1 5 false false +@SCAN_scale_Gamma 0.3 0.6 3 false false +@SCAN_Tau_Modif 0.5e-3 2e-3 2 false false +@SCAN_B_x 0 10 9 true false +END_OF_FITPARAMS + diff --git a/Main Code 64bits/Data/Ps/Ps_Levels_21.dat b/Main Code 64bits/Data/Ps/Ps_Levels_21.dat new file mode 100644 index 0000000..631debc --- /dev/null +++ b/Main Code 64bits/Data/Ps/Ps_Levels_21.dat @@ -0,0 +1,21 @@ +0 0 1 0 0 0 0 0 0 -10000.0000 0 0 +1 0 1 1 0 0 0 0 0 -6.817589266 0 0 +1 -2 1 2 0 0 2 0 2 -0.000000000001 0 0 +1 2 1 3 0 0 2 0 2 0.000000 0 0 +1 0 1 4 0 1 2 0 2 0.000000000001 0 0 +2 0 1 5 0 2 0 0 0 41147.81261 0 0 +2 -2 1 6 0 2 2 0 2 41148.66481 0 0 +2 0 1 7 0 2 2 0 2 41148.66481 0 0 +2 2 1 8 1 2 2 0 2 41148.66481 0 0 +2 -2 1 9 0 2 2 2 0 41148.29958 0 0 +2 0 1 10 0 2 2 2 0 41148.29958 0 0 +2 2 1 11 0 2 2 2 0 41148.29958 0 0 +2 0 1 12 0 2 0 2 2 41148.0561 0 0 +2 -2 1 13 0 2 2 2 2 41148.23871 0 0 +2 0 1 14 0 2 2 2 2 41148.23871 0 0 +2 2 1 15 0 2 2 2 2 41148.23871 0 0 +2 -4 1 16 0 2 4 2 2 41148.3848 0 0 +2 -2 1 17 0 2 4 2 2 41148.3848 0 0 +2 0 1 18 0 2 4 2 2 41148.3848 0 0 +2 2 1 19 0 2 4 2 2 41148.3848 0 0 +2 4 1 20 0 2 4 2 2 41148.3848 0 0 \ No newline at end of file diff --git a/Main Code 64bits/Data/Ps/Ps_Lines_21.dat b/Main Code 64bits/Data/Ps/Ps_Lines_21.dat new file mode 100644 index 0000000..7ff6ed7 --- /dev/null +++ b/Main Code 64bits/Data/Ps/Ps_Lines_21.dat @@ -0,0 +1,25 @@ +1 0 1 1 0 0 1 0 9993.18 7.98365e+009 -6.81759 -10000 8502.9 +1 -2 1 2 0 0 1 0 10000 6.99301e+006 -0.000000000001 -10000 7.4326 +1 2 1 3 0 0 1 0 10000 6.99301e+006 0 -10000 7.4326 +1 0 1 4 0 0 1 0 10000 6.99301e+006 0.000000000001 -10000 7.4326 +2 -2 1 9 1 0 1 1 41155.1 3.13499e+008 41148.3 -6.81759 4.78014 +2 0 1 10 1 0 1 1 41155.1 3.13499e+008 41148.3 -6.81759 4.78014 +2 2 1 11 1 0 1 1 41155.1 3.13499e+008 41148.3 -6.81759 4.78014 +2 0 1 12 1 -2 1 2 41148.1 1.04446e+008 41148.1 0 1.59338 +2 -2 1 13 1 -2 1 2 41148.2 1.56671e+008 41148.2 0 2.39007 +2 0 1 14 1 -2 1 2 41148.2 1.56671e+008 41148.2 0 2.39007 +2 -4 1 16 1 -2 1 2 41148.4 3.13345e+008 41148.4 0 4.78014 +2 -2 1 17 1 -2 1 2 41148.4 1.56672e+008 41148.4 0 2.39007 +2 0 1 18 1 -2 1 2 41148.4 5.22241e+007 41148.4 0 0.796691 +2 0 1 12 1 0 1 3 41148.1 1.04446e+008 41148.1 0 1.59338 +2 -2 1 13 1 0 1 3 41148.2 1.56671e+008 41148.2 0 2.39007 +2 2 1 15 1 0 1 3 41148.2 1.56671e+008 41148.2 0 2.39007 +2 -2 1 17 1 0 1 3 41148.4 1.56672e+008 41148.4 0 2.39007 +2 0 1 18 1 0 1 3 41148.4 2.08896e+008 41148.4 0 3.18676 +2 2 1 19 1 0 1 3 41148.4 1.56672e+008 41148.4 0 2.39007 +2 0 1 12 1 2 1 4 41148.1 1.04446e+008 41148.1 0 1.59338 +2 0 1 14 1 2 1 4 41148.2 1.56671e+008 41148.2 0 2.39007 +2 2 1 15 1 2 1 4 41148.2 1.56671e+008 41148.2 0 2.39007 +2 0 1 18 1 2 1 4 41148.4 5.22241e+007 41148.4 0 0.796691 +2 2 1 19 1 2 1 4 41148.4 1.56672e+008 41148.4 0 2.39007 +2 4 1 20 1 2 1 4 41148.4 3.13345e+008 41148.4 0 4.78014 \ No newline at end of file diff --git a/Main Code 64bits/Data/data_card.dat b/Main Code 64bits/Data/data_card.dat new file mode 100644 index 0000000..7c6e95e --- /dev/null +++ b/Main Code 64bits/Data/data_card.dat @@ -0,0 +1,180 @@ + Nb card 177 +DATA +@Nb_type_of_Mol 1 +@Nom_Mol[0] Ps + @N_Mol[0] 21 +@Temp_ini_x[0] 1e-10 +@Temp_ini_y[0] 1e-10 +@Temp_ini_z[0] 1e-10 +@Procedure_init_x[0] 0 +@Procedure_init_y[0] 0 +@Procedure_init_z[0] 0 +@size_x[0] 0.1e-6 +@size_y[0] 0.1e-6 +@size_z[0] 0.1e-6 +@offset_x[0] 0 +@offset_y[0] 0 +@offset_z[0] 0 + @v0_x[0] 0. + @v0_y[0] 0. + @v0_z[0] 0. +@Nom_Mol[1] P_bar + @N_Mol[1] 10 +@Temp_ini_x[1] 4 +@Temp_ini_y[1] 4 +@Temp_ini_z[1] 4 +@Procedure_init_x[1] 0 +@Procedure_init_y[1] 0 +@Procedure_init_z[1] 0 +@size_x[1] 1e-4 +@size_y[1] 1e-4 +@size_z[1] 6e-4 +@offset_x[1] 0. +@offset_y[1] 0. +@offset_z[1] 0. + @v0_x[1] 0. + @v0_y[1] 0. + @v0_z[1] 0. +@dt_dyn_epsilon_param 1e-10 + @t_fin 0.1e-9 + @dt_dia 5e-9 + @dt_out 2e-9 +@SIZE_affichage 7e-3 +@t_wait_affichage 1e-1 + @Graphics 1 +@rot_axe_x 1 +@rot_axe_y 0 +@rot_axe_z 0 +@is_velocity_scaling false +@time_max_vel_scaling 2e-7 + @dt_scal 1e-7 +@coupling_efficiency 0.2 +@num_manifold_not_studied -3 +@num_niveau_etudie -1 +@is_Levels_Lines_Diagonalized 1 +@type_of_default_field 0 +@type_of_field_for_internal_state_shift 0 +@type_field_read_E 0 +@type_field_read_B 0 +@Nb_bobines 1 +@is_Helmholtz -1 +@gap_bobines 25e-3 +@courant_bobines 1 +@rayon_bobines 25e-3 + @B_x 0.0000000001 + @B_y 0. + @B_z 0. + @grad_B_x 0. + @grad_B_y 0. + @grad_B_z 0. +@grad_grad_B_x 0. +@grad_grad_B_y 0. +@grad_grad_B_z 0. +@n_value_B 3 + @Bn_x 0. + @Bn_y 0. + @Bn_z 0 + @E_x 0. + @E_y 0. + @E_z 0. + @grad_E_x 0. + @grad_E_y 0. + @grad_E_z 0. +@grad_grad_E_x 0. +@grad_grad_E_y 0. +@grad_grad_E_z 0. +@n_value_E 3 + @En_x 0. + @En_y 0. + @En_z 0 +@scale_Power 1 +@Offset_Detuning_cm 0 +@scale_Gamma 1 + @Nb_laser 0 +@Is_Laser_Switched 0 +@dt_switch_1 3e-8 +@dt_switch_2 1e-8 +@waist_pos_x[0] 0. +@waist_pos_y[0] 0. +@waist_pos_z[0] 0 +@direction_x[0] 0. +@direction_y[0] 1. +@direction_z[0] 0. + @waist[0] 5e-3 +@Energie_cm[0] 41148.3848 +@Gamma_L_MHz[0] 1e-3 + @Power[0] 200 +@Pol_circulaire_left_sp[0] 1 +@Pol_circulaire_right_sm[0] 0. +@polar_angle_degree[0] 0. +@type_laser[0] 5 +@nu_offset_MHz[0] 0 +@nu_repetition_MHz[0] 80 +@nu_individual_comb_line_MHz[0] 80 +@coherent_avec_laser_num[0] -1 +@is_pompage[0] 0 +@is_rep[0] 0 +@waist_pos_x[1] 0. +@waist_pos_y[1] 0. +@waist_pos_z[1] 0 +@direction_x[1] 0. +@direction_y[1] 0. +@direction_z[1] -1. + @waist[1] 10e-3 +@Energie_cm[1] 41148.3848 +@Gamma_L_MHz[1] 1e5 + @Power[1] 1 +@Pol_circulaire_left_sp[1] 0.7071067812 +@Pol_circulaire_right_sm[1] -0.7071067812 +@polar_angle_degree[1] 45 +@type_laser[1] 5 +@coherent_avec_laser_num[1] -1 +@is_pompage[1] 0 +@is_rep[1] 0 +@num_niveau_first 1 +@num_niveau_second 6 +@num_niveau_exc 3 +@repompage_force 0 +@Pompage_optique_force 0 +@rate_repompe 1e7 +@E0_coupure_repompe_cm 33.37 +@scale_temp_pompage 3 +@scale_temp_rep 0.4 + @nb_repet 0 + @t_repet 1000000 +@is_DataCard_out 2 +@is_param_scanned_out 1 +@is_File_FC false +@nom_file_FC_vAvX Data/BaF/FC_vA_0_15Lignes_vX_0_14Colonnes.dat +@nom_file_E_vA Data/Ps/Ps_Levels_0B_photo.dat +@nom_file_E_vX Data/Ps/Ps_Lines_0B_photo.dat + @NXmax 15 + @NAmax 16 + @NX_out 8 + @NA_out 4 +@N_Two_JX_out_max 10; +@N_Two_JA_out_max 10; +@if_fixed_lifetime 0 +@duree_vie 15e9 +@nom_file_Levels Data/Ps/Ps_Levels_21.dat +@nom_file_Lines Data/Ps/Ps_Lines_21.dat +@nom_file_Laser_Spectrum Data/Ps/Laser_Spectrum.dat +@nom_sortie_donnees Data/donnee_Mol.dat +@nom_sortie_pulse Data/sortie_pulse.dat +@nom_sortie_rate Data/sortie_rate.dat +@nom_sortie_donnees_Data Data/data_card.dat +@nom_sortie_temp Data/sortie_temp.dat +@nom_sortie_scal Data/sortie_scal.dat +@nom_fichier_random_gen Data/random_gen.txt +@Choix_algorithme_Monte_Carlo 0 +@Choix_algorithme_N_corps 1 +@choix_epsilon 1e-8 +@Seed_Init_Random_Number_Generator 2 +@Tau_Modif 1e-3 +@is_Scan_Random false +@SCAN_scale_Power 5 40 4 false false +@SCAN_Offset_Detuning_cm -2.5 -1 5 false false +@SCAN_scale_Gamma 0.3 0.6 3 false false +@SCAN_Tau_Modif 0.5e-3 2e-3 2 false false + @SCAN_B_x 0.0000000001 5 1000 true false + diff --git a/Main Code 64bits/Data/donnee_Mol.dat b/Main Code 64bits/Data/donnee_Mol.dat new file mode 100644 index 0000000..e69de29 diff --git a/Main Code 64bits/Data/random_gen.txt b/Main Code 64bits/Data/random_gen.txt new file mode 100644 index 0000000..1114894 Binary files /dev/null and b/Main Code 64bits/Data/random_gen.txt differ diff --git a/Main Code 64bits/Data/sortie_rate.dat b/Main Code 64bits/Data/sortie_rate.dat new file mode 100644 index 0000000..b67222e --- /dev/null +++ b/Main Code 64bits/Data/sortie_rate.dat @@ -0,0 +1,21021 @@ + 1e-10 0.0322330287453 0 0 -10000 0 0 0 + 1e-10 0.0322330287453 1 -6.817589266 -6.817589266 0 0 8000012916.83 + 1e-10 0.0322330287453 2 -1e-12 -1e-12 0 0 6992843.28438 + 1e-10 0.0322330287453 3 0 0 0 0 6992843.28438 + 1e-10 0.0322330287453 4 1e-12 1.00000000128e-12 0 0 6992843.27789 + 1e-10 0.0322330287453 5 0 41147.81261 0 0 0 + 1e-10 0.0322330287453 6 41148.66481 41148.0561 104445365.361 104445365.361 313336096.084 + 1e-10 0.0322330287453 7 41148.66481 41148.23871 54110417.5906 102562294.747 313342385.865 + 1e-10 0.0322330287453 8 41148.66481 41148.23871 156665291.753 156662128.324 313342385.865 + 1e-10 0.0322330287453 9 41148.29958 41148.23871 144578969.808 12092223.1214 313342385.865 + 1e-10 0.0322330287453 10 41148.29958 41148.29958 0 0 313499205.027 + 1e-10 0.0322330287453 11 41148.29958 41148.29958 0 0 313499205.027 + 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78206940.8862 78206940.8856 313313805.072 + 4.98 0.0412080152757 8 41143.65978 41143.655112 78206940.8852 78206940.8852 313313805.07 + 4.98 0.0412080152757 9 41148.1658156 41148.1658153 156495626.43 156495626.42 313339742.749 + 4.98 0.0412080152757 10 41148.23871 41148.23871 156671192.934 156671192.931 313342385.865 + 4.98 0.0412080152757 11 41148.311752 41148.311752 0 0 313347441.475 + 4.98 0.0412080152757 12 41148.311752 41148.311752 0 0 313347441.475 + 4.98 0.0412080152757 13 41148.3848 41148.3848 0 313345378.675 313345378.675 + 4.98 0.0412080152757 14 41148.3848 41148.3848 27.647710431 313345351.028 313345378.676 + 4.98 0.0412080152757 15 0 41148.66481 0 0 0 + 4.98 0.0412080152757 16 0 41148.66481 0 0 0 + 4.98 0.0412080152757 17 0 41152.9081714 0 0 0 + 4.98 0.0412080152757 18 41152.9352444 41152.9399106 82339.9668737 82339.9668916 313420699.863 + 4.98 0.0412080152757 19 41152.951558 41152.956226 78465092.135 78465092.135 313526115.105 + 4.98 0.0412080152757 20 41152.951558 41152.956226 78465092.1399 78465092.1399 313526115.126 + 4.985 0.0412080152757 0 0 -10000 0 0 0 + 4.985 0.0412080152757 1 -9.1743985873 -9.17816453304 0 0 6550795315.13 + 4.985 0.0412080152757 2 -1e-12 -1e-12 0 0 6992843.28438 + 4.985 0.0412080152757 3 0 0 0 0 6992843.28438 + 4.985 0.0412080152757 4 2.3568093213 2.36057526705 0 0 1455554875.09 + 4.985 0.0412080152757 5 0 41143.5645995 0 0 0 + 4.985 0.0412080152757 6 41143.6347541 41143.6300882 91623.0155182 91623.0155294 313419986.592 + 4.985 0.0412080152757 7 41143.655112 41143.6504439 78207016.9788 78207016.9788 313313698.382 + 4.985 0.0412080152757 8 41143.655112 41143.6504439 78207016.9788 78207016.9788 313313698.38 + 4.985 0.0412080152757 9 41148.1658153 41148.165815 156495975.939 156495976.006 313339742.376 + 4.985 0.0412080152757 10 41148.23871 41148.23871 156671192.878 156671192.987 313342385.865 + 4.985 0.0412080152757 11 41148.311752 41148.311752 0 0 313347441.426 + 4.985 0.0412080152757 12 41148.311752 41148.311752 0 0 313347441.426 + 4.985 0.0412080152757 13 41148.3848 41148.3848 92.8616303945 313345285.814 313345378.675 + 4.985 0.0412080152757 14 41148.3848 41148.3848 1302.95461618 313344075.721 313345378.676 + 4.985 0.0412080152757 15 0 41148.66481 0 0 0 + 4.985 0.0412080152757 16 0 41148.66481 0 0 0 + 4.985 0.0412080152757 17 0 41152.9128205 0 0 0 + 4.985 0.0412080152757 18 41152.9399106 41152.9445768 82179.5006222 82179.5005629 313420699.684 + 4.985 0.0412080152757 19 41152.956226 41152.9608941 78465016.0547 78465016.0547 313526221.942 + 4.985 0.0412080152757 20 41152.956226 41152.9608941 78465016.0595 78465016.0587 313526221.963 + 4.99 0.0412080152757 0 0 -10000 0 0 0 + 4.99 0.0412080152757 1 -9.17816453304 -9.18193179765 0 0 6549314754.77 + 4.99 0.0412080152757 2 -1e-12 -1e-12 0 0 6992843.28438 + 4.99 0.0412080152757 3 0 0 0 0 6992843.28438 + 4.99 0.0412080152757 4 2.36057526705 2.36434253165 0 0 1457034783.15 + 4.99 0.0412080152757 5 0 41143.5599502 0 0 0 + 4.99 0.0412080152757 6 41143.6300882 41143.6254223 91434.5177666 91434.5177711 313419987.142 + 4.99 0.0412080152757 7 41143.6504439 41143.6457758 78207092.8674 78207092.8674 313313591.692 + 4.99 0.0412080152757 8 41143.6504439 41143.6457758 78207092.8664 78207092.8664 313313591.69 + 4.99 0.0412080152757 9 41148.165815 41148.1658147 156496324.478 156496324.458 313339742.005 + 4.99 0.0412080152757 10 41148.23871 41148.23871 156671192.921 156671192.944 313342385.865 + 4.99 0.0412080152757 11 41148.311752 41148.311752 0 0 313347441.378 + 4.99 0.0412080152757 12 41148.311752 41148.311752 0 0 313347441.378 + 4.99 0.0412080152757 13 41148.3848 41148.3848 313345377.218 1.45705122091 313345378.675 + 4.99 0.0412080152757 14 41148.3848 41148.3848 313345375.015 3.6612280843 313345378.676 + 4.99 0.0412080152757 15 0 41148.66481 0 0 0 + 4.99 0.0412080152757 16 0 41148.66481 0 0 0 + 4.99 0.0412080152757 17 0 41152.9174698 0 0 0 + 4.99 0.0412080152757 18 41152.9445768 41152.949243 82019.5028555 82019.5028675 313420699.506 + 4.99 0.0412080152757 19 41152.9608941 41152.9655622 78464940.1846 78464940.1846 313526328.8 + 4.99 0.0412080152757 20 41152.9608941 41152.9655622 78464940.1762 78464940.1762 313526328.764 + 4.995 0.0412080152757 0 0 -10000 0 0 0 + 4.995 0.0412080152757 1 -9.18193179765 -9.18570037855 0 0 6547835536.13 + 4.995 0.0412080152757 2 -1e-12 -1e-12 0 0 6992843.28438 + 4.995 0.0412080152757 3 0 0 0 0 6992843.28438 + 4.995 0.0412080152757 4 2.36434253165 2.36811111255 0 0 1458513349.49 + 4.995 0.0412080152757 5 0 41143.5553009 0 0 0 + 4.995 0.0412080152757 6 41143.6254223 41143.6207564 91246.6008114 91246.6007994 313419987.691 + 4.995 0.0412080152757 7 41143.6457758 41143.6411077 78207168.5437 78207168.5437 313313484.977 + 4.995 0.0412080152757 8 41143.6457758 41143.6411077 78207168.5493 78207168.5493 313313485 + 4.995 0.0412080152757 9 41148.1658147 41148.1658144 156496671.901 156496671.931 313339741.634 + 4.995 0.0412080152757 10 41148.23871 41148.23871 156671192.87 156671192.995 313342385.865 + 4.995 0.0412080152757 11 41148.311752 41148.311752 0 0 313347441.329 + 4.995 0.0412080152757 12 41148.311752 41148.311752 0 0 313347441.329 + 4.995 0.0412080152757 13 41148.3848 41148.3848 6.1140110119 313345372.561 313345378.675 + 4.995 0.0412080152757 14 41148.3848 41148.3848 5.46230702669 313345373.213 313345378.676 + 4.995 0.0412080152757 15 0 41148.66481 0 0 0 + 4.995 0.0412080152757 16 0 41148.66481 0 0 0 + 4.995 0.0412080152757 17 0 41152.9221191 0 0 0 + 4.995 0.0412080152757 18 41152.949243 41152.9539092 81859.9718234 81859.9718188 313420699.328 + 4.995 0.0412080152757 19 41152.9655622 41152.9702303 78464864.5148 78464864.5156 313526435.637 + 4.995 0.0412080152757 20 41152.9655622 41152.9702303 78464864.5062 78464864.5062 313526435.6 + 5 0.0412080152757 0 0 -10000 0 0 0 + 5 0.0412080152757 1 -9.18570037855 -9.18947027315 0 0 6546357658.73 + 5 0.0412080152757 2 -1e-12 -1e-12 0 0 6992843.28438 + 5 0.0412080152757 3 0 0 0 0 6992843.28438 + 5 0.0412080152757 4 2.36811111255 2.37188100715 0 0 1459990574.6 + 5 0.0412080152757 5 0 41143.5506516 0 0 0 + 5 0.0412080152757 6 41143.6207564 41143.6160905 91059.2621942 91059.2621803 313419988.238 + 5 0.0412080152757 7 41143.6411077 41143.6364396 78207244.028 78207244.028 313313378.313 + 5 0.0412080152757 8 41143.6411077 41143.6364396 78207244.0276 78207244.0276 313313378.311 + 5 0.0412080152757 9 41148.1658144 41148.1658141 156497018.293 156497018.348 313339741.265 + 5 0.0412080152757 10 41148.23871 41148.23871 156671192.932 156671192.933 313342385.865 + 5 0.0412080152757 11 41148.311752 41148.311752 0 0 313347441.281 + 5 0.0412080152757 12 41148.311752 41148.311752 0 0 313347441.281 + 5 0.0412080152757 13 41148.3848 41148.3848 27.1845478442 313345351.491 313345378.675 + 5 0.0412080152757 14 41148.3848 41148.3848 0 313345378.675 313345378.675 + 5 0.0412080152757 15 0 41148.66481 0 0 0 + 5 0.0412080152757 16 0 41148.66481 0 0 0 + 5 0.0412080152757 17 0 41152.9267684 0 0 0 + 5 0.0412080152757 18 41152.9539092 41152.9585754 81700.905677 81700.9056628 313420699.149 + 5 0.0412080152757 19 41152.9702303 41152.9748983 78464789.0502 78464789.0502 313526542.473 + 5 0.0412080152757 20 41152.9702303 41152.9748983 78464789.0407 78464789.0407 313526542.437 diff --git a/Main Code 64bits/Data/sortie_scal.dat b/Main Code 64bits/Data/sortie_scal.dat new file mode 100644 index 0000000..e69de29 diff --git a/Main Code 64bits/Data/sortie_temp.dat b/Main Code 64bits/Data/sortie_temp.dat new file mode 100644 index 0000000..e69de29 diff --git a/Main Code 64bits/Field.cpp b/Main Code 64bits/Field.cpp new file mode 100644 index 0000000..40d7df2 --- /dev/null +++ b/Main Code 64bits/Field.cpp @@ -0,0 +1,606 @@ +#include "Field.h" +#include +#include "constantes_SI.h" +#include "algorithmes.h" +// ------------ +// Constructors +// ------------ + + +Field::Field() // Constructeur par défaut +{ + F0.set(0.,0.,0.); + F1.set(0.,0.,0.); + F2.set(0.,0.,0.); + Fn.set(0.,0.,0.); + n = 3; + type_field = Magnetic_Field; // By default we look for Zeemnan effect + type_field_read=0; // Par défaut le champ est donné par F0,F1 et F2 + Nb_bobines=0; + gap_bobines=0.; + courant_bobines = 0.; + rayon_bobines = 1.; //Pour éviter des divisions par zéro (mais comme le courant est nul cela importe peu) + is_Helmholtz = 0; + potential = 0.; + // We start with empty matrix memory + matrix_field = vector< vector > (); + +}; + +//Field::~Field() // Destructeur +//{ +// matrix_field.clear(); +//} +//; + +// NOT CORRECT BECAUSE THE MATRIX IS NOT COPY +Field::Field(const Field & field) // Constructeur de (re)copie +{ + F0 = field.F0; + F1 = field.F1; + F2 = field.F2; + n = field.n; + Fn = field.Fn; + type_field = field.type_field; + type_field_read=field.type_field_read; + Nb_bobines=field.Nb_bobines; + gap_bobines=field.gap_bobines; + courant_bobines=field.courant_bobines; + rayon_bobines=field.rayon_bobines; + is_Helmholtz = field.is_Helmholtz; + potential = field.potential; + + // Bicubic_Interpolator_r_z = field.Bicubic_Interpolator_r_z; // Does not exist so !! +}; + +Field & Field::operator = (const Field & field) // Affectation par recopie +{ + if (this != &field) // On vérifie que les objets ne sont pas les mêmes ! + { + F0 = field.F0; + F1 = field.F1; + F2 = field.F2; + n = field.n; + Fn = field.Fn; + type_field = field.type_field; + type_field_read=field.type_field_read; + Nb_bobines=field.Nb_bobines; + gap_bobines=field.gap_bobines; + courant_bobines=field.courant_bobines; + rayon_bobines=field.rayon_bobines; + is_Helmholtz = field.is_Helmholtz; + potential = field.potential; + } + return *this; +} + +//-------------------------------------------- +// Surcharge des opérateurs +,-,*,/ +// + (-) = addition (soustraction) membre à membre. +//-------------------------------------------- + +Field operator +(const Field field1, const Field field2) +{ + Field sum; + + sum.set_F0(field1.get_F0()+field2.get_F0()); + sum.set_F1(field1.get_F1()+field2.get_F1()); + sum.set_F2(field1.get_F2()+field2.get_F2()); + sum.set_n(field1.get_n()+field2.get_n()); + sum.set_Fn(field1.get_Fn()+field2.get_Fn()); + sum.type_field = field1.type_field + field2.type_field; + sum.type_field_read = field1.type_field_read + field2.type_field_read; + sum.Nb_bobines = field1.Nb_bobines + field2.Nb_bobines; + sum.gap_bobines= field1.gap_bobines + field2.gap_bobines; + sum.courant_bobines = field1.courant_bobines + field1.courant_bobines; + sum.rayon_bobines = field1.rayon_bobines + field2.rayon_bobines; + sum.is_Helmholtz = field1.is_Helmholtz; // may be also field1.is_Helmholtz&&field2.is_Helmholtz + sum.potential = field1.potential + field2.potential; + + return sum; +} + + +//---------------------------------- +// Surdéfinition des entrées sorties +//---------------------------------- + +ostream& operator << (ostream &flux, Field field) +{ + field.write(flux); + return(flux); +} + +istream& operator >> (istream &flux, Field & field) //at est modifié! +{ + field.read(flux); + return(flux); +} + + +// Get field at a given position from the grid +Vecteur3D Field::get_Field_interpolation2D(const Vecteur3D pos, int type_field_read) const +{ + const double x= pos.x(), y = pos.y(), z=pos.z(); + const double r = sqrt(x*x + y*y); // cylindrical coordinates; + double Fz,Fr; + Fr = Interpolator2D.GetValue(matrix_field, r, z, 2, type_field_read ); //Return evaluation of Br(r,z). Br is on column 2 of the matrix + Fz = Interpolator2D.GetValue(matrix_field, r, z, 3, type_field_read ); //Return evaluation of Bz(r,z). Bz is on column 3 of the matrix + + + Vecteur3D field; + + if (r<=SMALL_NUMBER) // r==0 is too restrictive and we are safer like that + { + field = Vecteur3D(0,0,Fz); + } + else + { + field = Vecteur3D(Fr*x/r, Fr*y/r, Fz); // Fx=Fr Cos(theta); Fy= Fr Sin(theta) + } + return field; +} + + +// Get Grad (F.F) = gradient of the norm of the field squared at a given position from the grid +// Also give the field F +void Field::get_norm2_grad_Field_interpolation2D(const Vecteur3D pos, Vecteur3D &field, Vecteur3D &grad_F2, int type_field_read) const +{ + const double x= pos.x(), y = pos.y(), z=pos.z(); + const double r = sqrt(x*x + y*y); // cylindrical coordinates; + + double Fr,dFr_dr,dFr_dz; + double Fz,dFz_dr,dFz_dz; + + + Interpolator2D.GetValue(matrix_field, r, z, Fr, dFr_dr, dFr_dz, 2, type_field_read); // Fr is on column 2 of the matrix + Interpolator2D.GetValue(matrix_field, r, z, Fz, dFz_dr, dFz_dz, 3, type_field_read); + + double grad_F2_z = 2.*(Fr*dFr_dz + Fz*dFz_dz); // Grad (F.F) = 2 (F.grad) F + + if (r<=SMALL_NUMBER) + { + field = Vecteur3D(0,0,Fz); + grad_F2 = Vecteur3D(0,0,grad_F2_z); + } + else + { + field = Vecteur3D(Fr*x/r, Fr*y/r, Fz); // Fx=Fr Cos(theta); Fy= Fr Sin(theta) + double grad_F2_r = 2.*(Fr*dFr_dr + Fz*dFz_dr); + grad_F2 = Vecteur3D(grad_F2_r*x/r, grad_F2_r*y/r, grad_F2_z); + } + return; +} + +// Get field at a given position +Vecteur3D Field::get_Field(const Vecteur3D &pos) const +{ + Vecteur3D Field_value; + + if (this->type_field_read == 0 ) + { + Field_value = Vecteur3D(F0.x()+F1.x()*pos.x() + F2.x()*pos.x()*pos.x() + Fn.x()*pow(pos.x(),n), F0.y()+F1.y()*pos.y() + F2.y()*pos.y()*pos.y() + Fn.y()*pow(pos.y(),n), F0.z()+F1.z()*pos.z()+ F2.z()*pos.z()*pos.z() + Fn.z()*pow(pos.z(),n)); + + return Field_value; + } + + if (this->type_field_read == 1) // N-coils of Ox axis + + { + Field_value = get_field_coils(Vecteur3D(pos.y(),pos.z(),pos.x()), this->rayon_bobines, this->courant_bobines, this->Nb_bobines, this->gap_bobines, this->is_Helmholtz); + // les bobines sont calculées comme étant d'axes Oz alors qu'elle seront d'axe Ox en réalité. Il faudra donc appeler ces fonctions non pas en (x,y,z) mais en (y,z,x) + return Vecteur3D(Field_value.z(),Field_value.x(),Field_value.y()); + } + + + if (this->type_field_read == 2 || this->type_field_read == 3) // 2: Field map 3D but from 2D cylindrical symmetry: r,z + { + Field_value = get_Field_interpolation2D(pos,type_field_read); + } + + if (this->type_field_read >= 4) + { + cout << "need to be done " << endl; + } + + + return Field_value; + +} + + +// Get potential at a given position +// Be careful give the potential as if it was an electric potential (so it integrates the field) +double Field::get_electric_potential(const Vecteur3D pos) const +{ + double pot = 0.; + + if (this->type_field_read == 0) + { + double x= pos.x(), y= pos.y(), z = pos.z(); + pot += - F0.x()* x - F1.x()* x*x/2. - F2.x()* x*x*x/3. - Fn.x() * pow(x,n+1)/(n+1.); // Ex = - d/dx pot + pot += - F0.y()* y - F1.y()* y*y/2. - F2.y()* y*y*y/3. - Fn.y() * pow(y,n+1)/(n+1.); + pot += - F0.z()* z - F1.z()* z*z/2. - F2.z()* z*z*z/3. - Fn.z() * pow(z,n+1)/(n+1.); + return pot; + } + else + { + cout << " electric potential not implemented for this type of field " << endl; + } + + return pot; + +} + + +// Calcul du gradient de la norme (au carré) du champ local F +// Grad (F.F) = 2 (F.grad) F +Vecteur3D Field::get_grad_field_F2(const Vecteur3D& pos) const +{ + Vecteur3D grad_F2; + + if (this->type_field_read == 0) + { + double along_x = 2.*( F0.x()+F1.x()*pos.x() + F2.x()*pos.x()*pos.x() + Fn.x()*pow(pos.x(),n) )*( F1.x()+2.*F2.x()*pos.x() + n*Fn.x()*pow(pos.x(),n-1)); + double along_y = 2.*( F0.y()+F1.y()*pos.y() + F2.y()*pos.y()*pos.y() + Fn.y()*pow(pos.y(),n) )*( F1.y()+2.*F2.y()*pos.y() + n*Fn.y()*pow(pos.y(),n-1)); + double along_z = 2.*( F0.z()+F1.z()*pos.z() + F2.z()*pos.z()*pos.z() + Fn.z()*pow(pos.z(),n) )*( F1.z()+2.*F2.z()*pos.z() + n*Fn.z()*pow(pos.z(),n-1)); + grad_F2 = Vecteur3D(along_x, along_y, along_z); + return grad_F2; + } + + if (this->type_field_read == 1) + { + grad_F2 = get_grad_normfield2_coils(Vecteur3D(pos.y(),pos.z(),pos.x()), this->rayon_bobines, this->courant_bobines, this->Nb_bobines, this->gap_bobines, this->is_Helmholtz); + // les bobines sont calculées comme étant d'axes Oz alors qu'elle seront d'axe Ox en réalité. Il faudra donc appeler ces fonctions non pas en (x,y,z) mais en (y,z,x) + return Vecteur3D(grad_F2.z(),grad_F2.x(),grad_F2.y()); + } + + if (this->type_field_read == 2 || this->type_field_read == 3) + { + Vecteur3D field; + get_norm2_grad_Field_interpolation2D(pos, field, grad_F2,type_field_read); + } + + + if (this->type_field_read >= 4) + { + cout << "need to be done " << endl; + } + + return grad_F2; +} + + + +/*************** BOBINE *****************/ + +// CALCUL APPROCHE. Les formules analytiques existes mais sont complexes. +// Ici ce sont des formules plus simples mais très proche de la réalité (cf bz2, brho2 Mathematica ficher calcul_Sisyphus.nb (ou plutot magnetiqe.nb) +// Champ pour bobine rayon r centrée en z=0 axe Oz avec courant de I_coil ampère + +// Pour info le champ au centre est µ0 I/ (2 r) +// Champ crée par une bobine positionée en pos_bobine. Donne aussi les valeurs Brho_sur_rho et Bz +Vecteur3D Field::get_field_coil(const Vecteur3D pos, double r, double I_coil, const Vecteur3D pos_bobine, double &Brho_sur_rho, double &Bz) const +{ + + double x=pos.x() - pos_bobine.x(); + double y=pos.y() - pos_bobine.y(); + double z=pos.z() - pos_bobine.z(); + + + double rho = sqrt(x*x+y*y); + double intermediate = (r + rho)*(r + rho) + z*z; + double denominator = 2.*(z*z + (r - rho)*(r - rho) )*intermediate*sqrt(intermediate); // 2 (z^2 + (r -rho)^2) (z^2 + (r +rho)^2)^(3/2) + Brho_sur_rho = I_coil * MU0*(3./2.)*r*r*z/denominator; // j'ai changé 3 en 3/2 + // cerr << " attention error sur gradient " << endl; + double Bx = x*Brho_sur_rho;// Bx = brho Cos theta avec Cos theta = x/rho *) + double By = y*Brho_sur_rho; // By = brho Sin theta avec Sin theta = y/rho *) + Bz = I_coil * MU0*r*r*(r*r + r*rho - 2*rho*rho + z*z)/denominator; + + return Vecteur3D(Bx,By,Bz); +} + + +Vecteur3D Field::get_field_coil(const Vecteur3D pos, double r, double I_coil, const Vecteur3D pos_bobine) const +{ + + double Brho_sur_rho=0.; + double Bz=0.; + + return get_field_coil(pos, r, I_coil, pos_bobine, Brho_sur_rho, Bz); +} + + + +// Champ pour Nb_coils bobines de rayon r la première centrée en z=0 les autres séparées de z_gap +Vecteur3D Field::get_field_coils(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz, double &Brho_sur_rho_tot, double &Bz_tot) const +{ + Vecteur3D B(0.,0.,0.); + + double x=pos.x(); + double y=pos.y(); + double z=pos.z(); + + double Brho_sur_rho=0.; + double Bz=0.; + Brho_sur_rho_tot=0.; + Bz_tot=0.; + + for (int N = 0; N < Nb_coils; N++) + { + double z_bobine = (N-0.5) * z_gap; + B += get_field_coil(Vecteur3D(x, y, z), r, I_coil, Vecteur3D(0., 0., z_bobine), Brho_sur_rho, Bz); + Brho_sur_rho_tot += Brho_sur_rho; // Rho ne change pas lorsqu'on scan z! + Bz_tot += Bz; + } + + if (is_Helmholtz == 1) + for (int N = 0; N < Nb_coils; N++) + { + double z_bobine = r + (N-0.5) * z_gap; // On ajoute ue bobine décalée du rayon (configuration Helmholtz) + B += get_field_coil(Vecteur3D(x, y, z), r, I_coil, Vecteur3D(0., 0., z_bobine), Brho_sur_rho, Bz); + Brho_sur_rho_tot += Brho_sur_rho; // Rho ne change pas lorsqu'on scan z! + Bz_tot += Bz; + } + + if (is_Helmholtz == -1) //anti-Helmholtz + for (int N = 0; N < Nb_coils; N++) + { + double z_bobine = r + (N-0.5) * z_gap; // On ajoute ue bobine décalée du rayon (configuration Helmholtz) + B += get_field_coil(Vecteur3D(x, y, z), r, -I_coil, Vecteur3D(0., 0., z_bobine), Brho_sur_rho, Bz); + Brho_sur_rho_tot += Brho_sur_rho; // Rho ne change pas lorsqu'on scan z! + Bz_tot += Bz; + } + return B; +} + + +Vecteur3D Field::get_field_coils(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz) const +{ + double Brho_sur_rho_tot=0.; + double Bz_tot=0.; + return Field::get_field_coils(pos, r, I_coil, Nb_coils, z_gap, is_Helmholtz, Brho_sur_rho_tot, Bz_tot); +} + +// Gradient du champ pour une bobines rayon r centrée en z=0 axe Oz +// En fait donne dBz_drho, dBz_dz, dBrho_drho, dBrho_dz +void Field::get_grad_field_coil_4(const Vecteur3D pos, double r, double I_coil, double &dBz_drho_sur_rho, double &dBz_dz, double &dBrho_drho, double &dBrho_dz_sur_rho) const +{ + double x=pos.x(); + double y=pos.y(); + double z=pos.z(); + + double rho = sqrt(x*x+y*y); + + double d1= z*z + (r - rho)*(r - rho); + double d2 = z*z + (r + rho)*(r + rho) ; + double denominator = 2.*d1*d1 * d2*d2*sqrt(d2); + + dBz_drho_sur_rho = 3.*r*r * (-3.*z*z* (r*r + z*z) + 2.* r*r*r*rho - (2.* r*r + z*z) * rho*rho - 2.* r*rho*rho*rho + 2.*rho*rho*rho*rho); + dBz_dz = - 3. *r*r* z * ((r*r + z*z)*(r*r + z*z) + r * (r*r + z*z)*rho - (r*r + 3.*z*z)*rho*rho + 3.* r*rho*rho*rho - 4.*rho*rho*rho*rho); + dBrho_drho = 3.* r*r* z * ((r*r + z*z)*(r*r + z*z) - r * (r*r + z*z)* rho + 3. * (r - z) * (r + z) *rho*rho + r*rho*rho*rho - 4.*rho*rho*rho*rho); + dBrho_dz_sur_rho = 3. * r*r * (r*r*r*r - 4.* z*z*z*z + 2. * r * z*z*rho - 3. * z*z*rho*rho +rho*rho*rho*rho - r*r* (3.* z*z + 2.*rho*rho)); + + dBz_drho_sur_rho = dBz_drho_sur_rho * I_coil * MU0/denominator; + dBz_dz = dBz_dz*I_coil * MU0/denominator; + dBrho_drho = dBrho_drho *I_coil * MU0/denominator; + dBrho_dz_sur_rho = dBrho_dz_sur_rho * I_coil * MU0/denominator; + + return; +} + +// Gradient du champ pour des bobines rayon r centrée en z=0 axe Oz +// En fait donne dBz_drho, dBz_dz, dBrho_drho, dBrho_dz +void Field::get_grad_field_coils_4(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz, double &dBz_drho_sur_rho_tot, double &dBz_dz_tot, double &dBrho_drho_tot, double &dBrho_dz_sur_rho_tot) const +{ + double x=pos.x(); + double y=pos.y(); + double z=pos.z(); + + double dBz_drho_sur_rho=0.; + double dBz_dz=0.; + double dBrho_drho=0.; + double dBrho_dz_sur_rho=0.; + + dBz_drho_sur_rho_tot=0.; + dBz_dz_tot=0.; + dBrho_drho_tot=0.; + dBrho_dz_sur_rho_tot=0.; + + for (int N = 0; N < Nb_coils; N++) + { + double z_bobine = (N-0.5) * z_gap; + Field::get_grad_field_coil_4(Vecteur3D(x,y,z-z_bobine), r, I_coil, dBz_drho_sur_rho, dBz_dz, dBrho_drho, dBrho_dz_sur_rho); + + dBz_drho_sur_rho_tot += dBz_drho_sur_rho; + dBz_dz_tot += dBz_dz; + dBrho_drho_tot += dBrho_drho; + dBrho_dz_sur_rho_tot += dBrho_dz_sur_rho; + } + + if (is_Helmholtz == 1) + for (int N = 0; N < Nb_coils; N++) + { + double z_bobine = r+ (N-0.5) * z_gap; // On ajoute ue bobine décalée du rayon (configuration Helmholtz) + Field::get_grad_field_coil_4(Vecteur3D(x,y,z-z_bobine), r, I_coil, dBz_drho_sur_rho, dBz_dz, dBrho_drho, dBrho_dz_sur_rho); + + dBz_drho_sur_rho_tot += dBz_drho_sur_rho; + dBz_dz_tot += dBz_dz; + dBrho_drho_tot += dBrho_drho; + dBrho_dz_sur_rho_tot += dBrho_dz_sur_rho; + } + + + if (is_Helmholtz == -1) //anti-Helmholtz + for (int N = 0; N < Nb_coils; N++) + { + double z_bobine = r+ (N-0.5) * z_gap; // On ajoute ue bobine décalée du rayon (configuration anti-Helmholtz) + Field::get_grad_field_coil_4(Vecteur3D(x,y,z-z_bobine), r, -I_coil, dBz_drho_sur_rho, dBz_dz, dBrho_drho, dBrho_dz_sur_rho); + + dBz_drho_sur_rho_tot += dBz_drho_sur_rho; + dBz_dz_tot += dBz_dz; + dBrho_drho_tot += dBrho_drho; + dBrho_dz_sur_rho_tot += dBrho_dz_sur_rho; + } + + return; +} + + +// Gradient de la Norme du champ pour des bobines rayon r centrée en z=0 axe Oz +// Grad B.B = 2 (B.Grad) B +Vecteur3D Field::get_grad_normfield2_coils(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz) const +{ + Vecteur3D B(0.,0.,0.); + Vecteur3D gradB2(0.,0.,0.); + + double x=pos.x(); + double y=pos.y(); + double rho = sqrt(x*x+y*y); + + double Brho_sur_rho=0.; + double Bz=0.; + B = Field::get_field_coils(pos, r, I_coil, Nb_coils, z_gap, is_Helmholtz, Brho_sur_rho, Bz); + + double dBz_drho_sur_rho=0.; + double dBz_dz=0.; + double dBrho_drho=0.; + double dBrho_dz_sur_rho=0.; + Field::get_grad_field_coils_4(pos, r, I_coil, Nb_coils, z_gap, is_Helmholtz, dBz_drho_sur_rho, dBz_dz, dBrho_drho, dBrho_dz_sur_rho); + + + double GradB2rho_sur_rho = 2. *(Brho_sur_rho*dBrho_drho + Bz*dBz_drho_sur_rho); // Mettre le sur rho permet d'éviter les x/rho lorsque rho=0 + double GradB2z = 2. *(Brho_sur_rho*rho*dBrho_dz_sur_rho*rho + Bz*dBz_dz); + + + gradB2 += Vecteur3D(GradB2rho_sur_rho *x, GradB2rho_sur_rho*y, GradB2z); + + return gradB2; +} + + + +/** READ THE MATRIX ****/ + +// Erase and Read the matrix of discrete value from a file and return the number of elements +// The file depends on the type of field but should be ordered x By Bz. +// It should be first along the n1 axis [0,0,0], [1,0,0], ..., [n1-1,0,0], [0,1,0], ... +// and equally spaced along each axis, +// THE FIRST LINE CONTAINS ANY COMMENTS you want! +// THE SECOND CONTAINS NAMES like x,y,z, Bx, By, Bz, dBx_dx ... SEPARATED BY TABS +// Return number of lines; +int Field::Read_Matrix(const char* nom_file) +{ + ifstream file(nom_file); + + cout << "name file " << nom_file << endl << endl; + + if ( !file || nom_file == NULL) + { + cerr << "No able to open the file " << nom_file << endl; // Better to not put because sometimes their is no file (and so if this line is here, we will have all the time a message) and we just as the defautl values + file.close(); + return 0; + } + + cout << "Reading field map from ASCII file" << endl; + +// READ MATRIX SIZE! + int number_matrix_lines = number_line_file(nom_file) - 2; // To remove the first lines of comments + int number_matrix_columns = 1; + string line; + getline(file, line);// First line + getline(file, line); // second line + + + for (int i=0; i< (int) line.size(); i++) + { + if (line.data()[i]== '\t') // tab = '\t' + { + number_matrix_columns++; + } + } + + + matrix_field.clear(); // To avoid to insert the default file at the begigning + + vector column[100]; // column + // We assume that there is less than 100 columns x,y,z, BX By Bz dBx/dx etc ... ! + if (number_matrix_columns > 100) + { + cerr << "too many column in field map file " << endl; + exit(1); + } + + for (int i = 0; i < number_matrix_lines; ++i) + for (int j = 0; j < number_matrix_columns; ++j) + { + double current_value; + file >> current_value; + column[j].push_back(current_value); + } + + for (int j = 0; j < number_matrix_columns; ++j) + matrix_field.push_back(column[j]); // matrix_field[j] = column number j of the file + + // SO BE CAREFUL matrix_field[j][i] is the element [i,j] of the line i, column j + file.close(); + + return number_matrix_lines; +} + +// Calculation and output of partial derivation of the field +// For instance for the type_field 2 (that does not contains the derivatives. I calculate them) +void Field::Calculate_Derivative_Matrix(int number_matrix_lines, const char * output_filename) const +{ + + ofstream file_out(output_filename); + + for (int i = 0; i < number_matrix_lines; ++i) + { + for (int j = 0; j < 4; ++j) // THe first 4 columns are x,y, Fx,Fy + { + file_out << matrix_field[j][i] << " " ; + } // Then we add the derivates + file_out << Interpolator2D.XDerivative(matrix_field, i,2)<< " " ; + file_out << Interpolator2D.XDerivative(matrix_field, i,3)<< " " ; + + file_out << Interpolator2D.YDerivative(matrix_field, i,2)<< " " ; + file_out << Interpolator2D.YDerivative(matrix_field, i,3)<< " " ; + + file_out << Interpolator2D.XYDerivative(matrix_field, i,2)<< " " ; + file_out << Interpolator2D.XYDerivative(matrix_field, i,3); + + file_out << endl; + } +} + + +// Using the Matrix of the field (that should have been read before!) we extract the grid parameters and initialize the Interpolators +// Field[m_xindex][m_yindex] is given by matrix_field[j][i] where j is the column corresponding to the field and i = m_index*m_xdimension + m_yindex +void Field::Init_Interpolator() +{ + int number_matrix_lines = matrix_field[0].size(); + if (this->type_field_read == 2 || this->type_field_read == 3) // Field map 3D from 2D cylindrical symmetry: r,z, + { + double r0 = matrix_field[0][0]; // Recall matrix_field[j][i] is the element [i,j] of the line i, column j; + double z0 = matrix_field[1][0]; + double delta_z = matrix_field[1][1] - matrix_field[1][0] ; // The file is ordered first in 1st column then in second! + + double rfinal = matrix_field[0][number_matrix_lines-1]; + double zfinal = matrix_field[1][number_matrix_lines-1]; + + int zDimension = 1.001 + (zfinal-z0)/delta_z; // Number of different z values: z0, z0 +delta_z, ..., zfinal = z0 + (Zdimension-1) * delta_z + int rDimension = 0.001 + number_matrix_lines/zDimension; // Number of different r values: r0, r0 +delta r, ..., rfinal = r0 + (rdimension-1) * delta_r +// To avoid round errors (seen!) we add 0.001 + double delta_r = (rfinal - r0)/(rDimension-1); + + cout << " init Interpolator 2D " << endl; + Interpolator2D.Init(rDimension, zDimension, delta_r, delta_z, r0, z0); //Interpolator2D.Init(XDimension, YDimension, delta_x, delta_y, X0, Y0); + } + + if (this->type_field_read >= 4) + { + + cout << " init Interpolator : NOT DONE YET " << endl; + } +} diff --git a/Main Code 64bits/Field.h b/Main Code 64bits/Field.h new file mode 100644 index 0000000..13fd9db --- /dev/null +++ b/Main Code 64bits/Field.h @@ -0,0 +1,260 @@ +/* + Name: classe « Field » + Copyright: + Author: Daniel Comparat + Date: 15/9/2012 + +Class Field. + +A field F is defined by analytical formula in vector F0 + F1 + F2 + Fn for a given n +for the electric field we add also the electric_potential + +Initialisation to zero + +Il y a plusieurs type de champ possible donné par type_field_read + +0: donné au 2ème ordre: Field selon x,y et z. se décompose par composante: Example selon Ox: F0_x + F1_x x + F2_x x^2 + Fn_x x^n +1: Field in Helmoltz coils (so usualy goes with @type_of_default_field 0) +2: Field map 3D from 2D cylindrical symmetry: 4 columns r,z, F_r(r,z); F_z(r,z) +3: Field map 3D from 2D cylindrical symmetry: F_r(r,z); F_z(r,z)+ derivative d/dr; d/dz and d^2/drdz +4: Field map 3D: 6x,y,z, Bx, By, Bz (TO BE DONE) + + +REMARK: IF cylindrical Symmetry. Only the field on axis is needed +cf Formula from "Magnetic field with cylindrical symmetry": http://arxiv.org/pdf/physics/0610178v1.pdf + + */ + + +#ifndef Field_SEEN +#define Field_SEEN + +#include "Vecteur3D.h" +#include +#include "BicubicInterpolation_module.h" +#include "TricubicInterpolation_module.h" + +using namespace std; + + +enum // Différents types de champs +{ + Magnetic_Field = 0, + Electric_Field = 10 +}; + + +class Field +{ +protected: + Vecteur3D F0; // Bias (zero order Field) + Vecteur3D F1; // Gradient (first order) + Vecteur3D F2; // quadratic term + Vecteur3D Fn; // power n term + + +public: + int n; //power for the last term. Will be 3 by default + int type_field; // Magnetic_Field or Electric_Field + int type_field_read; + +// DEFAULT: 0: 2nd order plus a nth order +// 1: Field in Helmoltz coils (so usualy goes with @type_of_default_field 0) +// 2: Field map 3D from 2D cylindrical symmetry: 4 columns r,z, F_r(r,z); F_z(r,z) +// 3: Field map 3D from 2D cylindrical symmetry: F_r(r,z); F_z(r,z)+ derivative d/dr; d/dz and d^2/drdz +// 4: Field map 3D: 6x,y,z, Bx, By, Bz (TO BE DONE) + + int Nb_bobines; // Nombre de bobines + double gap_bobines; // Ecart entre les bobines + double courant_bobines; // Courant dans les bobines + double rayon_bobines; // rayon les bobines + int is_Helmholtz ; // Si true on ajoute à chaque bobine la même décalée du rayon + double potential; // 0 for magnetic (may be used for electric potential) + vector< vector > matrix_field; // gives the field on a regular grid. Depend on the type_field_read. This table can be r z Br Bz or x y z Bx By Bz or with derivative etc ... NO MORE THAN 100 columns! + // **matrix would be another choice cf http://www.cplusplus.com/forum/articles/7459/ + + // BE CAREFUL matrix_field[j][i] is the element [i,j] of the line i, column j of the file + // THUS matrix_field[j] is the column number j of the file. + + Bicubic_Interpolator Interpolator2D; // Class Bicubic Interpolator. Contains matrix size, spacing in grids and algorithm for interpolation + // LM_Interpolator Interpolator3D; // Class Triubic Interpolator + + // Forme canonique d'une classe + Field(); //constructeur + Field(const Field&); // Constructeur de copie + Field& operator = (const Field&); // Affectation par recopie + virtual ~Field() {}; // Destructeur par defaut + + + // Get components + Vecteur3D get_F0() const + { + return F0; + } + Vecteur3D get_F1() const + { + return F1; + } + Vecteur3D get_F2() const + { + return F2; + } + int get_n() const + { + return n; + } + + Vecteur3D get_Fn() const + { + return Fn; + } + + + + // Set components + void set_F0(const Vecteur3D& new_F0) + { + F0 = new_F0; + } + + void set_F1(const Vecteur3D& new_F1) + { + F1 = new_F1; + } + void set_F2(const Vecteur3D& new_F2) + { + F2 = new_F2; + } + void set_n(const int& new_n) + { + n = new_n; + } + void set_Fn(const Vecteur3D& new_Fn) + { + Fn = new_Fn; + } + + + + friend Field operator +(const Field , const Field); // surcharge de l'opérateur + + + +// I do not update it. So it is incomplete! + virtual void write(ostream & flux) + { + if (&flux == &cout) + cout << "Bias : " << F0 << "\t"; + else + flux << F0 << "\t"; + if (&flux == &cout) + cout << "Grad : " << F1 << "\t"; + else + flux << F1 << "\t"; + if (&flux == &cout) + cout << "Grad Grad : " << F2 << "\t"; + else + flux << F2 << "\t"; + if (&flux == &cout) + cout << "potential : " << potential << "\t"; + else + flux << potential << "\t"; + + } + + // read data + // Same incomplete + + virtual void read(istream & flux) + { + if (&flux == &cin) + cout << "entrez Bias field : "; + flux >> F0; + if (&flux == &cin) + cout << "entrez Grad : "; + flux >> F1; + if (&flux == &cin) + cout << "entrez Grad Grad : "; + flux >> F2; + if (&flux == &cin) + cout << "entrez potential : "; + flux >> potential; + } + + +// Get field at a given position from the grid + Vecteur3D get_Field_interpolation2D(const Vecteur3D pos, int type_field_read = 0) const; + + // Get Grad (F.F) = gradient of the norm of the field squared at a given position from the grid + // Also give the field F + void get_norm2_grad_Field_interpolation2D(const Vecteur3D pos, Vecteur3D &field, Vecteur3D &grad_F2, int type_field_read = 0) const; + + +// Get field at a given position + Vecteur3D get_Field(const Vecteur3D &pos) const; + + +// Get potential at a given position + // Be careful give the potential as if it was an electric potential (so it integrates the field) + double get_electric_potential(const Vecteur3D pos) const; + + // Calcul du gradient de la norme (au carré) du champ local F +// Grad (F.F) = 2 (F.grad) F + Vecteur3D get_grad_field_F2(const Vecteur3D& pos ) const; + + + + /*************** BOBINE *****************/ + + +// CALCUL APPROCHE. Les formules analytiques existes mais sont complexes. +// Ici ce sont des formules plus simples mais très proche de la réalité (cf bz2, brho2 Mathematica ficher calcul_Sisyphus.nb +// Champ pour bobine rayon r centrée en z=0 axe Oz avec courant de I_coil ampère + // ATTENTION ICI LES CALCULS SONT fait en supposant les bobines d'axes Oz alors qu'elle seront d'axe Ox en réalité. + // Il faudra donc appeler ces fonctions non pas en (x,y,z) mais en (y,z,x) + +// Pour info le champ au centre est Mu I0/ (2 r) + // Champ crée par une bobine positionée en pos_bobine + + + Vecteur3D get_field_coil(const Vecteur3D pos, double r, double I_coil, Vecteur3D pob_bobine, double &Brho_sur_rho, double &Bz ) const; + Vecteur3D get_field_coil(const Vecteur3D pos, double r, double I_coil, Vecteur3D pob_bobine ) const; + +// Champ pour Nb_coils bobines de rayon r la première centrée en z=0 les autres séparées de z_gap + Vecteur3D get_field_coils(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz, double &Brho_sur_rho, double &Bz) const; + Vecteur3D get_field_coils(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz) const; + + +// Gradient du champ pour une bobines rayon r centrée en z=0 axe Oz +// En fait donne dBz_drho, dBz_dz, dBrho_drho, dBrho_dz + void get_grad_field_coil_4(const Vecteur3D pos, double r, double I_coil, double &dBz_drho_sur_rho, double &dBz_dz, double &dBrho_drho, double &dBrho_dz_sur_rho) const; + // Gradient du champ pour des bobines rayon r axe Oz + // En fait donne dBz_drho, dBz_dz, dBrho_drho, dBrho_dz + void get_grad_field_coils_4(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz, double &dBz_drho_sur_rho, double &dBz_dz, double &dBrho_drho, double &dBrho_dz_sur_rho) const; + + +// Gradient de la Norme du champ pour des bobines rayon r centrée en z=0 axe Oz + Vecteur3D get_grad_normfield2_coils(const Vecteur3D pos, double r, double I_coil, int Nb_coils, double z_gap, int is_Helmholtz) const; + + +// Erase and Read the matrix of discrete value from a file and return the number of elements +// The file depends on the type of field but should be ordered x By Bz. +// It should be first along the n1 axis [0,0,0], [1,0,0], ..., [n1-1,0,0], [0,1,0], ... +// and equally spaced along each axis, + int Read_Matrix( const char * Fieldfilename); + +// Calculation and output of partial derivation of the field +// For instance for the type_field 2 (that does not contains the derivatives. I calculate them) + void Calculate_Derivative_Matrix(int number_matrix_lines, const char * Fieldfilename) const; + + +// Using the Matrix of the field (that should have been read before!) we extract the grid parameters and initialize the Interpolators depending on the type of field used + void Init_Interpolator(); + +}; + +ostream& operator << (ostream &flux, Field field); + +istream& operator >> (istream &flux, Field & field); //at est modifié! + + +#endif diff --git a/Main Code 64bits/Initialisation_programme.cpp b/Main Code 64bits/Initialisation_programme.cpp new file mode 100644 index 0000000..f3073b4 --- /dev/null +++ b/Main Code 64bits/Initialisation_programme.cpp @@ -0,0 +1,526 @@ + +#include "Initialisation_programme.h" + +/************************************************************************/ +/******************* INITIALISATION DU PROGRAMME ************************/ +/************************************************************************/ + + +// Initialisation des niveaux, des transitions, des forces de raies et des durées de vie +// retourne le nombre de niveaux +int initialisation_trans_mol(const char *nom_file_Levels, const char *nom_file_Lines, vector &Level, FitParams ¶ms) +{ + int nb_Levels = Pgopher_Level_List(nom_file_Levels, Level, params); + cout << "Nb de niveaux = " << nb_Levels << endl << endl; + cout << " Only Zeeman effect no Stark effect " << endl; + int nb_raies = Pgopher_Line_List(nom_file_Lines, Level, params); + cout << "Nb de raies (en absorption) = " << nb_raies << endl << endl; + + initialisation_Gamma(Level, params); // Initialisation des durées de vies + + return nb_Levels; +} + +//Initialise l'état du générateur de nombre aléatoire +void set_random_generator(gsl_rng * r, int nombre_seed, const char *nom_file) +{ + const gsl_rng_type * T; + gsl_rng_env_setup(); + T = gsl_rng_default; // "Mersenne Twister" generator by default. Plus rapide que RANLUX. cf. chapitre 17.12 de gsl_ref. + r = gsl_rng_alloc (T); + + +// if (nombre_seed>=0) +// gsl_rng_set(r,nombre_seed); // Pour débugage on initialise le générateur toujours de la même façon +// else +// { +// FILE *fp; +// fp=fopen("const char *nom_file", "rb"); // Fichier contenant les données du générateur de nombre aléatoire +// int ran_gen_result = gsl_rng_fread (fp, r); // This function writes the random number state of the random number generator r +// if (ran_gen_result == GSL_EFAILED) +// cout << " Problem writing to the file: Data/random_gen.txt" << endl; +// fclose(fp); +// } +// return; +} + + + + +// Initialise la position et la vitesse (gaussienne) des molecules +void Init_Molecule(const gsl_rng * r, vector &Mol, const Field fieldB, const Field fieldE, const int Nb_of_type_of_different_Mol, FitParams ¶ms, DataCards data) +{ +// Initialize 1st type of Mol from Mol[0] to Mol[Nom_Mol[0]-1] +// then second type from Mol[Nom_Mol[0]] to Mol[Nom_Mol[0]+Nom_Mol[1]-1] ... + Mol.clear(); + int nb_of_total_molecules_up_to_now = 0; + Molecule Mol_i; // Current molecule + for (int i=0; i < Nb_of_type_of_different_Mol ; i++) + { + std::ostringstream oss; + oss << "[" << i << "]"; + std::string num = oss.str(); // num = "[i]" + + int Nb_Mol = (int) params.LocateParam(string("N_Mol")+ num)->val; + string Nom_Mol = data.SParam(string("Nom_Mol")+ num); // nom de la molécule + + int proc[3]; // choix de l'initialisation si potentiel linéaire ou quadratique selon x (0), y(1) et z (2) + proc[0] = (int) params.LocateParam(string("Procedure_init_x")+ num)->val; + proc[1] = (int) params.LocateParam(string("Procedure_init_y")+ num)->val; + proc[2] = (int) params.LocateParam(string("Procedure_init_z")+ num)->val; + + Vecteur3D sigma_pos; + sigma_pos.set(0,params.LocateParam(string("size_x")+ num)->val); + sigma_pos.set(1,params.LocateParam(string("size_y")+ num)->val); + sigma_pos.set(2,params.LocateParam(string("size_z")+ num)->val); + + Vecteur3D const_pos_initial; + const_pos_initial.set(0,params.LocateParam(string("offset_x")+ num)->val); + const_pos_initial.set(1,params.LocateParam(string("offset_y")+ num)->val); + const_pos_initial.set(2,params.LocateParam(string("offset_z")+ num)->val); + + Vecteur3D v0; // Initial velocity added to the random one + v0.set(0,params.LocateParam(string("v0_x")+ num)->val); + v0.set(1,params.LocateParam(string("v0_y")+ num)->val); + v0.set(2,params.LocateParam(string("v0_z")+ num)->val); + + for (int i=nb_of_total_molecules_up_to_now; ival; + double Temp_ini_y = params.LocateParam(string("Temp_ini_y")+ num)->val; + double Temp_ini_z = params.LocateParam(string("Temp_ini_z")+ num)->val; + + + Vecteur3D pos,velocity; + + const double vitesse_therm_x = sqrt(kB*Temp_ini_x/Mol_i.get_mass()); // vitesse thermique en m/s 1/2 m vx^2 = 1/2 kB T + const double vitesse_therm_y = sqrt(kB*Temp_ini_y/Mol_i.get_mass()); // vitesse thermique en m/s 1/2 m vx^2 = 1/2 kB T + const double vitesse_therm_z = sqrt(kB*Temp_ini_z/Mol_i.get_mass()); // vitesse thermique en m/s 1/2 m vx^2 = 1/2 kB T + + + Vecteur3D Temp_ini(Temp_ini_x,Temp_ini_y,Temp_ini_z); + Vecteur3D sigmav(vitesse_therm_x,vitesse_therm_y,vitesse_therm_z); + velocity.gaussian_initialisation (r,sigmav); + + for (int j=0; j<=2; j++) // 3 axes: x, y ou z + { +// Exemple Taille de l'échantillion dans le potentiel U(x,y,z) = U(0) + Zeeman_x |x| + Zeeman_y |y| + Zeeman_z z^2 +// La distribution est exp(−U(x,y,z)/(k T)) est exp(−|x/sigma_x |) exp(−|y/sigma_y |) exp(−z^2/(2 sigma_z^2) ) +// const Vecteur3D sigmaSAMPLE(kB*Temp_ini_x/Zeeman_x, kB*Temp_ini_y/Zeeman_y, sqrt(kB*Temp_ini_z/(2.*Zeeman_z))); + + double delta_prime; // dérivée du shift permettant de calculer le moment magnétique effectif + double sigma_r; // Taille thermique de l'échantillon + + // We addapte the position for different model (some of them also implies velocity modification) + switch( proc[j] ) + { + + case -1: // ordonne les positions des molécules au départ (selon un axe mettre les autres axes aléatoires) + { + pos.set(j, 3.*(i-Nb_Mol/2.)*sigma_pos.get(j) /Nb_Mol ); + velocity.set(j, 3.*(i-Nb_Mol/2.)*(sigmav.get(j)) /Nb_Mol ); + break; + } + + case 0: // Taille fixe (aléatorie gaussien) + { + pos.set(j, gsl_ran_gaussian (r,sigma_pos.get(j))); + break; + } + + case 1: // Potentiel linéaire --> Laplace. On rappelle que gsl_ran_laplace (const gsl_rng * r, double a) returns a random variate: p(x) dx = {1 \over 2 a} \exp(-|x/a|) dx + { + delta_prime = fabs(delta_field_shift_B_E(Mol, i, fieldB.get_F1().get(j),0.)); + sigma_r = kB*Temp_ini.get(j)/(HBAR * delta_prime); + pos.set(j, gsl_ran_laplace (r,sigma_r)); + break; + } + + case 2: // Potentiel quadratique --> gaussien + { + delta_prime = fabs(delta_field_shift_B_E(Mol, i, fieldB.get_F2().get(j),0.)); // dérivée du shift permettant de calculer le moment magnétique effectif + sigma_r = sqrt(kB*Temp_ini.get(j)/(2.*HBAR * delta_prime)); + pos.set(j,gsl_ran_gaussian (r,sigma_r)); + break; + } + + case 3: // potential (voltage) elec. quadratique e (electric field linear) but for CHARGED particles (for instance in a Paul trap)--> Gaussien + { + double m_omega2 = - Mol_i.get_charge()* fieldE.get_F1().get(j); // m omega_j^2 in the potential q V(r_j)=1/2 m omega^2 r_j^2 so m omega_j^2 = - q F1.j() (E = - Grad pot) + sigma_r = sqrt(kB*Temp_ini.get(j)/m_omega2); // because 1/2 m omega^2 sigma_r^2 = 1/2 k_B T --> sigma_r^2=kB T/(m omega^2)) + // sqrt(3.*kB) is able to give the proper E_pot + pos.set(j,gsl_ran_gaussian (r,sigma_r)); + break; + } + + case 4: // random gaussian in r and pure gaussian (non random) in v + { + pos.set(j,gsl_ran_gaussian (r,sigma_pos.get(j))); + double vj = gsl_cdf_gaussian_Pinv((1+i)/(Nb_Mol+1.),sigmav.get(j) ); // x^2 = m v^2/(kB T) ; x = v/sigma_v so gaussian distribution is 1/(sqrt(2 pi)) * exp (-x^2/2) + velocity.set(j, vj); // We cut in N+1 interval with equiproba to have a molecule. + // So, we put a molecule exactly at x_(i+1) (i=0,...,N-1) where int_(x_(i)^x_(i+1)) e^(-x^2/2) dx =1/(N+1) + break; + } + + case 5: // 5 effusive beam. Meaning as in case 0 but we keep only the positive velocities + { + double vj; + do + { + vj = gsl_ran_gaussian (r,sigmav.get(j)); + } + while(vj<0); + velocity.set(j, vj); + pos.set(j, gsl_ran_gaussian (r,sigma_pos.get(j))); + break; + } + + } + } + + velocity = velocity + v0; + pos = pos + const_pos_initial; // Initial velocity and position added to the random one + + + Mol_i.set_pos(pos); // Initialise la position (gaussienne) des molecules + Mol_i.set_vel(velocity); // Initialise la vitesse (gaussienne) des molecules + Mol.push_back(Mol_i); // Mol[i]=Mol_i; + } + nb_of_total_molecules_up_to_now += Nb_Mol; + } + + return; +} + + +// Initialise les lasers +void Init_Laser(vector &laser, const int Nb_lasers, FitParams ¶ms, const char *nom_file) +{ + laser.clear(); + for (int i=0; i < Nb_lasers ; i++) + { + std::ostringstream oss; + oss << "[" << i << "]"; + std::string num = oss.str(); // num = "[i]" + + Vecteur3D waist_position; + waist_position.set(0,params.LocateParam(string("waist_pos_x") + num)->val); + waist_position.set(1,params.LocateParam(string("waist_pos_y") + num)->val); + waist_position.set(2,params.LocateParam(string("waist_pos_z") + num)->val); + + Vecteur3D Direction_laser; + Direction_laser.set(0,params.LocateParam(string("direction_x") + num)->val); + Direction_laser.set(1,params.LocateParam(string("direction_y") + num)->val); + Direction_laser.set(2,params.LocateParam(string("direction_z") + num)->val); + + Vecteur3D waist_laser; + waist_laser.set(0,params.LocateParam(string("waist") + num)->val); + waist_laser.set(1,params.LocateParam(string("waist") + num)->val); + + double Gamma_L_MHz = params.LocateParam(string("Gamma_L_MHz") + num)->val * params.LocateParam("scale_Gamma")->val; + double Power = params.LocateParam(string("Power") + num)->val * params.LocateParam("scale_Power")->val; // Parametre multiplicatif de la puissance des lasers + double Energie_cm = params.LocateParam(string("Energie_cm") + num)->val + params.LocateParam("Offset_Detuning_cm")->val; // Parametre multiplicatif de la puissance des lasers + + Vecteur3D polarisation_laser; // Polarisation -1,0,+1: sigma-,pi,sigma+ + polarisation_laser.set(0,params.LocateParam(string("Pol_circulaire_right_sm") + num)->val); + polarisation_laser.set(2,params.LocateParam(string("Pol_circulaire_left_sp") + num)->val); + + double polar_angle_degree = params.LocateParam(string("polar_angle_degree") + num)->val; + + int type_laser = (int) params.LocateParam(string("type_laser") + num)->val; + + int coherent_avec_laser_num = (int) params.LocateParam(string("coherent_avec_laser_num") + num)->val; + +// double Temp_ini = params.LocateParam("Temp_ini[0]")->val; // Température initiale de la molécule type 0 +// const double DE_temp_cm1 = (1./(hPlanck*100.*C)) * kB*Temp_ini ; // Energie (>0) correspondant à cette température initiale +// +// // 0 = false ; 1 = true +// if( ((int) params.LocateParam(string("is_pompage") + num)->val) == ((int) true) ) // Le laser est utilisé pour le pompage. Son énergie en excès varie comme scale_temp_pompage +// { +// double scale_temp_pompage = params.LocateParam("scale_temp_pompage")->val; +// Energie_cm -= scale_temp_pompage*DE_temp_cm1; // On met l'énergie de transition laser à la résonance en scale_temp +// } +// +// if( ((int) params.LocateParam(string("is_rep") + num)->val) == ((int) true) ) // Le laser est utilisé pour le repompage. Son énergie en excès varie comme scale_temp_rep +// { +// double scale_temp_rep = params.LocateParam("scale_temp_rep")->val; +// Energie_cm -= scale_temp_rep*DE_temp_cm1; +// } + + Laser current_Laser; + current_Laser.set_waist_pos(waist_position); + current_Laser.set_direction(Direction_laser); + current_Laser.set_waist(waist_laser); + current_Laser.set_energy_cm(Energie_cm); + current_Laser.set_Gamma_Laser_MHz(Gamma_L_MHz); + current_Laser.set_Power(Power); + current_Laser.set_polarisation(polarisation_laser); + current_Laser.set_polar_angle(polar_angle_degree); + current_Laser.set_type_laser(type_laser); + current_Laser.set_coherent_avec_laser_num(coherent_avec_laser_num); + string nom_file_short = (string(nom_file)).substr(0,string(nom_file).length() -4); // enlève le .dat + string nom_file_long = nom_file_short + num + ".dat"; + const char *nom_file_spectrum = (nom_file_long).c_str(); // Nom_file[numero_laser].dat + current_Laser.read_Spectrum(nom_file_spectrum); // Lit le fichier du spectre laser (rien si le ficheir n'existe pas) + laser.push_back(current_Laser); // laser[i] = current_Laser; + } + + return; +} + + +// Modification temporelle des paramètres +void Modif_Param(const double t, FitParams ¶ms) +{ + for (ParamIterator i=params.begin(); i != params.end(); ++i) // boucle sur les paramètres + { + Param &p = **i; + // cout << " t " << t << " " << p << endl << endl; + if( p.is_time_dependent == false ) // Pas de boucle pour ce paramètre + continue; + else + p.val = p.val_t0*exp(-t/p.tau); // On modifie le paramètre + } + return; +} + + + +/************************************************************************/ +/******************* INITIALISATION DES CHAMPS ************************/ +/************************************************************************/ + +// Initialise les champs, zero par défaut. +void Init_Field(Field &fieldB, Field &fieldE, FitParams ¶ms, const char *nom_Magn_file, const char *nom_Elec_file) +{ + + /******** Magnetic Field *************/ + + double B_x,B_y,B_z; + B_x = params.LocateOrAddNonConstParam("B_x")->val; + B_y = params.LocateOrAddNonConstParam("B_y")->val; + B_z = params.LocateOrAddNonConstParam("B_z")->val; + Vecteur3D B_Field = Vecteur3D(B_x, B_y, B_z); + + double grad_B_x,grad_B_y,grad_B_z; + grad_B_x = params.LocateOrAddNonConstParam("grad_B_x")->val; + grad_B_y = params.LocateOrAddNonConstParam("grad_B_y")->val; + grad_B_z = params.LocateOrAddNonConstParam("grad_B_z")->val; + Vecteur3D Grad_B = Vecteur3D(grad_B_x, grad_B_y, grad_B_z); + + double grad_grad_B_x, grad_grad_B_y, grad_grad_B_z; + grad_grad_B_x = params.LocateOrAddNonConstParam("grad_grad_B_x")->val; + grad_grad_B_y = params.LocateOrAddNonConstParam("grad_grad_B_y")->val; + grad_grad_B_z = params.LocateOrAddNonConstParam("grad_grad_B_z")->val; + Vecteur3D grad_grad_B = Vecteur3D(grad_grad_B_x, grad_grad_B_y, grad_grad_B_z); + + int n_value_B = (int) params.LocateOrAddNonConstParam("n_value_B")->val; + double Bn_x, Bn_y, Bn_z,r_cut; + Bn_x = params.LocateOrAddNonConstParam("Bn_x")->val; + Bn_y = params.LocateOrAddNonConstParam("Bn_y")->val; + Bn_z = params.LocateOrAddNonConstParam("Bn_z")->val; + r_cut = params.LocateOrAddNonConstParam("r_cut")->val; + Vecteur3D Bn = Vecteur3D(Bn_x, Bn_y, Bn_z); + + fieldB.set_F0(B_Field); + fieldB.set_F1(Grad_B); + fieldB.set_F2(grad_grad_B); + fieldB.set_n(n_value_B); + fieldB.set_Fn(Bn); + +// int type_field = params.LocateOrAddNonConstParam("type_field")->val; + + fieldB.type_field = Magnetic_Field; + fieldE.type_field = Electric_Field; + + int type_field_read_B = params.LocateOrAddNonConstParam("type_field_read_B")->val; + + int Nb_bobines = params.LocateOrAddNonConstParam("Nb_bobines")->val; + double gap_bobines = params.LocateOrAddNonConstParam("gap_bobines")->val; + double courant_bobines = params.LocateOrAddNonConstParam("courant_bobines")->val; + double rayon_bobines = params.LocateOrAddNonConstParam("rayon_bobines")->val; + int is_Helmholtz = params.LocateOrAddNonConstParam("is_Helmholtz")->val; + + int type_of_field_for_internal_state_shift = params.LocateOrAddNonConstParam("type_of_field_for_internal_state_shift")->val; + + fieldB.Nb_bobines = Nb_bobines; + fieldB.gap_bobines = gap_bobines; + fieldB.courant_bobines = courant_bobines; + fieldB.rayon_bobines = rayon_bobines; + fieldB.is_Helmholtz = is_Helmholtz; + fieldB.type_field_read = type_field_read_B; + + + if (fieldB.type_field_read >= 2) // We read the files + { + if(nom_Magn_file !=NULL) // At the first initialization we give the name of the file and we have to read the file and initialize the INterpolator + { + if (fieldB.Read_Matrix(nom_Magn_file)==0) + { + cerr << "Empty Magnetic field file " << nom_Magn_file << endl; + exit(1); + } + cout << "We read Magnetic field file " ; + cout << "Nb lignes " << fieldB.Read_Matrix(nom_Magn_file) << endl; // If no file this does not do anything and so do not modify the matrix_field + fieldB.Init_Interpolator(); // Give the size, offset and spacing of the grid used + } + } + + + + + /******** Electric Field *************/ + + double E_x,E_y,E_z; + E_x = params.LocateOrAddNonConstParam("E_x")->val; + E_y = params.LocateOrAddNonConstParam("E_y")->val; + E_z = params.LocateOrAddNonConstParam("E_z")->val; + Vecteur3D E_Field = Vecteur3D(E_x, E_y, E_z); + + double grad_E_x,grad_E_y,grad_E_z; + grad_E_x = params.LocateOrAddNonConstParam("grad_E_x")->val; + grad_E_y = params.LocateOrAddNonConstParam("grad_E_y")->val; + grad_E_z = params.LocateOrAddNonConstParam("grad_E_z")->val; + Vecteur3D Grad_E = Vecteur3D(grad_E_x, grad_E_y, grad_E_z); + + double grad_grad_E_x, grad_grad_E_y, grad_grad_E_z; + grad_grad_E_x = params.LocateOrAddNonConstParam("grad_grad_E_x")->val; + grad_grad_E_y = params.LocateOrAddNonConstParam("grad_grad_E_y")->val; + grad_grad_E_z = params.LocateOrAddNonConstParam("grad_grad_E_z")->val; + Vecteur3D grad_grad_E = Vecteur3D(grad_grad_E_x, grad_grad_E_y, grad_grad_E_z); + + fieldE.set_F0(E_Field); + fieldE.set_F1(Grad_E); + fieldE.set_F2(grad_grad_E); + + int n_value_E = (int) params.LocateOrAddNonConstParam("n_value_E")->val; + double En_x, En_y, En_z; + En_x = params.LocateOrAddNonConstParam("En_x")->val; + En_y = params.LocateOrAddNonConstParam("En_y")->val; + En_z = params.LocateOrAddNonConstParam("En_z")->val; + Vecteur3D En = Vecteur3D(En_x, En_y, En_z); + + fieldE.set_n(n_value_E); + fieldE.set_Fn(En); + + int type_field_read_E = params.LocateOrAddNonConstParam("type_field_read_E")->val; + fieldE.type_field_read = type_field_read_E; + + + if (fieldE.type_field_read >= 2) // We read the files + { + if(nom_Elec_file == NULL) // At the first initialization we give the name of the file and we have to read the file and initialize the INterpolator + { + cout << " because no Elec file name !" << endl; + } + + if(nom_Elec_file != NULL) // At the first initialization we give the name of the file and we have to read the file and initialize the INterpolator + { + if (fieldE.Read_Matrix(nom_Elec_file)==0) + { + cerr << "Empty Electric field file " << nom_Elec_file << endl; + exit(1); + } + fieldE.Read_Matrix(nom_Elec_file); + fieldE.Init_Interpolator(); // Give the size, offset and spacing of the grid used + } + } + +} + diff --git a/Main Code 64bits/Initialisation_programme.h b/Main Code 64bits/Initialisation_programme.h new file mode 100644 index 0000000..f73a9ee --- /dev/null +++ b/Main Code 64bits/Initialisation_programme.h @@ -0,0 +1,58 @@ +// Initialisation des niveaux, des transitions, des forces de raies et des durées de vie +// Des paramètres lasers, des positions, vitesses des molécules .... + +#ifndef Initialisation_programme_SEEN +#define Initialisation_programme_SEEN + + +#include +using namespace std; + +#include // for random generator +#include // for gaussian random generator +#include + +#include "Vecteur3D.h" +#include "Molecule.h" // Classe molecule +#include "Laser.h" // Classe Laser +#include "Field.h" // Classe Champ +#include "Transitions_initialisation.h" +#include "shift_molecule.h" +#include // pour ostringstream + + + + +/************************************************************************/ +/******************* INITIALISATION DU PROGRAMME ************************/ +/************************************************************************/ + + +// Initialisation des niveaux, des transitions, des forces de raies et des durées de vie +// Retroune le nb de niveaux +int initialisation_trans_mol(const char *nom_file_Levels, const char *nom_file_Lines , vector &Level, FitParams ¶ms); + +//Initialise l'état du générateur de nombre aléatoire +void set_random_generator(gsl_rng * r, int nombre_seed, const char *nom_file); + + +#include "params.h" +// Initialise la position et la vitesse (gaussienne) des molecules +void Init_Molecule(const gsl_rng * r, vector &Mol, const Field fieldB, const Field fieldE, const int Nb_of_type_of_different_Mol, FitParams ¶ms, DataCards data); + +// Initialise les lasers +void Init_Laser(vector &laser, const int Nb_lasers, FitParams ¶ms, const char *nom_file); + +// Modification temporelle des paramètres +void Modif_Param(const double t , FitParams ¶ms); + + +/************************************************************************/ +/******************* INITIALISATION DES CHAMPS ************************/ +/************************************************************************/ + +#include "params.h" +// Initialise les champs, zero par défaut +void Init_Field(Field &fieldB, Field &fieldE, FitParams ¶ms, const char *nom_Magn_file=NULL, const char *nom_Elec_file=NULL); + +#endif diff --git a/Main Code 64bits/Internal_state.cpp b/Main Code 64bits/Internal_state.cpp new file mode 100644 index 0000000..c5303ab --- /dev/null +++ b/Main Code 64bits/Internal_state.cpp @@ -0,0 +1,560 @@ +#include "Internal_state.h" + +// ------------ +// Constructors +// ------------ + +Internal_state::Internal_state() // Constructeur par défaut +{ + exc = 0; // 0 est l'état fondamental + two_Spin = two_Lambda = two_Omega = 0; + v =0; + two_J = two_N = two_M = 0; + Sym = 1; // Parity + deg_number = 0; // nombre de dégénérescence + Energy0_cm = Delta_FieldB = Linear_FieldB = Delta_FieldE = Linear_FieldE = 0.; + one_over_lifetime=0.; + Energy_cm = population = 0.; + liste_raies = vector < transition > (); +}; + +Internal_state::~Internal_state() +{} +; // Destructeur + + +Internal_state::Internal_state(const Internal_state & Intern) // Constructeur de (re)copie +{ + exc = Intern.exc; + two_Spin = Intern.two_Spin; + two_Lambda = Intern.two_Lambda; + two_Omega = Intern.two_Omega; + v = Intern.v; + two_J = Intern.two_J; + two_N = Intern.two_N; + two_M = Intern.two_M; + Sym = Intern.Sym; + deg_number = Intern.deg_number; + Energy0_cm = Intern.Energy0_cm; + Delta_FieldB = Intern.Delta_FieldB; + Linear_FieldB = Intern.Linear_FieldB; + Delta_FieldE = Intern.Delta_FieldE; + Linear_FieldE = Intern.Linear_FieldE; + one_over_lifetime = Intern.one_over_lifetime; + Energy_cm = Intern.Energy_cm; + population = Intern.population; + liste_raies = Intern.liste_raies; + +}; + + +Internal_state & Internal_state::operator = (const Internal_state & Intern) // opérateur d'affectation +{ + if (this != &Intern) // On vérifie que les objets ne sont pas les mêmes ! + { + exc = Intern.exc; + two_Spin = Intern.two_Spin; + two_Lambda = Intern.two_Lambda; + two_Omega = Intern.two_Omega; + v = Intern.v; + two_J = Intern.two_J; + two_N = Intern.two_N; + two_M = Intern.two_M; + Sym = Intern.Sym; + deg_number = Intern.deg_number; + Energy0_cm = Intern.Energy0_cm; + Delta_FieldB = Intern.Delta_FieldB; + Linear_FieldB = Intern.Linear_FieldB; + Delta_FieldE = Intern.Delta_FieldE; + Linear_FieldE = Intern.Linear_FieldE; + one_over_lifetime = Intern.one_over_lifetime; + Energy_cm = Intern.Energy_cm; + population = Intern.population; + liste_raies = Intern.liste_raies; + } + + return *this; +} + +// void set_int(const Internal_state & Intern) // opérateur d'affectation +// { +// exc = Intern.exc; +// v = Intern.v; +// J = Intern.J; +// MJ = Intern.MJ; +// } + + + +// Affichage (on ne met pas la liste des raies!) +void Internal_state::write(ostream & flux) +{ + if (&flux == &cout) + cout << "excitation : " << exc << "\t"; + else + flux << exc << "\t"; + + if (&flux == &cout) + cout << "Spin : " << two_Spin/2. << "\t"; + else + flux << two_Spin/2. << "\t"; + + if (&flux == &cout) + cout << "Lambda : " << two_Lambda/2. << "\t"; + else + flux << two_Lambda/2. << "\t"; + + if (&flux == &cout) + cout << "Omega : " << two_Omega/2. << "\t"; + else + flux << two_Omega/2. << "\t"; + + if (&flux == &cout) + cout << "vibration : " << v << "\t"; + else + flux << v << "\t"; + + if (&flux == &cout) + cout << "rotation J : " << two_J/2. << "\t"; + else + flux << two_J/2. << "\t"; + + if (&flux == &cout) + cout << "rotation N : " << two_N/2. << "\t"; + else + flux << two_N/2. << "\t"; + + if (&flux == &cout) + cout << "projection du moment total M : " << two_M/2. << "\t"; + else + flux << two_M/2. << "\t"; + + if (&flux == &cout) + cout << "Parité (+/- 1) : " << Sym << "\t"; + else + flux << Sym << "\t"; + + if (&flux == &cout) + cout << "Numéro pour lever la dégénérescence " << deg_number << "\t"; + else + flux << deg_number << "\t"; + + if (&flux == &cout) + cout << "Energy (cm^-1) " << Energy0_cm << "\t"; + else + flux << Energy0_cm << "\t"; + + if (&flux == &cout) + cout << "Delta Field B " << Delta_FieldB << "\t"; + else + flux << Delta_FieldB << "\t"; + + if (&flux == &cout) + cout << "Linear Field B " << Linear_FieldB << "\t"; + else + flux << Linear_FieldB << "\t"; + + if (&flux == &cout) + cout << "Delta Field E " << Delta_FieldE << "\t"; + else + flux << Delta_FieldE << "\t"; + + if (&flux == &cout) + cout << "Linear Field E " << Linear_FieldE << "\t"; + else + flux << Linear_FieldE << "\t"; + + if (&flux == &cout) + cout << "1/Lifetime " << one_over_lifetime << "\t"; + else + flux << one_over_lifetime << "\t"; + + if (&flux == &cout) + cout << "Energie shiftée (cm-1) " << Energy_cm << "\t"; + else + flux << Energy_cm << "\t"; + + if (&flux == &cout) + cout << "Population " << population << "\t"; + else + flux << population << "\t"; + +} + + +// Ecrit la liste des raies +void Internal_state::write_liste_raie(ostream & flux) +{ + if ((int) liste_raies.size() ==0) + { + cout << " VIDE " << endl; + flux << " VIDE " << endl; + return; + } + + if (&flux == &cout) + for( int i = 0; i < (int) liste_raies.size(); i++ ) + cout << "raie " << *(liste_raies[i].first) << " Force " << liste_raies[i].second << endl ; + else + for( int i = 0; i < (int) liste_raies.size(); i++ ) + flux << *(liste_raies[i].first) << liste_raies[i].second << endl; +} + + + + +// read des données (sans la liste des raies) +void Internal_state::read(istream & flux) +{ + if (&flux == &cin) + cout << "entrez excitation : "; + flux >> exc; + + if (&flux == &cin) + cout << "Spin (2*spin) : "; + flux >> two_Spin ; + + if (&flux == &cin) + cout << "Lambda (2*) : " ; + flux >> two_Lambda ; + + if (&flux == &cin) + cout << "Omega (2*) : " ; + flux >> two_Omega ; + + + if (&flux == &cin) + cout << "vibration : " ; + flux >> v ; + + if (&flux == &cin) + cout << "rotation J (2*) : " ; + flux >> two_J ; + + if (&flux == &cin) + cout << "rotation N (2*) : " ; + flux >> two_N ; + + if (&flux == &cin) + cout << "projection du moment total M (2*) : " ; + flux >> two_M ; + + if (&flux == &cin) + cout << "Parité (+/- 1) : " ; + flux >> Sym ; + + if (&flux == &cin) + cout << "Numéro pour lever la dégénérescence " ; + flux >> deg_number ; + + if (&flux == &cin) + cout << "Energy0_cm (cm^-1) " ; + flux >> Energy0_cm ; + + if (&flux == &cin) + cout << "Delta Field B " ; + flux >> Delta_FieldB ; + + if (&flux == &cin) + cout << "Linear Field B " ; + flux >> Linear_FieldB ; + + if (&flux == &cin) + cout << "Delta Field E " ; + flux >> Delta_FieldE ; + + if (&flux == &cin) + cout << "Linear Field E " ; + flux >> Linear_FieldE ; + + if (&flux == &cin) + cout << "1/Lifetime " ; + flux >> one_over_lifetime ; + + if (&flux == &cin) + cout << "Energie shiftée " ; + flux >> Energy_cm; + + if (&flux == &cin) + cout << "Population " ; + flux >> population; + +} + + +// True si l'état est = à w, false sinon +// On ne teste que l'état électronique, M, parité et numéro. +bool Internal_state::is_equal (const Internal_state & w) const +{ + if( (exc == w.exc) && (two_M == w.two_M) && (Sym == w.Sym) && (deg_number == w.deg_number) ) + { + return true; + } + + return false; +} + + + +//---------------------------------- +// Lecture des fichiers en Energie +//---------------------------------- + +// Read Energy List +// THE FILE CONTAINS: +// Manifold (1 for upper or 0 for lower typically) +// M (in Field it is real M) +// Sym(Parity +/-) +// #(number to discriminate the levels) +// Population +// v +// J +// N +// Omega +// Energy0(in 0 field) +// Delta +// C + + +// Ecriture dans le flux du niveau avec le format souhaité +void Internal_state::write_Level_PgopherB(ostream & flux) +{ + flux << exc << " "; + flux << two_M << " "; + flux << Sym << " "; + flux << deg_number << " "; + flux << population << " "; + flux << v << " "; + flux << two_J << " "; + flux << two_N << " "; + flux << two_Omega << " "; + flux << Energy0_cm << " "; + flux << Delta_FieldB << " "; + flux << Linear_FieldB << endl; +} + + +void Internal_state::read_Level_Pgopher_B(istream & flux) +{ + flux >> exc; + flux >> two_M; + flux >> Sym ; + flux >> deg_number ; + flux >> population ; + flux >> v ; + flux >> two_J; + flux >> two_N; + flux >> two_Omega; + flux >> Energy0_cm ; + Energy_cm = Energy0_cm; + flux >> Delta_FieldB ; + flux >> Linear_FieldB ; +} + +void Internal_state::read_Level_Pgopher_E(istream & flux) +{ + flux >> exc; + flux >> two_M; + flux >> Sym ; + flux >> deg_number ; + flux >> population ; + flux >> v ; + flux >> two_J; + flux >> two_N; + flux >> two_Omega; + flux >> Energy0_cm ; + Energy_cm = Energy0_cm; + flux >> Delta_FieldE ; + flux >> Linear_FieldE ; +} + + +// Signe d'une variable -1 si négatif et +1 si positif et 0 si nul +int signe(const double x) +{ + if (x < 0.) return -1; + if (x > 0.) return 1; + return 0 ; +} + + +// Calcul du shift en champ +//via E0 + signe(C)*(-Delta/2+sqrt((Delta/2)^2+(C F)^2)) +double Internal_state::Energy_Shift_B_cm(const double B) const +{ + return signe(Linear_FieldB)*(-Delta_FieldB/2.+sqrt((Delta_FieldB/2.)*(Delta_FieldB/2.)+(Linear_FieldB * B)*(Linear_FieldB * B))); +} + +double Internal_state::Energy_Shift_E_cm(const double E) const +{ + return signe(Linear_FieldE)*(-Delta_FieldE/2.+sqrt((Delta_FieldE/2.)*(Delta_FieldE/2.)+(Linear_FieldE * E)*(Linear_FieldE * E))); +} + + + +// Calcul du gradient du shift (en unité SI pas cm^-1) en champ +// Grad(F.F) * C*C*signe(C)*/[2*sqrt((Delta/2)^2+(C F)^2))] +Vecteur3D Internal_state::Grad_Energy_Shift_B(const double B, const Vecteur3D gradient_B2) +{ + if (abs(Linear_FieldB) < VERY_SMALL_NUMBER) return Vecteur3D(0.,0.,0.); // Pour éviter des divisions par zéro + return HBAR*Conv_Ecm_delta*0.5*gradient_B2*signe(Linear_FieldB)*Linear_FieldB*Linear_FieldB/sqrt((Delta_FieldB/2.)*(Delta_FieldB/2.)+(Linear_FieldB * B)*(Linear_FieldB * B)); +} + +Vecteur3D Internal_state::Grad_Energy_Shift_E(const double E, const Vecteur3D gradient_E2) +{ + if (abs(Linear_FieldE) < VERY_SMALL_NUMBER) return Vecteur3D(0.,0.,0.); // Pour éviter des divisions par zéro + return HBAR*Conv_Ecm_delta*0.5*gradient_E2*signe(Linear_FieldE)*Linear_FieldE*Linear_FieldE/sqrt((Delta_FieldE/2.)*(Delta_FieldE/2.)+(Linear_FieldE * E)*(Linear_FieldE * E)); +} + + + +// Calcul du champ F correspondant au shift E_cm: via E0 + signe(C)*(-Delta/2+sqrt((Delta/2)^2+(C F)^2)) = E_cm = Eshift +double Internal_state::Field_Shift_B_cm(const double Eshift) +{ + if (abs(Linear_FieldB) < VERY_SMALL_NUMBER) return 0.; // Pour éviter des divisions par zéro + return sqrt(Eshift*(Eshift+ Delta_FieldB*signe(Linear_FieldB)))/(signe(Linear_FieldB)*Linear_FieldB); +} + + + +double Internal_state::Field_Shift_E_cm(const double Eshift) +{ + if (abs(Linear_FieldE) < VERY_SMALL_NUMBER) return 0.; // Pour éviter des divisions par zéro + return sqrt(Eshift*(Eshift+ Delta_FieldE*signe(Linear_FieldE)))/(signe(Linear_FieldE)*Linear_FieldE); +} + + + +// Somme les taux de desexcitation +double Internal_state::Einstein_desex_rate() +{ + double Gamma = VERY_SMALL_NUMBER; // Not 0. To avoid division by zero + + for( int i = 0; i < (int) liste_raies.size(); i++ ) + { + double dip_Debye = sqrt(3.*liste_raies[i].second); // dipole en Debye de la transiton + double energie_cm = Energy_cm - (liste_raies[i].first)->Energy_cm ; // Energie en cm^-1 de la transition + if (energie_cm > 0.) // Transition en émission + Gamma += dip_Debye*dip_Debye*Spol_Debye_A_s*energie_cm*energie_cm*energie_cm; + // Spol_Debye_A_s = (8e6*pi*pi*C*C*C*Debye*Debye)/(3.*EPSILON0*C*C*C*HBAR); // 3.13618932*10^-7 = Conversion HonlLondon (en Debye) en A Einstein (s^-1) si energie en cm^-1 + } + return Gamma; +} + + +//---------------------------------- +// Lecture des fichiers en Raies +//---------------------------------- + + +void Internal_state::add_transition (Internal_state *v,const double strenght) +{ + transition raie; + raie = make_pair (v,strenght); + liste_raies.push_back (raie); + return; +} + + +/* + PGOPHER GIVES: + +Molecule responsible for this transition. +M' Manifold for the upper state of the transition +J' Upper state total angular momentum or M'. (M' in the presence of static field, otherwise J' in the absence of hyperfine structure, otherwise F'). +S' Symmetry of the upper state. +#' Eigenvalue number for upper state. This gives the index (starting from 1) of the upper energy level with respect to other levels of the same total angular momentum and symmetry. +M'' for the lower state of the transition +J'' Lower state total angular momentum or M". (M" in the presence of static field, otherwise J' in the absence of hyperfine structure, otherwise F'). +S'' Symmetry of the lower state. +#'' Eigenvalue number for lower state. This gives the index (starting from 1) of the upper energy level with respect to other levels of the same total angular momentum and symmetry. +Position The position of the transition; the units for this are the units used in the main simulation window. For line position fitting, alter this number to the position of the observed peak, either manually or (more usually) with the assignment process described under line position fits. +Std Dev The (relative) standard deviation of this transition, used to calculate the weight of the observation in a line position fit. If this is negative, zero or blank this transition will not be included in the fit. Entries will initially have this blank or negative, and the automatic assignment process will set this to 1. Less certain measurements can be given larger values. Note that the parameters produced by a fit only depend on the relative values of the weights. If UNREGISTERED EVALUATION VERSION is set at the top level, then this column is set to the negative of the estimated uncertaInternal_statey of the transition, based on the errors in the most recent fit, if available. +strengths The Internal_stateensity of the rotational transition. +Width The width of the transition. (Note that this does not include the Gaussian or Lorentzian width set on the plot window.) +deltaJ(J'') The transition strength in branch notation, such as P(1). The display will depend on the molecule type and the electronic and nuclear angular momenta included in the calculation. +Name Details of the transition, including other quantum numbers where appropriate. The assignment process will also add the source of the measurement (typically a filename) where possible. + +Name contains: + The manifold and state name + J: The J quantum number; not shown if ShowJ is false at the Molecule level + N: The N quantum number; not shown if ShowN is false at the Molecule level or all states are singlet states + Ω: The Ω quantum number; not shown if ShowOmega is false at the Molecule level (the default) or all states are singlet states + Fn: The component of the multiplet numbered from 1 in order of increasing energy; not shown if ShowFNumber is false at the Molecule level or all states are singlet states. + This contains the same information as the Ω quantum number, so it does not usually make sense to show both. + e/f: The parity; not shown if Showef is false at the Molecule level. + Hyperfine: quantum numbers are added at the end as required. + + BUT HERE WE USE ONLY: + UpperManifold M' Sym' #' LowerManifold M" Sym" #" Position Intensity Eupper Elower Spol + +REMEMBER That we use Pgopher with the option 2J thus tjhe quantum numbers are *2: two_J +*/ + + +void read_Line_Pgopher(istream & flux, Internal_state & Upper_state,Internal_state & Lower_state, double & Spol, double & position, double & Intensity) +{ + + flux >> Upper_state.exc; + flux >> Upper_state.two_M; + flux >> Upper_state.Sym ; + flux >> Upper_state.deg_number ; + + flux >> Lower_state.exc; + flux >> Lower_state.two_M; + flux >> Lower_state.Sym ; + flux >> Lower_state.deg_number ; + + flux >> position; + flux >> Intensity; + + flux >> Upper_state.Energy0_cm; + flux >> Lower_state.Energy0_cm; + flux >> Spol; + + return; +} + + + +// Ecriture dans le flux la transition (ligne) avec le format souhaité +void write_Line_Pgopher(ostream & flux, Internal_state & Upper_state, Internal_state & Lower_state, const double Spol, const double position, const double Intensity) +{ + flux << Upper_state.exc << " "; + flux << Upper_state.two_M << " "; + flux << Upper_state.Sym << " "; + flux << Upper_state.deg_number << " "; + + flux << Lower_state.exc << " "; + flux << Lower_state.two_M << " "; + flux << Lower_state.Sym << " "; + flux << Lower_state.deg_number << " "; + + flux << position << " "; + flux << Intensity << " "; + + flux << Upper_state.Energy0_cm << " "; + flux << Lower_state.Energy0_cm << " "; + flux << Spol << endl; + + return; +} + + +//---------------------------------- +// Surdéfinition des entrées sorties (sans la liste des raies) +//---------------------------------- + +ostream & operator << (ostream & flux, Internal_state Intern) +{ + Intern.write(flux); + return(flux); +} + +istream& operator >> (istream &flux, Internal_state & Intern) //Intern est modifié! +{ + Intern.read(flux); + return(flux); +} + + diff --git a/Main Code 64bits/Internal_state.h b/Main Code 64bits/Internal_state.h new file mode 100644 index 0000000..9b0e20a --- /dev/null +++ b/Main Code 64bits/Internal_state.h @@ -0,0 +1,156 @@ +/* + Name: classe « internal_state » + Copyright: + Author: Daniel Comparat + Date: 15/10/06 11:01 +MODIFIER 12/02/2012. J'AI ENLEVER LES get ET set EN RENDANT TOUT PUBLIC! + + +Contient: +Level electronique: exc (excitation de la molecule, par exemple niveau électronique), Spin, Lambda, Omega +niveau vibrationel: v +niveau rotationel: J, N, (Omega déjà donné) +projection du moment total J (ou F) sur un axe supposé connu: M +parité: -1 ou +1 +nombre pour lever la dégénérescence +1/durée de vie (A Einstein du niveau) +shift en énergie > 0 si le niveau initial gagne de l'énergie (se rapproche des états excité vers la ionisation) +population: La population (non normalisée) + +Coefficient pour un fit en champ F via formule: Energy (en cm^-1) + signe(Linear)*(-Delta/2+sqrt((Delta/2)^2+(Linear F)^2)). Ici l'unité n'est pas spécifiée mais souvent nous utiliserons comme unité d'énergie le cm^-1. +Liste des raies = la liste des transitions vers d'autres états + + * Tout initialisée à 0. (sauf parité et dégénérescence +1) + + * write et read permettent d'écrire et de lire dans un flux (cout (pas cerr ou clog) ou fichier) + * write_list_raie écrit la liste des raies + +IL y a aussi la lecture des fichiers de PGOPHER + d'où le choix des unités DEBYE^2 pour force de raie (dipole^2) et CM^-1 pour énergie +* Levels +* Liste des raies = la liste des transitions vers d'autres états + + +La comparaison des niveaux se fait uniquement sur +Level electronique (Manifold), M, parité et nombre pour lever la dégénérescence + + */ + +/*** +ATTENTION TOUS LES NOMBRES QUANTIQUES SONT EN FAIT *2 +Ainsi J=1/2 est stocké en 1 d'ou le nom de two_J. +***/ + + +#ifndef Internal_state_SEEN +#define Internal_state_SEEN + +#include "Vecteur3D.h" +#include "constantes_SI.h" +#include + +#include +using namespace std; + + + +class Internal_state +{ +public: + int exc; // état excité ou non (0 est l'état fondamental) + int two_Spin, two_Lambda, two_Omega; + int v; + int two_J, two_N, two_M; + int Sym; // Parity + int deg_number; // nombre de dégénérescence + double Energy0_cm, Delta_FieldB, Linear_FieldB, Delta_FieldE, Linear_FieldE; // Energie en cm^-1. Coefficient pour un fit de l'énergie en champ B ou E via formule: E0 + signe(C)*(-Delta/2+sqrt((Delta/2)^2+(C F)^2)) + double one_over_lifetime; // 1/(durée de vie en seconde) + double Energy_cm, population; // Energie réelle due au shift en énergie et population initiale de l'état + + typedef pair transition; // Une transition est vers un (pointeur vers) un état final (INTERNAL STATE) avec une force de raie (un double) + + vector < transition > liste_raies; //La liste des raies possibles est: vecteur donnant la liste des états finaux et de la force de transition + +public: + Internal_state(); // constructeurs autres que par recopie + Internal_state(const Internal_state & Intern); // constructeur de recopie + ~Internal_state(); // destructeur + Internal_state & operator = (const Internal_state & Intern); // opérateur d'affectation + +// Affichage (on ne met pas la liste des raies!) + void write(ostream & flux); + + // read des données (sans la liste des raies) + void read(istream & flux); + + // Ecrit la liste des raies + void write_liste_raie(ostream & flux); + + +// True si l'état est = à w, false sinon +// On ne teste que l'état électronique, v, M, parité et numéro. + bool is_equal (const Internal_state & w) const; + + +//---------------------------------- +// Lecture des fichiers PGOPHER de niveaux +//---------------------------------- + +// Les fichiers contiennent +// Manifold, M, Sym(Parity +/-), #, J, N, Omega, Energy0, Delta, C + + +// Ecriture dans le flux du niveau avec le format souhaité + void write_Level_PgopherB(ostream & flux); + +// Si variation en B ou E + void read_Level_Pgopher_B(istream & flux); + void read_Level_Pgopher_E(istream & flux); + +// Calcul du shift en champ: via E0 + signe(C)*(-Delta/2+sqrt((Delta/2)^2+(C F)^2)) + double Energy_Shift_B_cm(const double B) const; + double Energy_Shift_E_cm(const double E) const; + +// Calcul du gradient du shift (en unité SI pas cm^-1) en champ +// Grad(F.F) * signe(C)*/[2*sqrt((Delta/2)^2+(C F)^2))] + Vecteur3D Grad_Energy_Shift_B(const double B, const Vecteur3D gradient_B2); + Vecteur3D Grad_Energy_Shift_E(const double E, const Vecteur3D gradient_E2); + +// Calcul du champ F correspondant au shift E_cm: via E0 + signe(C)*(-Delta/2+sqrt((Delta/2)^2+(C F)^2)) = E_cm + double Field_Shift_B_cm(const double Eshift); + double Field_Shift_E_cm(const double Eshift); + +//---------------------------------- +// Etudes des raies +//---------------------------------- + +// ajoute la transition -->v et la force de raie à la liste + void add_transition (Internal_state *v,const double strenght); + +// Somme les taux de desexcitation + double Einstein_desex_rate(); + + +}; + + + +// Lecture des fichier Pgopher qui contiennent +// UpperManifold M' Sym' #' LowerManifold M" Sym" #" Position Intensity Eupper Elower Spol +void read_Line_Pgopher(istream & flux, Internal_state & Upper_state,Internal_state & Lower_state, + double & Spol, double & position, double & Intensity); + +// Ecriture dans le flux la transition (ligne) avec le format souhaité +void write_Line_Pgopher(ostream & flux, Internal_state & Upper_state, Internal_state & Lower_state, const double Spol, const double position, const double Intensity); + + +//---------------------------------- +// Surdéfinition des entrées sorties (sans la liste des raies) +//---------------------------------- + +ostream & operator << (ostream & flux, Internal_state Intern); + +istream& operator >> (istream &flux, Internal_state & Intern); + + +#endif diff --git a/Main Code 64bits/Kinetic_Monte_Carlo.cpp b/Main Code 64bits/Kinetic_Monte_Carlo.cpp new file mode 100644 index 0000000..ff318a1 --- /dev/null +++ b/Main Code 64bits/Kinetic_Monte_Carlo.cpp @@ -0,0 +1,257 @@ +/* + Name: Algorithme de calcul Monte Carlo cinétique + Author: Daniel Comparat + Date: 17/09/06 08:14 + +Résoult les équations de taux + +Il y a plusieurs algorithmes +cf +Kinetic Monte Carlo modeling of dipole blockade in +Rydberg excitation experiment +Amodsen Chotia1, Matthieu Viteau, Thibault Vogt, Daniel Comparat and Pierre Pillet +New Journal of Physics 10 (2008) 045031 +ou le ReadMe + ++ Fast Rough Method . That evolves several molecules during the same time step. + + +*/ + + + +#include "Kinetic_Monte_Carlo.h" + + +// Permet de tirer avec une proba uniforme dans une liste rate[] +// Il faut utiliser gsl_ran_discrete_preproc si on doit tirer plusieur fois ? + +int tirage_random_discrete(const gsl_rng *r, const vector &array, const int nb_rate, double &sum_rate_tot) +{ + + double *Sum_array = new double[(nb_rate+1)]; // cannot used vector because binarySearch + Sum_array[0]=0.; + for (int i = 0; i < nb_rate; i++) + Sum_array[i+1] = Sum_array[i] + array[i]; // On crée la liste croissante de taux intégré en temps + + double u=1.-gsl_rng_uniform(r); // pour tirer au hasard dans (0,1] car gsl_rng_uniform(r) dans [0,1) + int sol = binarySearch(Sum_array, 0, nb_rate, Sum_array[nb_rate]*u) ; + // la réaction qui a été choisi est telle que R_{i-1} < u R <= R_i, i.e. rate_tot[nat] < u*R <= rate_tot[nat+1] + + sum_rate_tot = Sum_array[nb_rate]; + + delete [] Sum_array; + return(sol); +} + + + + + + +/************************************************************************ +************************************************************************ + FONCTION PRINCIPALE POUR LE Monte Carlo + + + Remarque 1: Pour se retrouver dans le cas des théorèmes d'évolution indiquant que le KMC est correct + il faut que TOUTES les réactions soient prises en compte par le KMC. + + Remarque 2: Les taux varient car les positions varient mais on néglige cela ici. + +Les fonctions (selon l'algorithme choisi) retournent le numéro de la réaction et changent le temps. +*/ + + + +/***** +THE KMC ALGORITHM IS THE FOLLOWING +• Initializing the system to its given state called k at the actual time t. +• Creating a new rate list Gamma_lk for the system, l = 1, . . . , N. +• Choosing a unit-interval uniform random number generator r : 0 < r < 1 and calculating +the first reaction rate time t0 by solving Int_t^t_0 Sum_l Gamma_kl(t) = - ln r +(for constant rate it is Delta_t * Sum_l Gamma_kl = - ln r +• Choosing the new state l from the uniform probability of the rate Gamma_kl(t_0) + +*/ + + + +// Voici l'algorithme pour des taux INDEPENDANT du temps (c'est généralement notre cas). +// Un algorithme plus poussé avec évolution N_corps existe dans le programme Rydberg +// retourne le numéro de la réaction +int KMC_step(const gsl_rng * r, const vector &rate, double &dt) +{ + + double sum_rate; // somme des taux + int nb_rate = rate.size(); + int n_reac = tirage_random_discrete(r, rate, nb_rate, sum_rate); // Choix de la réaction (et calcul de la somme) + + // Choix du temps Delta_t = - ln random/ Sum_l Gamma_kl; + double random = 1.-gsl_rng_uniform(r); // uniform random number u \in (0,1] + dt = - log(random)/sum_rate; // Incrémentation aléatoire du temps pour rendre compte du caractère Poissonien du processus + + return n_reac; +} + + + + + +/************************************************************************ +************************************************************************ + FONCTION PRINCIPALE POUR LE Kinetic Monte Carlo avec First Reaction Method : + +ALGORITHME AVEC TAUX DEPENDANT DU TEMPS +An Introduction To Monte Carlo Simulations Of Surface Reactions +A. P. J. Jansen: cond-mat/0303028 + + +Evolution temporelle First Reaction Method (FRM) +appellée aussi Discrete Event Simulation + + +According to this method, when the system is in a given configuration a, +the set of all possible reactions is determined, +and a time of occurrence tab is generated for EACH reaction +Then, the reaction with the SMALLEST tab is selected, +the configuration is changed accordingly, and the time t is incremented in tab +Finally, the set of possible reactions is generated according +to the new configuration b, and the procedure is repeated + +CE QUI CHANGE comparé au KMC précédent est que l'on calcule +integrall_{t_0}^{t_0+\Delta t_i} rate_i[t] dt = -\log u_i. +Et on choisi le plus petit \Delta t_i, i.e. la première réaction. + + +************************************************************************/ + + +// Cherche le temps minimal pour l'évolution FRM +// Retourne le numéro de la réaction ayant ce temps minimal (la FRM !) + +int FRM_step(const gsl_rng * r, const vector &rate, double &dt) +{ + int nb_rate = rate.size(); + //Calcul, via l'intégrale temporelle int_{t_0}^(t_0+t_KMC_estimé) des taux de transition, du temps t_KMC + double *random_number = new double[nb_rate]; + for (int i=0; i 0) dtime = (-log(random_number[i]))/rate[i]; + else dtime= VERY_LARGE_NUMBER; + // On calcul aléatoirement un temps pour chaque transition + + if (dtime < dt) + { + i_time_min = i; // On cherche le temps minimum + dt = dtime; + } + } + delete[] random_number; + + return i_time_min; +} + + + + +/* +Evolution temporelle Random Selection Method (RSM) +Choix aléatoire de l'atome et de sa réaction et du temps. +Parfois il n'y a pas de réaction +*/ + +int RSM_step(const gsl_rng * r, const vector &rate, double &dt) +{ + int nb_rate = rate.size(); + double rate_max = 0. ; // Initialisation pour le taux de transition maximum + for (int i = 0; i < nb_rate; i++) // Recherche des taux de transition maximum + { + if (rate[i] > rate_max) + rate_max = rate[i]; // Taux de transition maximum + } + + dt = 1/(nb_rate*rate_max) ; // Calcul d'un intervalle de temps "aléatoire" où une seule réaction au maximum est possible + + int n_reac = (int) (gsl_rng_uniform(r)*nb_rate); // Tirage au hasard d'un état entre 0 et nb_rate-1 + + double Delta_t = gsl_rng_uniform(r)/rate[n_reac]; // Tirage au hasard du temps de transition pour cet état + if (Delta_t < dt) + return n_reac; // L'état change si son "temps" de transition est plus court que celui prévu + else + return -1; // Aucun changement d'état + + +} + + + +// Calculate a small time step dt to have Gamma dt ~0.1 +// So in the futur will realize only the reaction having a rate Gamma that verifies +// Gamma dt *(random) < 1 we do it +// Very efficient for a large number of molecules because typically N_Mol/10 will evolve. +int Fast_Rough_Method_step(const gsl_rng * r, const vector &rate, double &dt) +{ + int nb_rate = rate.size(); + double rate_max = 0. ; // Initialisation pour le taux de transition maximum + for (int i = 0; i < nb_rate; i++) // Recherche des taux de transition maximum + { + if (rate[i] > rate_max) + rate_max = rate[i]; // Taux de transition maximum + } + + dt = 0.1/rate_max; // This will be the dt_KMC the 0.1 is arbitrary. Here a tens of the rate will typically be performed + + return 0; // arbitrary (but I put n_reac= 0 in order to avoid problems in rate[n_reac] after). Because several reaction will then be performed in do_reaction +} + + + + +// Trouve la réaction (son numéro dans la liste des taux rate[] +// Trouve le temps où elle doit être effectuée +int find_reaction(MC_algorithmes Algorithme_MC , const gsl_rng * r, const vector &rate, double & dt) +{ + int nb_rate = rate.size(); + int n_reac=0; // numéro de la réaction dans la liste reaction_list[] + // Fait une évolution N-corps et s'il y a lieu effectue la réaction KMC. + // Met à jour les intégration temporelle Trate et sum_rate_t et les potentiels et champs + switch (Algorithme_MC) + { + case Aucun_MC : // Il n'y a aucune réaction, on ne sort jamais des boucles + n_reac = -1; + dt = VERY_LARGE_NUMBER; // No reaction so infinit time to realize it + break; + + + case Kinetic_Monte_Carlo : + n_reac = KMC_step(r, rate, dt); + break; + + case Random_Selection_Method : + n_reac = RSM_step(r, rate, dt); + break; + + case First_Reaction_Method : + n_reac = FRM_step(r, rate, dt); + break; + + case Fast_Rough_Method : + n_reac = Fast_Rough_Method_step(r, rate, dt); + + break; + + } + return n_reac; +} + + + diff --git a/Main Code 64bits/Kinetic_Monte_Carlo.h b/Main Code 64bits/Kinetic_Monte_Carlo.h new file mode 100644 index 0000000..8406506 --- /dev/null +++ b/Main Code 64bits/Kinetic_Monte_Carlo.h @@ -0,0 +1,133 @@ +/* + Name: Algorithme de calcul Monte Carlo cinétique + Author: Daniel Comparat + Date: 17/09/06 08:14 + +Résout les équations de taux + +Il y a plusieurs algorithmes +cf +Kinetic Monte Carlo modeling of dipole blockade in Rydberg excitation experiment +Amodsen Chotia, Matthieu Viteau, Thibault Vogt, Daniel Comparat and Pierre Pillet +New Journal of Physics 10 (2008) 045031 + ++ Fast Rough Method = several Random choice to evolve typically N_Mol/10 times faster. + +*/ + + + + + +#ifndef KMC_SEEN +#define KMC_SEEN + +using namespace std; + +#include +#include // to include cout, cin +#include "algorithmes.h" // to include binarySearch +#include // to include sqrt(), etc. +#include // for random generator +#include // for gaussian random generator +#include "constantes_SI.h" + + +enum MC_algorithmes { Aucun_MC = -1, + Kinetic_Monte_Carlo = 0, + Random_Selection_Method = 1, + First_Reaction_Method = 2, + Fast_Rough_Method = 3 + }; + + + +// Permet de tirer avec une proba uniforme dans une liste rate[] +// Il faut utiliser gsl_ran_discrete_preproc si on doit tirer plusieur fois ? + +int tirage_random_discrete(const gsl_rng *r, const vector &array, const int nb_rate, double &sum_rate_tot); + + + + +/************************************************************************ +************************************************************************ + FONCTION PRINCIPALE POUR LE Monte Carlo + + +Les fonctions (selon l'algorithme choisi) retournent le numéro de la réaction et changent le temps. +*/ + + + +/***** +THE KMC ALGORITHM IS THE FOLLOWING +• Initializing the system to its given state called k at the actual time t. +• Creating a new rate list Gamma_lk for the system, l = 1, . . . , N. +• Choosing a unit-interval uniform random number generator r : 0 < r < 1 and calculating +the first reaction rate time t0 by solving Int_t^t_0 Sum_l Gamma_kl(t) = - ln r +(for constant rate it is Delta_t * Sum_l Gamma_kl = - ln r +• Choosing the new state l from the unifor probability of the rate Gamm_kl(t_0) + +*/ + + +// Voici l'algorithme pour des taux INDEPENDANT du temps (c'est généralement notre cas). +// Un algorithme plus poussé avec évolution N_corps existe dans le programme Rydberg +// retourne le numéro de la réaction +int KMC_step(const gsl_rng * r, const vector &rate, double &dt); + + +/************************************************************************ +************************************************************************ + FONCTION PRINCIPALE POUR LE Kinetic Monte Carlo avec First Reaction Method : + +ALGORITHME AVEC TAUX DEPENDANT DU TEMPS +An Introduction To Monte Carlo Simulations Of Surface Reactions +A. P. J. Jansen: cond-mat/0303028 + + +Evolution temporelle First Reaction Method (FRM) +appellée aussi Discrete Event Simulation + + +According to this method, when the system is in a given configuration a, +the set of all possible reactions is determined, +and a time of occurrence tab is generated for EACH reaction +Then, the reaction with the SMALLEST tab is selected, +the configuration is changed accordingly, and the time t is incremented in tab +Finally, the set of possible reactions is generated according +to the new configuration b, and the procedure is repeated + +CE QUI CHANGE comparé au KMC précédent est que l'on calcule +integralle_{t_0}^{t_0+\Delta t_i} rate_i[t] dt = -\log u_i. +Et on choisi le plus petit \Delta t_i, i.e. la première réaction. + + +************************************************************************/ + + +// Cherche le temps minimal pour l'évolution FRM +// Retourne le numéro de la réaction ayant ce temps minimal (la FRM !) + +int FRM_step(const gsl_rng * r, const vector &rate, double &dt); + +/* +Evolution temporelle Random Selection Method (RSM) +Choix aléatoire de l'atome et de sa réaction et du temps. +Parfois il n'y a pas de réaction +*/ + +int RSM_step(const gsl_rng * r, const vector &rate, double &dt); + + +// Calculate the max rate and then give the time for an evolution 1/rate_Max +int Fast_Rough_Method_step(const gsl_rng * r, const vector &rate, double &dt); + +// Trouve la réaction (son numéro dans la liste des taux rate[] +// Trouve le temps où elle doit être effectuée +int find_reaction(MC_algorithmes Algorithme_MC , const gsl_rng * r, const vector &rate, double & dt); + + +#endif + diff --git a/Main Code 64bits/Laser_interaction_in_fields.cbp b/Main Code 64bits/Laser_interaction_in_fields.cbp new file mode 100644 index 0000000..b14a369 --- /dev/null +++ b/Main Code 64bits/Laser_interaction_in_fields.cbp @@ -0,0 +1,99 @@ + + + + + + diff --git a/Main Code 64bits/Laser_interaction_in_fields.layout b/Main Code 64bits/Laser_interaction_in_fields.layout new file mode 100644 index 0000000..6afe8aa --- /dev/null +++ b/Main Code 64bits/Laser_interaction_in_fields.layout @@ -0,0 +1,65 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/Main Code 64bits/LekienMarsdenMatrix.h b/Main Code 64bits/LekienMarsdenMatrix.h new file mode 100644 index 0000000..282fe84 --- /dev/null +++ b/Main Code 64bits/LekienMarsdenMatrix.h @@ -0,0 +1,126 @@ +#ifndef LEKIEN_MARSDEN_MATRIX +#define LEKIEN_MARSDEN_MATRIX + +// tricubic interpolation matrix +// cf http://en.wikipedia.org/wiki/Tricubic_interpolation +// and Article 2005 tricubic interpolation Lekien Marsden IntJNumMethEngin.pdf + + +namespace Global +{ + +static int LekienMarsdenMatrix[64][64] = +{ + { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 2,-2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 9,-9,-9, 9, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {-6, 6, 6,-6, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {-6, 6, 6,-6, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 4,-4,-4, 4, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0}, + {-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 9,-9, 0, 0,-9, 9, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {-6, 6, 0, 0, 6,-6, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9, 0, 0,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0}, + { 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0}, + {-27,27,27,-27,27,-27,-27,27,-18,-9,18, 9,18, 9,-18,-9,-18,18,-9, 9,18,-18, 9,-9,-18,18,18,-18,-9, 9, 9,-9,-12,-6,-6,-3,12, 6, 6, 3,-12,-6,12, 6,-6,-3, 6, 3,-12,12,-6, 6,-6, 6,-3, 3,-8,-4,-4,-2,-4,-2,-2,-1}, + {18,-18,-18,18,-18,18,18,-18, 9, 9,-9,-9,-9,-9, 9, 9,12,-12, 6,-6,-12,12,-6, 6,12,-12,-12,12, 6,-6,-6, 6, 6, 6, 3, 3,-6,-6,-3,-3, 6, 6,-6,-6, 3, 3,-3,-3, 8,-8, 4,-4, 4,-4, 2,-2, 4, 4, 2, 2, 2, 2, 1, 1}, + {-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0}, + {18,-18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6, 9,-9, 9,-9,-9, 9,-9, 9,12,-12,-12,12, 6,-6,-6, 6, 6, 3, 6, 3,-6,-3,-6,-3, 8, 4,-8,-4, 4, 2,-4,-2, 6,-6, 6,-6, 3,-3, 3,-3, 4, 2, 4, 2, 2, 1, 2, 1}, + {-12,12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-6, 6,-6, 6, 6,-6, 6,-6,-8, 8, 8,-8,-4, 4, 4,-4,-3,-3,-3,-3, 3, 3, 3, 3,-4,-4, 4, 4,-2,-2, 2, 2,-4, 4,-4, 4,-2, 2,-2, 2,-2,-2,-2,-2,-1,-1,-1,-1}, + { 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {-6, 6, 0, 0, 6,-6, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 4,-4, 0, 0,-4, 4, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4, 0, 0,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0}, + {-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0}, + {18,-18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6,12,-12, 6,-6,-12,12,-6, 6, 9,-9,-9, 9, 9,-9,-9, 9, 8, 4, 4, 2,-8,-4,-4,-2, 6, 3,-6,-3, 6, 3,-6,-3, 6,-6, 3,-3, 6,-6, 3,-3, 4, 2, 2, 1, 4, 2, 2, 1}, + {-12,12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-8, 8,-4, 4, 8,-8, 4,-4,-6, 6, 6,-6,-6, 6, 6,-6,-4,-4,-2,-2, 4, 4, 2, 2,-3,-3, 3, 3,-3,-3, 3, 3,-4, 4,-2, 2,-4, 4,-2, 2,-2,-2,-1,-1,-2,-2,-1,-1}, + { 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + { 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0}, + {-12,12,12,-12,12,-12,-12,12,-8,-4, 8, 4, 8, 4,-8,-4,-6, 6,-6, 6, 6,-6, 6,-6,-6, 6, 6,-6,-6, 6, 6,-6,-4,-2,-4,-2, 4, 2, 4, 2,-4,-2, 4, 2,-4,-2, 4, 2,-3, 3,-3, 3,-3, 3,-3, 3,-2,-1,-2,-1,-2,-1,-2,-1}, + { 8,-8,-8, 8,-8, 8, 8,-8, 4, 4,-4,-4,-4,-4, 4, 4, 4,-4, 4,-4,-4, 4,-4, 4, 4,-4,-4, 4, 4,-4,-4, 4, 2, 2, 2, 2,-2,-2,-2,-2, 2, 2,-2,-2, 2, 2,-2,-2, 2,-2, 2,-2, 2,-2, 2,-2, 1, 1, 1, 1, 1, 1, 1, 1} +}; + +/** +http://en.wikipedia.org/wiki/Bicubic_interpolation + +When the function values f and the derivatives f_x, f_y and f_{xy} are known at the four corners (0,0), (1,0), (0,1), and (1,1) of the unit square. +The interpolated surface can then be written + +f(x,y) = \sum_{i=0}^3 \sum_{j=0}^3 a_{ij} x^i y^j. + +Grouping the unknown parameters a_{ij} in a vector a, values of f, df/dx, df/dy, d2f/dxdy at 4 corner point in a vector F +the interpolation can be reformulated into a matrix for the linear equation: BicubicMatrix a = F. + The order of point is the one of the + 2005 tricubic interpolation Lekien Marsden IntJNumMethEngin.pdf + article + not the same than in Wikipedia +**/ + +// BECAREFUL THE ORDER is not the same than in Wikipedia +// in wikipedia it is (0,0) (1,0) (0,1) (1,1) +// Here it seems to be (0,0) (1,0) (1,1) (0,1) + + static int BicubicMatrix[16][16]= +{ + {1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0}, + {-3,0,0,3,0,0,0,0,-2,0,0,-1,0,0,0,0}, + {2,0,0,-2,0,0,0,0,1,0,0,1,0,0,0,0}, + {0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0}, + {0,0,0,0,-3,0,0,3,0,0,0,0,-2,0,0,-1}, + {0,0,0,0,2,0,0,-2,0,0,0,0,1,0,0,1}, + {-3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0}, + {9,-9,9,-9,6,3,-3,-6,6,-6,-3,3,4,2,1,2}, + {-6,6,-6,6,-4,-2,2,4,-3,3,3,-3,-2,-1,-1,-2}, + {2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0}, + {-6,6,-6,6,-3,-3,3,3,-4,4,2,-2,-2,-2,-1,-1}, + {4,-4,4,-4,2,2,-2,-2,2,-2,-2,2,1,1,1,1} + +}; + + +}; + + + +#endif diff --git a/Main Code 64bits/Stat_Molecule.cpp b/Main Code 64bits/Stat_Molecule.cpp new file mode 100644 index 0000000..2920f93 --- /dev/null +++ b/Main Code 64bits/Stat_Molecule.cpp @@ -0,0 +1,207 @@ +/* + Name: + Copyright: + Author: + Date: 23/10/06 10:01 + Description: Paramètres (température, positions, dispersion, moyenne des molécules) (utilisé dans Affichage_Mol.h) + + +*/ + +#include "Stat_Molecule.h" +#include // Pour log + + +// sort le tableau nexc du nombre de molécule par niveau nexc[n° Level] +void stat_molecule_nb_par_etat(const vector &Mol, Internal_state *Levels, int *nexc, const int Nb_Mol, const int Nb_state, FitParams ¶ms) +{ + for (int i=0; i!= Nb_state; i++) // Nombre de particules excitées dans chaque état exc + nexc[i]=0; + + for (int i=0; i!= Nb_state; i++) + { + for (int j=0; j!= Nb_Mol; j++) + { + if (Mol[j].is_equal(Levels[i])) nexc[i]++; // Calcul le nombre de particules excitées dans chaque état j + } + } + + return; +} + +// Paramètres statistiques d'une assemblée de Molecule; +// Le dernier niveau stat_Mol[nb_Levels] donne la statistique globale (tout niveaux confondus) +void stat_molecule(const vector &Mol, vector &stat_Mol, const vector &Level, const Field &fieldB, const Field &fieldE, const int Nb_Mol, const int Nb_state, FitParams ¶ms) +{ + stat_Mol.clear(); + Stat stat_Mol_current; + for (int i=0; i!= Nb_state; i++) + { + stat_molecule_un_niveau(Mol,stat_Mol_current, Level, fieldB, fieldE, i, Nb_Mol, params); // Statistique pour le niveau i + stat_Mol.push_back(stat_Mol_current); + } + stat_molecule_un_niveau(Mol, stat_Mol_current, Level, fieldB, fieldE, all , Nb_Mol, params); // Statistiques pour toutes les molécules + stat_Mol.push_back(stat_Mol_current); +} + +// Paramètres statistiques d'une assemblée de Molecule; Retourne le nb de molécules n dans l'état étudié +int stat_molecule_un_niveau(const vector &Mol, Stat &stat, const vector &Level, const Field &fieldB, const Field &fieldE, const int num_niveau_etudie, const int Nb_Mol, FitParams ¶ms) +{ + + int num_manifold_not_studied = (int) params.LocateParam("num_manifold_not_studied")->val; + + + /***************** Liste des molécules de l'état choisi leurs positions et vitesse *************************/ + + vector liste_Adresses_Mol_dans_niveau; //Liste des molécules dans ce niveau + + for (int i=0; i!= Nb_Mol; i++) + if ( (num_niveau_etudie == all || Mol[i].is_equal(Level[num_niveau_etudie])) && Mol[i].exc != num_manifold_not_studied) // NE PREND QUE LES MOL DANS l'état spécifique + liste_Adresses_Mol_dans_niveau.push_back(Mol[i]); + + + int n = liste_Adresses_Mol_dans_niveau.size(); + stat_molecule_form_list(Mol, liste_Adresses_Mol_dans_niveau, stat, Level, fieldB, fieldE, Nb_Mol, params); + +// erase the vector: + liste_Adresses_Mol_dans_niveau.clear(); + + return n; +} + + +// Paramètres statistiques d'une assemblée de Molecule; Retourne le nb de molécules n dans l'état étudié +int stat_molecule_form_list(const vector &Mol, vector &liste_Adresses_Mol_dans_niveau, Stat &stat, const vector &Level, const Field &fieldB, const Field &fieldE, const int Nb_Mol, FitParams ¶ms) +{ + int n = liste_Adresses_Mol_dans_niveau.size(); + stat.population = n; + if (n == 0) return n; // Ne calcul rien si aucune molécules dans l'état spécifique + + double **pos = new double*[3]; // Tableau des positions + double **vel = new double*[3]; // Tableau des vitesses + double **E_cinetique_Temp = new double*[3]; // Tableau des energies cinétiques (sans le mouvement du centre de masse) + for (int j=0; j<3; j++) // 3 axes: x, y ou z + { + pos[j] = new double[n]; + vel[j] = new double[n]; + E_cinetique_Temp[j] = new double[n]; + } + + stat.E_cin = 0.; // Energie totale + stat.E_pot = 0.; + + int nb =0; + double mass = 0.; // Mass on the particles. But BE CAREFUL if several mass and global motion, the temperature is not well defined!) + + for ( vector ::iterator i=liste_Adresses_Mol_dans_niveau.begin(); i != liste_Adresses_Mol_dans_niveau.end(); ++i) // boucle sur les molécules de l'état considéré + { + Molecule Mol_i = *i; + mass = Mol_i.get_mass(); + + for (int j=0; j<=2; j++) // 3 axes: x, y ou z + { + pos[j][nb] = Mol_i.get_pos().get(j); + vel[j][nb] = Mol_i.get_vel().get(j); + E_cinetique_Temp[j][nb] = 0.5* mass * vel[j][nb]* vel[j][nb] ; // 1/2 m v_j^2 + } + + stat.E_pot += get_pot(Mol_i, fieldB, fieldE); + stat.E_pot += 0.5*Mol_i.get_charge()*get_coulomb_potential(Mol, Mol_i.get_pos(), Nb_Mol); // add colombian interaction will be 1/2 sum_i qi sum_j=1^n not i qj/(r_ij)/4 pi epsilon_0 + // HERE we have to sum over all level because the coulomb field exist for all states + + stat.E_cin += get_kin(Mol_i); + nb++; + } + + + + /***************** Statistiques sur leurs positions et vitesse *************************/ + + + for (int j=0; j<=2; j++) // 3 axes: x, y ou z + { + stat.mean_pos.set(j,gsl_stats_mean (pos[j], 1 , n)); + stat.mean_v.set(j,gsl_stats_mean (vel[j], 1 , n)); + stat.sigma_pos.set(j,sqrt(gsl_stats_variance_m (pos[j], 1 , n, stat.mean_pos.get(j)))); // Sigma = sqrt(variance) + stat.sigma_v.set(j,sqrt(gsl_stats_variance_m (vel[j], 1 , n, stat.mean_v.get(j)))); + } + + + // We remove the center of mass velocity to calculate 1/2 kB T is average of 1/2 m (v-)^2 + nb =0; + for (vector ::iterator i=liste_Adresses_Mol_dans_niveau.begin(); i != liste_Adresses_Mol_dans_niveau.end(); ++i) // boucle sur les molécules de l'état considéré + { + for (int j=0; j<=2; j++) // 3 axes: x, y ou z + { + double mean_v = stat.mean_v.get(j); + E_cinetique_Temp[j][nb] += 0.5 * mass * ( -2.*mean_v*vel[j][nb] + mean_v*mean_v); // 1/2 m (v-)^2 = 1/2 m (v^2 - 2 v + ^2) + } + nb++; + } + + +// for (int j=0; j<=2; j++) // 3 axes: x, y ou z +// { +// stat.Temp_cin.set(j,2.*gsl_stats_mean (E_cinetique_Temp[j], 1 , n)/k_Boltzmann); // 1/2 kB T = 1/2 m >^2 +// qsort(E_cinetique_Temp[j], n, sizeof(double), &compare_doubles); // Ordonne E_cinetique[j] +// double median_j = gsl_stats_median_from_sorted_data (E_cinetique_Temp[j], 1, n); +// stat.Temp_1D_50.set(j,median_j /(0.227468*k_Boltzmann)); // 1D Boltzmann proba density distribution propto 1/sqrt(pi kB T E) e^{- E/ KB T} ; E =1/2 m v_i^2 --> median = 0.227468 k T +// } + + + for (int j=0; j<=2; j++) // 3 axes: x, y ou z + { + stat.Temp_cin.set(j,2.*gsl_stats_mean (E_cinetique_Temp[j], 1 , n)/k_Boltzmann); // 1/2 kB T = 1/2 m >^2 + qsort(vel[j], n, sizeof(double), &compare_doubles); // Ordonne vel[j] + double v25 = gsl_stats_quantile_from_sorted_data (vel[j], 1, n, 0.25); // v25 = velocity of the molecule that have the 25th velocity + double v75 = gsl_stats_quantile_from_sorted_data (vel[j], 1, n, 0.75); // v75 = velocity of the molecule that have the 25th velocity + double dv = (v75-v25)/(2.*0.67449); // 0.67449 is the quantil at 75% of a Normal (Gaussian distribution) e(-x^2/2). THis is =\Phi^{-1}(0.75) where \Phi(x)= P[X\leq x], lorsque X suit la loi normale centrée réduite \scriptstyle \mathcal N(0,1). + stat.Temp_1D_50.set(j,dv*dv*mass/k_Boltzmann); + } + + + stat.Temp_3D_50 = stat.Temp_1D_50.mag()/sqrt(3.); // T_3D^2 = (Tx^2+Ty^2+Tz^2)/3 + + + + + /***************** Delete table *************************/ + + for (int j=0; j<3; j++) + { + delete [] pos[j]; + delete [] vel[j]; + delete [] E_cinetique_Temp[j]; + } + delete [] pos; + delete [] vel; + delete [] E_cinetique_Temp; + + return n; +} + + +// Statistique sur les trajectoires +// distance Min, moyenne (somme) et max +void stat_traj_molecule(const vector &Mol, double & dist_min, double & dist_sum, double & dist_max, int & nb_call, const int Nb_Mol) +{ + for (int i=0; i!= Nb_Mol; i++) + { + double dist_mol = (Mol[i].get_pos()).mag(); // Distance de la molécule au centre (0,0,0) + + if ( dist_mol < dist_min) // position + dist_min = dist_mol; + + if ( dist_mol > dist_max) // position + dist_max = dist_mol; + + dist_sum += dist_mol; + } + + nb_call++; + + cout << "min (mm) " << dist_min/mm << "avg " << dist_sum/nb_call/Nb_Mol/mm << " max " << dist_max/mm << endl; + + return; + +} diff --git a/Main Code 64bits/Stat_Molecule.h b/Main Code 64bits/Stat_Molecule.h new file mode 100644 index 0000000..aaa1d14 --- /dev/null +++ b/Main Code 64bits/Stat_Molecule.h @@ -0,0 +1,75 @@ +/* + Name: + Copyright: + Author: + Date: 23/10/06 10:01 + Description: Paramètres (température, positions, dispersion, moyenne des molécules) (utilisé dans Affichage_Mol.h) + + +*/ + +#ifndef Stat_Mol_SEEN +#define Stat_Mol_SEEN + +#include +using namespace std; + + +#include "Molecule.h" +#include "one_body.h" +#include // pour les stat (mean, variance, ...) +#include "algorithmes.h" // Pour qsort +#include "params.h" + +/************************************************************************/ +/****************** structure des données Stat *************************/ +/************************************************************************/ + +// Paramètres statistiques d'une assemblée de Molecule; +// Moyenne, ecart type (= standard deviation) des vitesses et position +// Energie et température +// Il y a plusieurs température: +// T_cin sigma_(v-)^2 /k_Boltzmann +// Mais afin d'éviter les molécules qui ont "explosées" (ejectées du piège et avec grande vitesses), on prend plutôt m sigma^2 /k_Boltzmann où sigma = standard deviation of the velocity sqrt(v^2) +// Enfin Temp_ordonnee est donné par ordonancement de la norme des vitesse des molécules pour extraire une température effective en utilisant 1/2 m v_i^2 + + +class Stat +{ +public: + int population; // population du niveau étudié + + Vecteur3D mean_v; + Vecteur3D mean_pos; +// ecart type (racine carrée de la variance) + Vecteur3D sigma_v; + Vecteur3D sigma_pos; + + double E_pot; // sum_i [q V_elec(r_i) - m g z_i + hbar [E_cm-Ecm0] + 0.5 sum_j not i qi qj /(4 pi epsilon_0 r_ij) ] + double E_cin; // 1/2 m (v_x^2 +v_y^2 + v_z^2) + + Vecteur3D Temp_cin; // from 1/2 m >^2 + Vecteur3D Temp_1D_50; // for 50% of the best particles + double Temp_3D_50; // / T_3D^2 = (Tx_50^2+Ty_50^2+Tz_50^2)/3 + +//constructeur + Stat(): population(0), mean_v(Vecteur3D(0.,0.,0.)), mean_pos(Vecteur3D(0.,0.,0.)), sigma_v(Vecteur3D(0.,0.,0.)), sigma_pos(Vecteur3D(0.,0.,0.)), E_pot(0.), E_cin(0.), Temp_cin(Vecteur3D(0.,0.,0.)), Temp_1D_50(Vecteur3D(0.,0.,0.)), Temp_3D_50(0.) {}; +}; + + + +// Paramètres statistiques d'une assemblée de Molecule; +// Le dernier niveau donne la statistique globale (tout niveaux confondus) +void stat_molecule(const vector &Mol, vector &stat_Mol, const vector &Level, const Field &fieldB, const Field &fieldE, const int Nb_Mol, const int Nb_state, FitParams ¶ms); + +// Paramètres statistiques d'une assemblée de Molecule; Retourne le nb de molécules n dans l'état étudié +int stat_molecule_un_niveau(const vector &Mol, Stat &stat, const vector &Level, const Field &fieldB, const Field &fieldE, const int num_niveau_etudie, const int Nb_Mol, FitParams ¶ms); +// Statistique sur les trajectoires +// distance Min, moyenne (somme) et max + +int stat_molecule_form_list(const vector &Mol, vector &liste_Adresses_Mol_dans_niveau, Stat &stat, const vector &Level, const Field &fieldB, const Field &fieldE, const int Nb_Mol, FitParams ¶ms); + +void stat_traj_molecule(const vector &Mol, double & dist_min, double & dist_sum, double & dist_max, int & nb_call, const int Nb_Mol=1); + + +#endif diff --git a/Main Code 64bits/Transition_rate_calcul.cpp b/Main Code 64bits/Transition_rate_calcul.cpp new file mode 100644 index 0000000..48f6246 --- /dev/null +++ b/Main Code 64bits/Transition_rate_calcul.cpp @@ -0,0 +1,1058 @@ +/* + Name: Algorithme de calcul des taux + Author: Daniel Comparat + Date: 16/12/08 + + +REMARQUES: +On pourrait traiter la (pré ou photo)-dissociation comme un parametre phénoménologue ainsi que les transition a deux photons aussi +la desexcitation dans le continuuum peut être prise en compte avec Sum_FC != 1 la partie non 1 est le continuum + + +ATTENTION +Unités des fichier (cm^-1) +*/ + + + +#include "Transition_rate_calcul.h" +#include "diagonalization.h" + +#include // + + +/************************************************************************/ +/************************** Interaction laser - 2 niveaux *************/ +/************************************************************************/ + + + +// Taux d'emission spontanée d'une transition (sans prendre en compte l'ordre des états: +// Voir aussi Internal_state::Einstein_desex_rate() qui lui est zéro si l'ordre est initial en bas! +double Gamma_spon(const double dip_Debye, const double energie_cm) +{ + return dip_Debye*dip_Debye*Spol_Debye_A_s*energie_cm*energie_cm*energie_cm; + // Spol_Debye_A_s = (8e6*pi*pi*C*C*C*Debye*Debye)/(3.*EPSILON0*C*C*C*HBAR); // 3.13618932*10^-7 = Conversion HonlLondon (en Debye) en A Einstein (s^-1) si energie en cm^-1 +} + + +// Forme gaussienne Gamma = FWHM +inline double Gauss(const double I_tot, const double delta, const double Gamma) +{ + double sigma = Gamma/(2.* sqrt(2.*log(2))); // Gamma = FWHM = 2 \sqrt{2 \ln(2)} \sigma = 2,3548 \sigma + return (I_tot/(sigma * sqrt(2.*pi))) * exp(-delta*delta/(2.*sigma*sigma)); +} + +// Forme laser plate +// retourne l'intensité (spectrale) au décalage delta souhaité +// Gamma = FWHM +inline double intensity_flat(const double I_tot, const double delta, const double Gamma) +{ + if (abs(delta) < Gamma/2.) + return I_tot/Gamma; // Gamma = FWHM + else + return 0.; +} + + +// Forme laser lorentzienne Gamma = FWHM +// I(omega) = I*Gamma_L/(2.*pi)/(Gamma_L^2/4 + delta^2) +inline double Lorentz(const double I_tot, const double delta, const double Gamma) +{ + return I_tot*(Gamma/(2.*pi))/((Gamma/2.)*(Gamma/2.) + delta*delta); +} + + + +/** + +There is several possible approximation for the Voigt profile (Lorentzian covlution with Gaussian) that we could use when dealing with gaussian laser shape. +CF RAPID COMPUTATION OF THE VOIGT PROFILE S. R. DRAYNI or J.L. Kielkopf, J. Opt. Soc. Am. 63 , 987 (1973) or "Empirical fits to the Voigt line width: A brief review" +"Simple empirical analytical approximation to the Voigt profile" or "the Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions" + or http://arxiv.org/pdf/0805.2274.pdf or "Determination of the Gaussian and Lorentzian content of experimental line shapes" +We shall use the simple Pseudo-Voigt-Profil : Voigt ~ η·Lorentz + (1-η)·Gauss +We use the result by "Extended pseudo-Voigt function for approximating the Voigt profile" cf http://www.crl.nitech.ac.jp/~ida/research/reprints/expv.pdf + +eta = 1.36603 (G_L/G) - 0.47719 (G_L/G)^2 + 0.11116(G_L/G)^3 +where G = ([G_G^5 + 2.69269 G_G^4 G_L + 2.42843 G_G^3 G_L^2 + 4.47163 G_G^2 G_L^3 + 0.07842 G_G G_L^4 + G_L^5]^1/5 +for G_G and G_L beeing the FWHM of the functions: G_G = 2 sqrt (ln 2) sigma_G and G_L = 2 gamma_L + +The worst error is 1% and occurs at the center and for G_G = G_L +**/ + + +// Approximation of the Voigt profile [Lorentz*Gaussian](omega) where Lorentz and Gaussian FWHM values of G_L and G_G and centered on 0. +// From "Extended pseudo-Voigt function for approximating the Voigt profile" +double Pseudo_Voigt(double delta, const double G_L, const double G_G) +{ + double Gfive = pow(G_G,5) + 2.69269*pow(G_G,4)*G_L + 2.42843*pow(G_G,3)*pow(G_L,2) + 4.47163*pow(G_G,2)*pow(G_L,3) + 0.07842*G_G*pow(G_L,4) + pow(G_L,5); + double G = pow(Gfive,1./5.); + double eta = 1.36603*(G_L/G) - 0.47719*(G_L/G)*(G_L/G) + 0.11116*(G_L/G)*(G_L/G)*(G_L/G); + double fG = Gauss(1., delta, G); + double fL = Lorentz(1., delta, G); + double Voigt = (1-eta)*fG + eta*fL; + return Voigt; +} + +// comb spectum = gaussian laser but with individual Lorentzian comb lines +// the comb line are positioned at nu_offset + n*nu_repetition +// The intensity is taken at the detuning of the nearest (lorentzian) comb line +// The linewidth is due to the spontaneous emission of the 2 levels system drived by the comb laser +double comb_shape(double I,double delta, const double G_L, const double G_G, const int n_las, const double Energy_transition_cm, FitParams ¶ms) +{ + double IGaussien=I*Pseudo_Voigt(delta, G_L, G_G); // INtensity of the broadband gaussian spectral shape + + std::ostringstream oss; + oss << "[" << n_las << "]"; + std::string num = oss.str(); // num = "[i]" + +// Should be put on laser Class! +// The position of the n^th comb line is nu_offset_MHz + n nu_repetition_MHz and its linewidth is nu_individual_comb_line_MHz + (natural linewidth of the transition) + double nu_offset_MHz = params.LocateParam(string("nu_offset_MHz") + num)->val; + double nu_repetition_MHz = params.LocateParam(string("nu_repetition_MHz") + num)->val; + double nu_individual_comb_line_MHz = params.LocateParam(string("nu_individual_comb_line_MHz") + num)->val; + double nu_transition_MHz = 100* C *Energy_transition_cm/MHz; + + int n_comb = double ((nu_transition_MHz - nu_offset_MHz)/nu_repetition_MHz + 0.5) ; // number of the closest comb line. Simple assumption to calcultae the rate. We do not sum over all lines byut just take the closest one! + double delta_comb =2*pi*MHz*(nu_transition_MHz - (n_comb*nu_repetition_MHz + nu_offset_MHz)); // detuning from the comb line + double Gamma_line = 2*pi*MHz*nu_individual_comb_line_MHz;// linewidth of individual line + double I_transition = Lorentz(Gamma_line*pi/2., delta_comb, Gamma_line); // Lorentzian normalized to 1 at the center + + return IGaussien*I_transition; +} + + + +// intensity (irradiance) of a pseudo_BBR (pseudo_Black Body Radiation) that is a BBR spectrum but with a gaussian beam +//I(w)=rho(w)*c, et I(w)=Itot*cste*w^3/(exp(hb w/kT) -1) avec Itot= (sigmaT^4)/4 +inline double pseudo_BBR_intensity(const double I, const double Energy_transition_cm, const double T) +{ + double integrated_spectrum= pow((kB* pi *T)/(4.*100. * hPlanck *C),4) /15.;//1/4 of (kB^4 Pi^4 T^4)/(15*100^4 h^4 c^4) + double convolutionFactor = 2* pi * 100. * C; //L(omega) convolué à I(omega) équation B7 Molecular Cooling via Sisyphus + return (I/integrated_spectrum/convolutionFactor)*Energy_transition_cm*Energy_transition_cm*Energy_transition_cm/(exp(hPlanck*100*C*Energy_transition_cm/(k_Boltzmann*T))-1.); // the spectral desnity is proportional to omega^3/(exp^(hbar omega/kB T) -1) and integrate x^3/(exp-x -1) = pi^4/15 +} + + + + +// Calcul de l'intensité locale [Lorentz*I](omega) with a natural Cauchy-Lorents linewitdh with FWHM Gamma_atomic = Gamma_spon_fond+Gamma_spon_exc. +// delta = omega_Laser - omega_atomic +double intensity_Convolution_linewidth(const double I, const double delta, const double Gamma_atomic, const double Gamma_Laser, const int laser_type, const int n_las, const double Energy_transition_cm, const double Energy_transition_laser_cm, FitParams ¶ms) +{ + if (laser_type == lorentzien || laser_type == field_ionization) // for the field ionization it is here just to select roughly the region where the power is not too big + return Lorentz(I, delta, Gamma_Laser + Gamma_atomic); // Convolution of 2 Lorentzian + if (laser_type == gaussien) + return I*Pseudo_Voigt(delta, Gamma_atomic, Gamma_Laser); // Voigt = Lorentz convoluted by Gaussian + if (laser_type == comb) + return comb_shape(I,delta, Gamma_atomic, Gamma_Laser, n_las, Energy_transition_cm, params); // Voigt = Lorentz convoluted by Gaussian + if (laser_type == pseudo_BBR) + return pseudo_BBR_intensity(I, Energy_transition_cm, Energy_transition_laser_cm); // BBR spectra. Temperature is in Energy_transition_laser_cm in Liste_Param + return 0.; +} + + + +/************* +The rates are explained in the appendix of the article +"Molecular cooling via Sisyphus processes." +*********/ + +// Excitation rate +double rate_two_level(const double I_loc, const double dip_Debye) +{ + double dipole = dip_Debye*Debye; + double rate_0 = dipole*dipole*I_loc*pi/(HBAR*HBAR*epsilon0*C); + return rate_0; +} + +// Rate for (photo-)ionization +double rate_ionization(const double I_tot, const double dip_Debye, const double delta, const double Energy_transition_cm) +{ + double cross_section = cm*cm*dip_Debye*dip_Debye/3.; // This is how it is implemented in the file containing lines! but we have dipole_debye = sqrt(3.*my_mol.liste_raies) + double nu = 100* C * (Energy_transition_cm) + delta/(2*pi); // Frequency of the laser + double flux = I_tot/( hPlanck * nu); + return cross_section*flux; +} + +// Field ionization rate +double rate_field_ionization(const Laser& my_laser, const vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE) +{ + Molecule my_mol = Mol[n_mol]; + int n = Mol.size(); + + Vecteur3D r,E,E_coulomb; + r = my_mol.get_pos(); + E = fieldE.get_Field(r); + // double Vcoulomb = get_coulomb_potential(Mol, r, n); + + E_coulomb = get_coulomb_field(Mol, n_mol, r); // SI on veux ajouter le champ coulombien + E = E + E_coulomb; + + double Gamma; + Gamma = (4900-E.mag())*1e+7; + return max(Gamma,0.); +} + + +//If we use BBR, the ionization cross section is given by another formula +// According to (23) Bezuglov 2009 NJP 11 2009 013052 +double rate_ionization_BBR(const double I, const Laser& my_laser, const Molecule &my_mol,const double Energy_transition_cm) +{ + double Temp_BBR=cm/my_laser.get_lambda(); // Température codée dans ListParam par energie_cm + double N_BBR=1/(1.-exp(-hPlanck*100*C*Energy_transition_cm/(k_Boltzmann*Temp_BBR))); + double n = double (my_mol.exc)-2.47; + double l = double ((my_mol.deg_number)-(my_mol.two_J))/1000.; //# is 1000l+2j + // double rate_ioni_BBR=((k_Boltzmann*Temp_BBR/hbar_Planck)/(pi2*C*C*C))*(2.80/pow(n,7./3.)+(2.09*l*l)/pow(n,11./3.))*log(N_BBR)*conv_ua_smoins1; + // return rate_ioni_BBR*(4.*I/(sigmaSB*pow(Temp_BBR,4))); + //return rate_ioni_BBR; + return 0.; +} + +double rate_ionization_BBR_bis(const double I, const Laser& my_laser, const Molecule &my_mol) +{ + double Temp_BBR_2=cm/my_laser.get_lambda(); // Température codée dans ListParam par energie_cm + double n_bis = double (my_mol.exc)-2.47; + double C_log = 1/(1-exp(-157890./(Temp_BBR_2*n_bis*n_bis))); + double l_bis = double ((my_mol.deg_number)-(my_mol.two_J))/1000.; //# is 1000l+2j + double C_1 = 14423./pow(n_bis,7./3.); + double C_2 = (10770.*l_bis*l_bis)/pow(n_bis,11./3.); + double rate_ioni_BBR_bis = Temp_BBR_2*(C_1 + C_2)*log(C_log); + return rate_ioni_BBR_bis*(I/(sigmaSB*pow(Temp_BBR_2,4))); + //return rate_ioni_BBR_bis; +} +// Calculation of the excitation rate for a laser (or a class of coherent laser) for a given transition (bound or ionization) +// Add this rate only is is_rate_calculated is true +double rate_excitation(vector &reaction_list, vector &rate,const Laser& my_laser, const vector &Mol, const int n_mol, const int n_las, const Vecteur3D k, const double Itot_loc, + const double Itot, const double dipole_debye, const double delta, const double Energy_transition_cm, const Field &fieldB, const Field &fieldE, const int is_bound_transition, const Internal_state Internal_state_out, const bool is_rate_calculated) // calculate rate and reaction_list for this transition +{ + Molecule my_mol = Mol[n_mol]; + double rate_exc = 0.; // rate of excitation + + if ((bool) is_bound_transition) // transition bound-bound (abs; permet de traiter les symmetrie +1 et -1 comme +1 donc true) + rate_exc = rate_two_level(Itot_loc, dipole_debye); + else // bound_free transition (potential photo_ionization) + if (my_laser.get_type_laser() == pseudo_BBR) //If we study BBR + rate_exc= rate_ionization_BBR(Itot, my_laser, my_mol,Energy_transition_cm); + else if (delta>0 ) // Test if the laser transition is above the ionization continuum. O.K. also for photodetachment + { + if (my_laser.get_type_laser() == field_ionization) + rate_exc = rate_field_ionization(my_laser, Mol, n_mol, fieldB, fieldE); + else + rate_exc = rate_ionization(Itot, dipole_debye, delta, Energy_transition_cm); // photoionization + } + + + if (rate_exc < SMALL_NUMBER_RATE) + return 0; // It is not useful to calculate too small rates. So if the rate is too small we do not calculate it + + if (is_rate_calculated == true) + { + type_codage_react reaction = { n_mol, n_las, k, k, k, Internal_state_out}; // {n_mol; n_laser; quant_axis; pol_vector; k_eff_laser; final_internal_state;}. IN this case the quant_axis; pol_vector are not important (we put k but any other values will do ) + reaction_list.push_back( reaction ); // transition de la molécule n_mol avec l'impulstion k_tot vers l'état out + rate.push_back(rate_exc); + } + return rate_exc; +} + + + +/************************************************************************/ +/************************** Fonctions transition Molecule ***************/ +/************************************************************************/ + + +// Calcul et ajoute de tous les taux d'emission spontanée de la molécule. +int rates_molecule_spon(vector &Level, vector &reaction_list, vector &rate, const Molecule &my_mol, const Field &fieldB, const Field &fieldE, const int num_mol, FitParams ¶ms) +{ + Vecteur3D axe_quant,r,v,k_spon; + r = my_mol.get_pos(); + v = my_mol.get_vel(); + Internal_state Internal_state_in = my_mol ; // état interne de la molecule + + axe_quant = fieldB.get_Field(r)+ fieldE.get_Field(r); // A priori les deux champs doivent avoir le même axe on choisi. Cela permetra d'orienter l'émission spontanée +// TODO (Daniel#2#): CAREFUL THE QUANTIZATION AXIS IS given by the sum of the fields!!!! Should not be like this should be the dominant field!!! Check elsewhere also + + Vecteur3D Bfield; + Bfield= fieldB.get_Field(r); + double B = Bfield.mag(); + double E = fieldE.get_Field(r).mag(); + double Energy_transition_cm =0.; + + double Gamma=0.; // Spontaneous emission rate + double k=0.; // Spontaneous emission lenght wave vector + + + /********** WE DIAGONALIZED THE ENERGY LEVELS so the transition dipole moment are not constant and need to be calculated + BUt we do not know the real k vector of the sponteneous emission so we do not correct for the recoil energy level **********/ + + + + + if ( (params.LocateParam("is_Levels_Lines_Diagonalized")->val) ) + { + MatrixXd d[3] ; // d[0] = dipole transition for sigma minus = d0_ij in field ; d[1] dipole transition for pi in field and d[2] is dipole transition for sigma plus in field + SelfAdjointEigenSolver es; // eigenstates and eigenvalues + double v_perp = (v.cross(Bfield)).mag()/B; + Diagonalization_Energy_dipole(Level, B, v_perp, es, d); + // diagonalized the Hamiltionian for B field and v velocity and give the eigenvectors and eigenvalues and update all Level[n].Energy_cm + + int i = my_mol.deg_number; // The molecules is in the Level number n_level_in.// so Level[ # = deg_number] shall be the Level itself// So in the Level file the deg_number is the Level number (START FROM 0) + Internal_state_in = Level[i]; // Internal_state_in = my_mol ; // état interne de la molecule + + for (int j=0; jj + { + Gamma =0.; + for(int n_polar = -1; n_polar <= 1; n_polar++) // Gamma_ij propto ||^2 = + { + double dipole_ij = d[n_polar+1](i,j); // dipole_ij = + // is coded here as d[q+1][i][j] (real), i = line, j = column ; that is for a i<-->j transition (with E_i> E_j) + + double S_pol= dipole_ij*dipole_ij/3.; + Energy_transition_cm = Level[i].Energy_cm - Level[j].Energy_cm; + k = 2*pi*100.*Energy_transition_cm; + Gamma += 3.* S_pol * Spol_Debye_A_s * Energy_transition_cm*Energy_transition_cm*Energy_transition_cm; + } + if (Gamma < SMALL_NUMBER_RATE) + continue; // Pour une transition trop faible inutile de la calculer + + k_spon = Vecteur3D(k,0.,0.) ; // Will be used to give the proper photon recoil + rate.push_back(Gamma); // rate[nb_rate]=Gamma + type_codage_react reaction = { num_mol, -1, axe_quant, Vecteur3D(d[0](i,j),d[1](i,j),d[2](i,j)), k_spon, Level[j]}; // {n_mol; n_laser; quant_axis; pol_vector; k_eff_laser; final_internal_state;}. + reaction_list.push_back (reaction); + // numéro laser -1=spon_emission pour émission spontanée. + // for the spontaneous emission we give the polarization vector to determine the emitted photon (not the impulsion photon as for stimulated or absorption) + // So we give the polarization vector (dipole transition for polar -1, 0, +1 ) in the local quantization axis frame axis (the one where OZ = axe_quant) + + } + } + + /********** THE ENERY LEVELS ARE not diagonalized and so the transition dipole moment are constant **********/ + + else + { + for( int i = 0; i < (int) my_mol.liste_raies.size(); i++ ) // Boucle sur les transitions accessibles + { + Internal_state Internal_state_out = *(my_mol.liste_raies[i].first) ; // état interne de la molecule après la réaction + double Energy_in = Internal_state_in.Energy0_cm + (Internal_state_in.Energy_Shift_B_cm(B) + Internal_state_in.Energy_Shift_E_cm(E)); + double Energy_out = Internal_state_out.Energy0_cm + (Internal_state_out.Energy_Shift_B_cm(B) + Internal_state_out.Energy_Shift_E_cm(E)); + Energy_transition_cm = Energy_in - Energy_out; // TODO (dc#4#): On ne prend pas le déplacement lumineux. ...Il faudrait revoir sérieusement cet affaire de Energie mise à jour + + if (Energy_transition_cm < 0.) + continue; // Etat en dessous de l'autre donc pas de photon spontané + + double dipole_debye = sqrt(3.*my_mol.liste_raies[i].second) ; // dipole de la transition en debye + Gamma= Gamma_spon(dipole_debye, Energy_transition_cm); + + if (Gamma < SMALL_NUMBER_RATE) + continue; // Pour une transition trop faible inutile de la calculer + + k = 2*pi*100.*Energy_transition_cm; + k_spon = Vecteur3D(k,0.,0.) ; // Will be used to give the proper photon recoil + + rate.push_back(Gamma); // rate[nb_rate]=Gamma + type_codage_react reaction = { num_mol, -1, axe_quant, axe_quant, k_spon, Internal_state_out}; // {n_mol; n_laser; quant_axis; pol_vector; k_eff_laser; final_internal_state;}. + // IN this case the pol_vector, is not important (the photon will be calculated by the Delta_M given by the Internal_states) so we put axe_quant but any other values will do ) + reaction_list.push_back (reaction); // numéro laser -1=spon_emission pour émission spontanée. Le vecteur impulsion sera calculé plus tard + } + } + + return rate.size(); +} + + + + +// Calcul of rate (if no interferece between laser) between level in and out for a given laser and for a given molecule. This add the light shift effect to the dipolar potential (delta_pot_dipolaire) +// update the detuning (delta), the polarization vector also updated), Gamma_spot_total, sqrt of the local intensity of the laser +int rates_single_molecule_laser_level(const int n_las, double dipole, double &delta, double &eps_pol, double &Gamma_spon_tot, double sqrt_intensity_loc[], + vector &Level, Internal_state &Internal_state_in, Internal_state &Internal_state_out, vector &reaction_list, + vector &rate, const vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const Laser &my_laser, const double t, double &delta_pot_dipolaire, + FitParams ¶ms, bool is_rate_calculated, int is_bound_transition, const int n_level_in, const int n_level_out, const double Gamma_in, MatrixXd d[]) +{ + Molecule my_mol= Mol[n_mol]; + + if ( (params.LocateParam("is_Levels_Lines_Diagonalized")->val) ) + { + Internal_state_out = Level[n_level_out]; + is_bound_transition = abs(Internal_state_out.Sym); // To know if the transition is towards continuum for instance + } + + + Vecteur3D k,v,r; + k = my_laser.wave_vector(); + r = my_mol.get_pos(); + v = my_mol.get_vel(); + + double Gamma_Las = my_laser.get_Gamma_Laser(); // Largeur spectrale FWHM (en s^-1) + + // we treat absorption and emission together. + double Energy_transition_cm = abs(Internal_state_out.Energy_cm - Internal_state_in.Energy_cm) + k*v/Conv_Ecm_delta; // Il faut mettre le detuning car c'est la fréquence vue par les particules et donc par le spectre du laser. + double Energy_transition_laser_cm = cm/my_laser.get_lambda(); // Energie de la transition laser en cm^-1 + delta =(Energy_transition_laser_cm - Energy_transition_cm)*Conv_Ecm_delta ;// detuning de la transition en s^-1. delta = omega_L - k.v - omega_transition + double I_laser_tot = my_laser.intensity_lab_axis(r) * my_laser.transmission_spectrum(Energy_transition_cm); // Intensité laser à la position de la molécule + + Vecteur3D axe_quant,dipole_vector(0.,0.,0.); + axe_quant = fieldB.get_Field(r)+ fieldE.get_Field(r); // A priori les deux champs doivent avoir le même axe on choisi. Cela permetra d'orienter l'émission spontanée + + double rate_exc=0.; + double dipole_debye_trans =0.; + + // the rate is proportional to dipole*dipole*I noted dipole_debye_trans*dipole_debye_trans*Itot_loc in rate_excitation function + // but in reality comes from ||^2 = |sum_q E^(q) |^2 = E^2 |sum_q eps^(q) |^2. + // So destructive interference can appears and so the epsilon_vector has to be included in the dipole not in the intensity + + +// dipole_q_ij is coded here as d[q+1][i][j] (real), i = line, j = column ; that is for a i<-->j transition (WITH E_i> E_j) + if ( (params.LocateParam("is_Levels_Lines_Diagonalized")->val) ) + { + for(int q = -1; q <= 1; q++) // scan over the polarization d^(q) sur -1, 0, +1 ;d[0]=dsigma-, d[1] =dpi , d[2]=dsigma+ for polarization in absorption ; d0[q+1]_ij = 0__0 + { // We choose the proper dipole because d[q+1][i][j] (WITH E_i> E_j to get m_i = m_j+q + if (Internal_state_in.Energy_cm > Internal_state_out.Energy_cm) // EMISSION up=i=n_level_in low=j=n_level_out + dipole_vector = Vecteur3D( d[0](n_level_in,n_level_out), d[1](n_level_in,n_level_out), d[2](n_level_in,n_level_out)); + else // ABSORPTION up=i=n_level_out low=j=n_level_in + dipole_vector = Vecteur3D( d[0](n_level_out,n_level_in), d[1](n_level_out,n_level_in), d[2](n_level_out,n_level_in)); + } + Gamma_spon_tot = Gamma_in + Gamma_Level_from_diagonalized_dipole(Level, d, n_level_out); + } + else // No diagonalization but fixed transition strength and a give Delta M transition + { + int two_M_up,two_M_low; // Projection du moment angulaire + if (Internal_state_in.Energy_cm > Internal_state_out.Energy_cm) // EMISSION up=i=n_level_in low=j=n_level_out + { + two_M_up = Internal_state_in.two_M; + two_M_low = Internal_state_out.two_M; + } + else // ABSORPTION + { + two_M_low = Internal_state_in.two_M; + two_M_up = Internal_state_out.two_M; + } + dipole_vector[(two_M_up-two_M_low)/2+1]=dipole; // dipole_vector[M_up-M_low+1] est la composante du champ ayant la bonne polarisation pour la transition que ce soit en absorption ou émission + Gamma_spon_tot = Internal_state_in.one_over_lifetime + Internal_state_out.one_over_lifetime; // Spontaneous decay on the transition Sum_k Gamma_k + } + + dipole_debye_trans = effectif_dipole_local(dipole_vector, axe_quant, my_laser); // (asbolute value of) effectif dipole d.e_laser = sum_p d_p epsilon^p + sqrt_intensity_loc[n_las] = sqrt(intensity_Convolution_linewidth(I_laser_tot, delta, Gamma_spon_tot, Gamma_Las, my_laser.get_type_laser(),n_las, Energy_transition_cm, Energy_transition_laser_cm, params)); // Proportional to the Rabi Frequency + + if (dipole_debye_trans < SMALL_DIPOLE_DEBYE && is_bound_transition) // Pour une transition trop faible inutile de calculer le taux! (les "dipole" sont des "petite section pour la photoinizaiton donc on fait exception) + return rate.size(); + + if (my_laser.get_coherent_avec_laser_num() == -1) // Laser seul, pas d'interférence avec les autres, on le calcul maintenant pour ne pas le recalculer ensuite + { + + double Itot_loc = sqrt_intensity_loc[n_las]* sqrt_intensity_loc[n_las]; + if (Itot_loc < SMALL_NUMBER) + return rate.size();; // Pour une transition trop faible inutile de calculer le taux! + rate_exc = rate_excitation(reaction_list, rate,my_laser, Mol, n_mol, n_las, k, Itot_loc, I_laser_tot, dipole_debye_trans, delta,Energy_transition_cm, fieldB, fieldE, is_bound_transition, Internal_state_out, is_rate_calculated); // calculate rate and reaction_list for this transition. If we do not wat to calculate the rate we just use reaction_list[0] which is *reaction_list + delta_pot_dipolaire += sgn(Internal_state_out.Energy_cm - Internal_state_in.Energy_cm) * rate_exc * delta/Gamma_spon_tot; + } + return rate.size(); +} + + + + + +// Calcul de tous les taux de la molécule pour tous les lasers +// On les ajoutes aux taux des autres +// return nb_rate + +int rates_molecule(vector &Level, vector &reaction_list, vector &rate, const vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, + const double t, double &delta_pot_dipolaire, FitParams ¶ms, bool is_rate_calculated ) +{ + Molecule my_mol = Mol[n_mol]; + delta_pot_dipolaire = 0.; + double Gamma_spon_tot=0.; + double eps_pol=0.; + double dipole_debye =0.; + double rate_exc=0; + double sqrt_intensity_loc[100], delta[100]; // intensities ~sqrt(I), détuning + int is_bound_transition ; // Trick to treat the ionization. An ionizing state is of 0 symmetry. All other states are -1 or +1 thus transform to +1 = true + Internal_state Internal_state_in,Internal_state_out; // State for transitions + + Vecteur3D r,v,Bfield; + r = my_mol.get_pos(); + v = my_mol.get_vel(); + Bfield= fieldB.get_Field(r); + double B = Bfield.mag(); + double E = fieldE.get_Field(r).mag(); + + const int Nb_laser = laser.size(); + int number_las_min = 0 ; // First laser used (0 by default but can be Nlaser/2 if we switch and t>T1 modulo (T1+T2) + int number_las_max_plus_1 = Nb_laser; // Last laser used. Nb_laser by default but can be Nlaser/2 if we switch and t=100) + cerr << "Nb de laser trop grand: modifier la taille du tableau et recompiler " << endl; + +// TO summarize by default we scan between 0 and Nb_laser. But if we switch it is between 0 and N_laser/2 and then (t>T1) N_laser/2+1 and N_laser + if ( (params.LocateParam("Is_Laser_Switched")->val) ) + { + int zero_if_t_0_T1_one_if_t_T1_T2 = Is_Switch(params.LocateParam("dt_switch_1")->val, params.LocateParam("dt_switch_2")->val, t); + // 0 (DEFAULT) if t is between 0 and T1 (modulo T1+T2); 1 if t is between T1, T1+T2 (modulo T1+T2) + number_las_min = zero_if_t_0_T1_one_if_t_T1_T2 * Nb_laser/2; + number_las_max_plus_1 = Nb_laser/2 + zero_if_t_0_T1_one_if_t_T1_T2 * Nb_laser/2; + } + + + /********** WHEN WE DIAGONALIZED THE ENERGY LEVELS,the transition dipole moment are not constant and need to be calculated (we do not treat interference between lasers) **********/ + + if ( (params.LocateParam("is_Levels_Lines_Diagonalized")->val) ) + { + MatrixXd d[3] ; // d[0] = dipole transition for sigma minus = d0_ij in field ; d[1] dipole transition for pi in field and d[2] is dipole transition for sigma plus in field + SelfAdjointEigenSolver es; // eigenstates and eigenvalues + double v_perp = (v.cross(Bfield)).mag()/B; + Diagonalization_Energy_dipole(Level, B, v_perp, es, d); // calcul of the new dipole transition for the new levels. + + int n_level_in = my_mol.deg_number; //The molecules is in the Level number n_level_in.// so Level[ # = deg_number] shall be the Level itself// So in the Level file the deg_number is the Level number (START FROM 0) + Internal_state Internal_state_in = Level[n_level_in]; // Internal_state_in = my_mol ; // état interne de la molecule + double Gamma_in = Gamma_Level_from_diagonalized_dipole(Level, d, n_level_in); // Initial spontaneous decay rate of the state + + for (int n_las = number_las_min ; n_las < number_las_max_plus_1; n_las++) // On scan sur les lasers pour calculer l'intensité sur la transtion // If we switch we add Nb_laser to the number + { + Laser my_laser = laser[n_las]; + Vecteur3D k; + k = my_laser.wave_vector(); + double m=my_mol.get_mass(); + double v_perp_recoil ; + + /*** We assume that there is no level crossing with the initial level so that absorption and emission are well define by the energy ordering . But the upper or lower level ordering may change due to hbar k modification ****/ + + /***** Stimulated emission: v--> v-HBAR*k/m *****/ + + v_perp_recoil = ((v-HBAR*k/m).cross(Bfield)).mag()/B; +// TODO (Daniel#9#): this test works only if the loweslt level is a dead level. May be remove this part (which is here only for speed reasons + if (n_level_in>0) // 0 is the dead level so it can not change + Diagonalization_Energy_dipole(Level, B, v_perp_recoil, es, d); // calcul of the new dipole transition for the new levels (after the emission of photons). The energy levels order may have changed + for( int n_level_out = 0; n_level_out < n_level_in; n_level_out++ ) // Emission so we scan only on level below + { + rates_single_molecule_laser_level( n_las, dipole_debye, delta[n_las], eps_pol, Gamma_spon_tot, sqrt_intensity_loc, Level, Internal_state_in, Internal_state_out, + reaction_list, rate, Mol, n_mol, fieldB, fieldE, my_laser, t, delta_pot_dipolaire, + params, is_rate_calculated, is_bound_transition, n_level_in, n_level_out, Gamma_in, d); + } + + /***** Absorption: v--> v+HBAR*k/m *****/ + + v_perp_recoil = ((v+HBAR*k/m).cross(Bfield)).mag()/B; + if (n_level_in< Level.size()) // to make the loop over all levels + Diagonalization_Energy_dipole(Level, B, v_perp_recoil, es, d); // calcul of the new dipole transition for the new levels (after the absorption of photons). The energy levels order may have changed + for( int n_level_out = n_level_in+1; n_level_out < Level.size(); n_level_out++ ) // Absorption so we scan only on level above + { + is_bound_transition = abs(Level[n_level_out].Sym); + rates_single_molecule_laser_level(n_las, dipole_debye, delta[n_las], eps_pol, Gamma_spon_tot, sqrt_intensity_loc, Level, Internal_state_in, Internal_state_out, + reaction_list, rate, Mol, n_mol, fieldB, fieldE, my_laser, t, delta_pot_dipolaire, params, is_rate_calculated, is_bound_transition, n_level_in, n_level_out, Gamma_in, d); + } + } + } + + /********** THE ENERGY LEVELS ARE not diagonalized and so the transition dipole moment are constant **********/ + + else + { + Internal_state_in = my_mol ; // état interne de la molecule + Internal_state_in.Energy_cm = Internal_state_in.Energy0_cm + (Internal_state_in.Energy_Shift_B_cm(B) + Internal_state_in.Energy_Shift_E_cm(E)); + +// If looking with debugger here this create Segmentaion fault. this is due (but not understood !) by the copy my_mol=Mol[n_mol] and look at my_mol.liste_raies.size() + for( int n_trans = 0; n_trans < (int) my_mol.liste_raies.size(); n_trans++ ) // Boucle sur les transitions accessibles + { + dipole_debye = sqrt(3.*my_mol.liste_raies[n_trans].second) ; // dipole de la transition en debye + Internal_state_out = *(my_mol.liste_raies[n_trans].first) ; // état interne de la molecule après la réaction + is_bound_transition = abs(Internal_state_out.Sym); + + if (dipole_debye < SMALL_DIPOLE_DEBYE && is_bound_transition) + continue; // Pour une transition trop faible inutile de calculer le taux! (les "dipole" sont des "petite section pour la photoinizaiton donc on fait exception) + + Internal_state_out.Energy_cm = Internal_state_out.Energy0_cm + (Internal_state_out.Energy_Shift_B_cm(B) + Internal_state_out.Energy_Shift_E_cm(E)); +// The dipolar potential is not included in the shift for the transition. ... +//This avoids accumulatiion, but for some case it may be good to have it + + for (int n_las = number_las_min ; n_las < number_las_max_plus_1; n_las++) // On scan sur les lasers pour calculer l'intensité sur la transtion // If we switch we add Nb_laser to the number + { + Laser my_laser = laser[n_las]; + + // Calcul les taux dans le cas où il n'y a pas d'interférence lasers + if (my_laser.get_coherent_avec_laser_num() == -1) // Laser seul, pas d'interférence avec les autres + rates_single_molecule_laser_level( n_las, dipole_debye, delta[n_las], eps_pol, Gamma_spon_tot, sqrt_intensity_loc, Level, Internal_state_in, Internal_state_out, reaction_list, + rate, Mol, n_mol, fieldB, fieldE, laser[n_las], t, delta_pot_dipolaire, params, is_rate_calculated, is_bound_transition); +// Calcul of rate (if no interferece between lasers) between level in and out for a given laser and for a given molecule. This add the light shift effect to the dipolar potential (delta_pot_dipolaire) +// update the detuning (delta), the polarization vector also updated), Gamma_spot_total, sqrt of the local intensity of the laser + } + + /** Il y a des interférences: on va calculer l'interférence ainsi que l'absorption + Itot_loc c'est proportionel à |Ω|^2= Σ j,i |Ωi||Ωj|cos[(ωi − ωj )t − (ki − kj).(r + vt)] + I_ktot c'est proportionel à |Ω|^2 ktot= Σ j,i (ki+kj)/2 |Ωi||Ωj|cos[(ωi − ωj )t − (ki − kj).(r + vt)] donc ktot = I_ktot/Itot + + We could use the total Rabi Frequency but when the laser is shaped it is not easy. So we prefer to use the local intensity. + So |Ω| is proportional to sqrt(I_tot_loc) and |Ωi| to sqrt(I_loc) with the same proportionality factors (for instance (Gamma_tot/2pi)/((Gamma_tot/2)^2 + delta^2) ) so it will be remove at the end. + This is true because all lasers are similar (if not we will have no interferences!) + ***/ + + double omegai,omegaj,Itot_loc; + Vecteur3D ki,kj,I_ktot; + for (int n_classe_coh_las = number_las_min; n_classe_coh_las < number_las_max_plus_1; n_classe_coh_las++) // On scan sur les classes de lasers cohérents. un laser j interfère avec un laser i<=j et le plus petit i interfère avec lui même! + { + int num_laser_coherent = laser[n_classe_coh_las].get_coherent_avec_laser_num(); // Numéro de la classe (en fait du premier laser de la classe de cohérence) + if (n_classe_coh_las != num_laser_coherent) + continue; // Ce laser n'est pas le premier de la classe. On a donc déjà calculé cette classe on passe au suivant! + Itot_loc = 0.; + I_ktot = Vecteur3D(0.,0.,0.); + double Energy_transition_class_cm = abs(Internal_state_out.Energy_cm - Internal_state_in.Energy_cm) + laser[num_laser_coherent].wave_vector()*v/Conv_Ecm_delta ;// k.v effet Doppler (à resonnance) + + for (int i = n_classe_coh_las; i < number_las_max_plus_1; i++) // On scan sur les lasers de la classe (qui sont ordonnés donc n_classe_coh_las est le premier + { + if (laser[i].get_coherent_avec_laser_num() != num_laser_coherent) + continue ; // Si pas cohérent on stoppe avec ce laser et on continue avec un autre + double Itoti = sqrt_intensity_loc[i]*sqrt_intensity_loc[i]; + ki = laser[i].wave_vector(); + omegai = laser[i].get_omega(); + I_ktot += ki*Itoti; + Itot_loc += Itoti; + + /**** + Calcul de l'intensité locale liée à l'interférence + |Ω|^2= Σ L′,L |ΩL||ΩL'|cos[(ωL − ωL′ )t − (kL − kL′ ).(r + vt)] avec Ω^2 ~I + Le moment transféré est calculé par + |Ω|^2 ktot= Σ j,i (ki+kj)/2 |Ωi||Ωj|cos[(ωi − ωj )t − (ki − kj).(r + vt)] + et Σ j,i = Σi + 2 Σ j>i + Remark: In the case of lattice, we can have an absorption rate but no force. That mean that the momentum transfer at the absorption is zero. + But we still have the "random" spontaneous emission existing. I think this is how it works in reality! + It calculate also the dipole detuning in s^-1 which is just rate * Gamma/delta. + In this case we do not necessarily to calculate the rate, for instance when calculate only dipolar shift, so is_rate_calculated would be false + **/ + + + for (int j = i+1; j < number_las_max_plus_1; j++) // On scan les autres lasers j>i et on ne va garder que ceux cohérent avec i + { + if (laser[j].get_coherent_avec_laser_num() != num_laser_coherent) + continue ; // Si pas cohérent on stoppe avec ce laser et on continue avec un autre + kj = laser[j].wave_vector(); + omegaj = laser[j].get_omega(); +// We should put the phase given by the polarizations sometimes to take into account linear polarisation + double sqrt_Ii_Ij = sqrt_intensity_loc[i]*sqrt_intensity_loc[j]*cos((omegai-omegaj)*t - (ki-kj)*r); + Itot_loc += 2.*sqrt_Ii_Ij; + I_ktot += 2.*sqrt_Ii_Ij*(ki+kj)/2.; // + } + } + double I_laser_tot = laser[num_laser_coherent].intensity_lab_axis(r) * laser[num_laser_coherent].transmission_spectrum(abs(Internal_state_out.Energy_cm - Internal_state_in.Energy_cm)); // Intensité laser à la position de la molécule. WE DO NOT USE THE INTERFERENCE HERE + double I_tot = I_laser_tot*Itot_loc/(sqrt_intensity_loc[num_laser_coherent]*sqrt_intensity_loc[num_laser_coherent]); // phenomenoligue way to treate I_tot. We take the same rationfor the total laser intensity that for the loca one! + if (I_laser_tot < SMALL_NUMBER) + continue; // Pour une transition trop faible inutile de calculer le taux! + rate_exc = rate_excitation(reaction_list, rate,laser[n_classe_coh_las], Mol, n_mol, num_laser_coherent, I_ktot/Itot_loc, Itot_loc, I_tot, dipole_debye*eps_pol, delta[num_laser_coherent], Energy_transition_class_cm, + fieldB, fieldE, is_bound_transition, Internal_state_out, is_rate_calculated); // calculate rate and reaction_list for this laser class and transition + delta_pot_dipolaire += sgn(Internal_state_out.Energy_cm - Internal_state_in.Energy_cm) * rate_exc * delta[num_laser_coherent]/Gamma_spon_tot; + } + } + } + return rate.size(); +} + + + +// return the decay rate from Level i = sum_j &Level, MatrixXd d[], const int i) +{ + double Gamma=0.; + + for (int j=0; j &reaction_list, vector &rate, const int numero_mol, const int nombre_old_rate) +{ + + int n_mol; // Numéro de la molécule + int nb_rate = 0; + + for (int n_reac = 0; n_reac < nombre_old_rate; n_reac++) + { + n_mol = reaction_list[n_reac].n_mol; // Numéro de la molécule affectée + if (n_mol == numero_mol) + continue; // Fait la boucle sauf si c'est la molécule numero_mol + rate[nb_rate] = rate[n_reac]; // A mon avis il n'y a pas de risque car nb_rate <= n_reac + reaction_list[nb_rate] = reaction_list[n_reac]; + nb_rate ++; + } + + rate.erase(rate.begin()+nb_rate,rate.end()); // Remove the other rates rate[nb_rate], rate[nb_rate + 1] .... So we keep all rates except the one form the n_mol + reaction_list.erase(reaction_list.begin()+nb_rate,reaction_list.end()); + return nb_rate; +} + + +// Calcul de tous les taux de toutes les molécules si numero_mol = aucune +// Sinon on ne recalcule que celui de la molécule numero_mol +int calcul_rates_molecules(vector &Level, MC_algorithmes Algorithme_MC, vector &reaction_list, vector &rate, const vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, + const int numero_mol, const int N_Mol, FitParams ¶ms) +{ + if (Algorithme_MC == Aucun_MC) + { + rate.clear(); + reaction_list.clear(); + return -1; + } + + double delta_pot_dipolaire = 0.; // not used here but needed to call the functions + + if (numero_mol != aucune) // Une molécule a été affectée donc on ne recalcule que ses taux, les autres sont recopiés + { + copie_rates_molecules(reaction_list, rate, numero_mol, rate.size()); + rates_molecule_spon(Level, reaction_list, rate, Mol[numero_mol], fieldB, fieldE, numero_mol, params); // Emission spontanée + rates_molecule(Level, reaction_list, rate, Mol, numero_mol, fieldB, fieldE, laser, t, delta_pot_dipolaire, params); // Absorption ou Emission stimulée + if( ((int) params.LocateParam("repompage_force")->val) == ((int) true) ) + Repompage( rate, reaction_list, Mol[numero_mol], t, numero_mol, laser, N_Mol, params); + } + else // Si on a (forcé) numero_mol = aucune on recalcule tout + { + rate.clear(); + reaction_list.clear(); + for (int n_mol = 0; n_mol < N_Mol; n_mol++) + { + rates_molecule_spon(Level, reaction_list, rate, Mol[n_mol], fieldB, fieldE, n_mol, params); // Emission spontanée + rates_molecule(Level, reaction_list, rate, Mol, n_mol, fieldB, fieldE, laser, t, delta_pot_dipolaire, params); // Absorption ou Emission stimulée + if( ((int) params.LocateParam("repompage_force")->val) == ((int) true) ) + Repompage( rate, reaction_list, Mol[n_mol], t, n_mol, laser, N_Mol, params); + } + } + + if( ((int) params.LocateParam("Pompage_optique_force")->val) == ((int) true) ) + { + pompage_rv(rate, reaction_list, Mol, t); // Pompage forcé des molécules + // dt_KMC = 10000000.; + cout << " verif nb rate POMPAGE FORCE " << endl; + int n_reac = 0; + } + + return rate.size(); +} + + +/***********************************************/ +/********** réalisation d'une réaction *********/ +/***********************************************/ + + +// We scan all molecules and for each of them calculate one random +// Scan all rates and realize the reaction if the rate*random < dt=0.1/rate_max +// Typically a tens of Molecules will be affected +int do_reaction_FastRoughMethod(const MC_algorithmes Algorithme_MC, const gsl_rng * r, const vector &rate, const vector &reaction_list, vector &Mol, + const int n_reac, const vector &laser, const double dt_KMC, ofstream & file_rate, int &number_photons, FitParams ¶ms) +{ + int nb_rate = rate.size(); + int nb_molecule_affected = -1; // number of the molecule that has undergone a reaction (none at the begining of this loop) + + double random = 1.-gsl_rng_uniform(r); // uniform random number u \in (0,1] + + for (int n_reac = 0; n_reac < nb_rate; n_reac++) // Scan all the rates (for all molecules) + { + int numero_mol = reaction_list[n_reac].n_mol; // Number for molecule to be affected + if (numero_mol == nb_molecule_affected) + continue; // we do only one rate per molecule to avoid problems + + double Delta_t = (- log(random))/rate[n_reac]; // Typical time for this reaction to occur + if (Delta_t < dt_KMC) // The reaction occurs only if Gamma dt (random) < 0.1. Calculated like: (random)/ Gamma < 0.1/rate_Max. + { + do_reaction(Algorithme_MC, r, rate, reaction_list, Mol, n_reac, laser, dt_KMC, file_rate, false, number_photons, params); // Do the reaction as if it was + nb_molecule_affected = numero_mol; + random = 1.-gsl_rng_uniform(r); // New random number for the other molecule + } + } + return aucune; // In a sens "Aucune" Molecule has not been affected. So "all" (a lot) of Molecules have been affected and thus we will have to calculate all potential again +} + +// Makes the reaction that has been chosen: reaction {n_mol; n_laser; quant_axis; pol_vector; k_eff_laser; final_internal_state;}. +int do_reaction(const MC_algorithmes Algorithme_MC, const gsl_rng * r, const vector &rate, const vector &reaction_list, vector &Mol, + const int n_reac, const vector &laser, const double dt_KMC, ofstream & file_rate, bool first_call, int &number_photons, FitParams ¶ms ) +{ + if (n_reac == -1) + return -1; // No Reaction like in Aucun_MC + if (Algorithme_MC == Fast_Rough_Method && first_call == true) + do_reaction_FastRoughMethod(Algorithme_MC, r, rate, reaction_list, Mol, n_reac, laser, dt_KMC, file_rate, number_photons, params); // Do the reaction as if it was + + int numero_mol = reaction_list[n_reac].n_mol; // Numéro de la molécule affectée + int numero_laser = reaction_list[n_reac].n_laser; // Numéro du laser +// cout << " laser numéro " << numero_laser << endl; + + Internal_state Internal_state_in = Mol[numero_mol]; // état interne de la molecule initialement + Internal_state Internal_state_out = reaction_list[n_reac].final_internal_state; // état interne de la molecule après la réaction + Vecteur3D k_photon_transfer_to_particle; // momentum (wave vector) of the photon transfert to the atoms + Vecteur3D k_laser = reaction_list[n_reac].k_eff_laser; // it can be zero in the case of lattice for instance (no momentum transfer) + // Is Vecteur3D(k,0.,0.) in spontaneous emission and laser_wavector for absorption or emission. + + if (numero_laser != spon_emission) // Absorption or stimulated emission + { + if (Internal_state_out.Energy_cm > Internal_state_in.Energy_cm) // TODO (dc#8#): Could be a problem for real diagonalization but here all upper states are above the lower ones so this order is respected + k_photon_transfer_to_particle = k_laser; // For emission + else + k_photon_transfer_to_particle = -k_laser; // For absorption (low --> up) photon = photon laser but for stimulated emission (up --> low) k_photon = - k_photon laser + } + else // Il y a de l'emission spontanée + { + int delta_M = (Internal_state_out.two_M - Internal_state_in.two_M)/2 ; + Vecteur3D e_pol_dipole_transition = reaction_list[n_reac].pol_vector; + Vecteur3D quantization_axis = reaction_list[n_reac].quant_axis; + Vecteur3D k_photon_unit_vector = get_unit_vector_spontaneous_emission(r, e_pol_dipole_transition, quantization_axis, delta_M, params); // Gives a random unit vector (in the lab frame) for the spontaneous emission + // double p_trans = 100.*hPlanck*(Internal_state_in.Energy_cm - Internal_state_out.Energy_cm); // impulsion de recul (i.e. celle du photon pour l'absorption, - celle pour l'émission) // Impulsion p = hbar*k = 100 h sigma(cm^-1) + k_photon_transfer_to_particle = k_laser.mag()*k_photon_unit_vector; + } + Mol[numero_mol] = Internal_state_out; // c'est l'état interne de la molecule après réaction + Vecteur3D delta_v = HBAR*k_photon_transfer_to_particle / Mol[numero_mol].get_mass(); // Emission spontanée aléatoire, p = hbar k + Mol[numero_mol].inc_vel(delta_v); // impulsion p = \hbar k = m v ; + + // MODIFY THE STATUS OF THE PARTICLES + // May be also need to change the name ? + if (Mol[numero_mol].exc == photoionized) + { + Mol[numero_mol].set_mass (Mol[numero_mol].get_mass() - ME); + Mol[numero_mol].set_charge(-QE); + } + if (Mol[numero_mol].exc == photodetached) + { + Mol[numero_mol].set_mass(Mol[numero_mol].get_mass() - ME); + Mol[numero_mol].set_charge(0.); + } + if (Mol[numero_mol].exc == annihilation) + { +// Mol[numero_mol].set_mass(0.); // We keep the same mass for now + Mol[numero_mol].set_charge(0.); // Change only the charge --> No problem for Lorentz force + } + + number_photons ++; + + return numero_mol; +} + +// Gives a random unit vector (in the lab frame) for the spontaneous emission for a transition delta_M=-1,0,+1 and a quantization axis +// Or (if diagonalized) for a polarization vector e_pol: +// e_pol[q] = normalized dipole transition ; q=-1,0,1. So in the quantification axis e_pol = sum_q epol_q E^q +// the probability distribution linked with f(r)= (3/8Ï€)[1-|r.e_pol|^2] +Vecteur3D get_unit_vector_spontaneous_emission(const gsl_rng * r, Vecteur3D e_pol_dipole_transition, Vecteur3D quantization_axis, int delta_M, FitParams ¶ms) +{ + Vecteur3D point; + if ( (params.LocateParam("is_Levels_Lines_Diagonalized")->val) ) + /** There is diagonalization so vector e_pol + + + So to produce the desired spontaneous emission patern for the random variable r. We use the + Acceptance-rejection sampling method (Von Neumann): + https://fr.wikipedia.org/wiki/Méthode_de_rejet (The wikipedia algorithm is better in the French version) + + + such that r(θ, φ) has the probability distribution linked with f(r)= (3/8Ï€)[1-|r.e_pol|^2] + + But because the differential element is dΩ = d(cos θ)dφ. + + + We first choose randomly an r in an isotropy distribution: + (Isotropy means the density is proportional to solid angle + (so cos θ is uniform u=(2u1 − 1) and φ is uniform (2Ï€ u2) for u1 and u2 uniform in [0,1]). + + 1) we choose u randomly in [-1,1] et φ uniform in [0,2Ï€]. + + So with the probability distribution g(u,φ)=1/(4 Ï€) X_[-1,1](u) X_[0,2 Ï€](φ) (that is uniform =1/(4pi)) + + f(u,φ) = 3/(8 Ï€) [1-|r(u,φ).e_p|^2] =< 3/(8 Ï€) X_[-1,1](u) X_[0,2 Ï€](φ) = 3/(8 Ï€) * (4 Ï€) g(u,φ) = 1.5 g(u,φ) + + 2) we choose v randomly in [0,1] and keep the r(theta is given by the angle phi, theta) found if v < f(u,φ) / (1.5 g(u,φ)). If not we go back to 1. + + We use 3/(8 Ï€) F= f and 1/(4 Ï€) G = g so v < f(u,φ) / (1.5 g(u,φ)) = 3/(8 Ï€) F/(1.5 * 1/(4 Ï€) G ) = F/G + + **/ + { + double cos_theta,phi,v; // random variables u = cos_theta + double sin_theta; + Vecteur3D e_pol = e_pol_dipole_transition/e_pol_dipole_transition.mag(); // e_pol[q] = normalized dipole transition ; q=-1,0,1 + // e_pol = sum_q epol_q E^q in the quantification frame + double F; // probability distribution + do + { + cos_theta = gsl_ran_flat (r, -1., 1.); // cos (theta) + phi= gsl_ran_flat (r, 0, 2.*pi); + v = gsl_ran_flat (r, 0, 1); + sin_theta = sqrt(1.-cos_theta*cos_theta); + // f= is ( 3. /(8.*pi) )* F + F= 1. - pow((sin_theta)*(e_pol(2)-e_pol(0))*cos(phi)/sqrt(2.)+e_pol(1)*cos_theta,2) - pow((sin_theta)*(e_pol(0)+e_pol(2))*sin(phi)/sqrt(2.),2) ; // F=1-|r(uφ,),.e_p|^2 + } + while (v > F); + point= Vecteur3D(sin_theta*cos(phi),sin_theta*sin(phi),cos_theta);// Vecteur unitaire du vecteur d'émission spontanée dans le repère de l'axe de quantification. + } + else /** There is no diagonalization so + the states are Pure and transition are between given M states so the calcul is analytical + + Selon D. Steck "Classical and Modern Optics" 17.70 ou "Quantum and Atom Optics" 1.47 ou De façon plus générale les formules sont données par Eq. (7.436) + angular-distribution function for linear and circular polarization are + fˆz(θ, φ) = 3/8Ï€ sin^2(θ) et f±(θ, φ) = 3/16Ï€ (1 + cos^2(θ)) + De facon générale la formule est donnée par + f_(e_p)(r)= (3/8Ï€)[1-|r.e_p|^2] + avec e_p le vecteur de polarisation e_p = z pour linéaire (pi) et e_(+/-) = ∓(ˆx ± iˆy)/√2 en circulaire + + On retrouve aussi ( the probability density distribution for the projection of spontaneous emission along one axis + (3/8p_recoil)[1 + p^2/p_recoil^2]) + + Pauline Yzombard made the calculation (cf Master thesis)! ON utilise ses résultats ici + + **/ + { + double u = gsl_ran_flat (r, -1., 1.); // tirage au hazard distribution uniforme sur [-1,1]; // nombre aléatoire pour ennsuite calculé la distribution pour theta par F^-1(u) + double theta=0.; // Angle de l'émission spontanée + + if (delta_M !=0) //Pour transition sigma+/sigma-. Densité de proba :3/(16 PI)* 1+cos²(théta) + { + double D1=2.*u+sqrt(1.+4.*u*u); + double g1=(-1.+pow(D1,2./3.))/(1.*pow(D1,1./3.)); + theta=acos(g1); + } + else // transition Pi. densité de proba :3/(8 PI)sin²(théta) + { + complex D2; + complex g2; + D2 =complex(u,0.)+sqrt(complex(-1.+u*u,0.)); + g2=(-1.*(complex(1.,0.)+pow(D2,2./3.))+complex(0,sqrt(3.))*((complex(1.,0.)-pow(D2,2./3.))))/(2.*pow(D2,1./3.)); + theta=acos(g2.real()); + } + + double phi = gsl_ran_flat (r, 0., 2.*pi); + point= Vecteur3D(sin(theta)*cos(phi),sin(theta)*sin(phi),cos(theta));// Vecteur unitaire du vecteur d'émission spontanée dans le repère de l'axe de quantification. + } + + Vecteur3D Angles_quantization_labo; + Angles_quantization_labo = Euler_angles(quantization_axis); // We rotate the axis. because the quantization frame is not the lab frame + return rotation_axis_lab(point, Angles_quantization_labo.x(), Angles_quantization_labo.y(), Angles_quantization_labo.z()); // k_spon_unit_vector +} + + +/***********************************************/ +/********** taux forcés *********/ +/***********************************************/ + +// Repompage forcé +void Repompage( vector &rate, vector &reaction_list,const Molecule &Mol, const double t, const int numero_mol, const vector &laser, const int N_Mol, FitParams ¶ms) +{ + const int Num_laser = laser.size(); + const int num_niveau_first = (int) params.LocateParam("num_niveau_first")->val; // numéro du niveau étudié pour faire des stats. -1 pour toutes les molécules + const int num_niveau_second = (int) params.LocateParam("num_niveau_second")->val; // numéro du niveau de moindre pente pour le Sisyphe + const int num_niveau_exc = (int) params.LocateParam("num_niveau_exc")->val; // numéro du niveau excité + + double Temp_ini = params.LocateParam("Temp_ini")->val ; // température initiale + const double DE_temp_cm1 = - (1./(hPlanck*100.*C)) * kB*Temp_ini ; + + double scale_temp_rep = params.LocateParam("scale_temp_rep")->val; + // double Tau_Modif = params.LocateParam("Tau_Modif")->val ; + double DE_repomp_cm = scale_temp_rep*DE_temp_cm1; // Nouvelle énergie de transition kB T * scale > 0 + double rate_repompe = params.LocateParam("rate_repompe")->val; // taux de repompage + double E0_coupure_repompe_cm = params.LocateParam("E0_coupure_repompe_cm")->val; // valeur seuil sous laquel on repompe (même à T=0) + +// cout << " Ratio E_repom/KB T " << DE_repomp_cm/E_Temp_estime_cm << endl; + + + // + // Repompage si r < waist laser repompeur + //if (( Mol[i].get_pos().mag() < (my_laser[1].get_waist()).x() ) && !Mol[i].is_equal(Levels[num_niveau_first])) + // if ( Mol[i].Energy_cm < 33.35601 + DE_repomp_cm && !Mol[i].is_equal(Levels[num_niveau_first]) ) + int nb_rate = rate.size(); + if ( Mol.Energy_cm < E0_coupure_repompe_cm + DE_repomp_cm ) + { + Internal_state Internal_state_out = *( Mol.liste_raies[0].first) ; // état interne de la molecule après la réaction + rate[nb_rate] = rate_repompe; + type_codage_react reaction = { numero_mol, Num_laser, Vecteur3D(1.,0.,0.), Vecteur3D(1.,0.,0.), Vecteur3D(1.,0.,0.), Internal_state_out}; // {n_mol; n_laser; quant_axis; pol_vector; k_eff_laser; final_internal_state;}. IN this case the k_eff_laser is not important (we put axe_quant but any other values will do ) + + reaction_list[nb_rate] = reaction; // On met un numéro de laser quelconque Num_laser = Nb_laser et pas d'impuslion + nb_rate++; + // cout << " repompage vers " << Internal_state_out.Energy0_cm << endl; + // Mol[i] = Levels[num_niveau_exc]; // repompage + // set_all_pot_state(Mol[i], my_laser, nombre_niveaux); //Met à jour (pour recalculer les bonnes transitions) du potentiel + } + +// double scale_temp_pompage = params.LocateParam("scale_temp_pompage")->val; +// double DE_pomp = scale_temp_pompage*E_Temp_estime_cm; +// double B_Field_estime2 = Levels[num_niveau_second].Field_Shift_B_cm(DE_pomp); // Champ magnétique correspondant au shift +// double DE_pomp_max = Levels[num_niveau_first].Energy_Shift_B_cm(B_Field_estime2); // Energy max permise pour le pompage Sisyphe. Sinon on retombe dans la zone dénergie que l'on pompe! +// + + +// cout << " Ratio E_pom_max/KB T " << DE_pomp_max/E_Temp_estime_cm << endl; // + + + // double DE_pomp = - DE_temp_cm1*param[1]*exp(-t/param[3]); // >0 ici + // Dépompage forcée si Energie > seuil + // if ( Mol[i].Energy_cm - Mol[i].Energy0_cm > DE_pomp && Mol[i].is_equal(Levels[num_niveau_first]) ) +// if ( (Mol[i].Energy_cm - Mol[i].Energy0_cm > DE_pomp) && (Mol[i].Energy_cm - Mol[i].Energy0_cm < DE_pomp + 0.0001 ) ) +// { +// Mol[i] = Levels[num_niveau_exc]; // pompage vers excité +// // Mol[i] = Levels[num_niveau_second]; // pompage vers M=0 +// +// cout << " MOL " << i << " pompée à distance (mm)= " << Mol[i].get_pos().mag()*1000. << endl; +// +// set_all_pot_state(Mol[i], my_laser, nombre_niveaux); //Met à jour (pour recalculer les bonnes transitions) du potentiel +// } + + + + +} + + +// Pompage optique forcé en bord extérieur pour transferer dans le potentiel moins piégeant +// SI la distance diminue on est dans le piège le moins profond +// Si la distance augmente afin de perdre de l'énergie on est dans l'autre potentiel +void pompage_rv(vector &rate, vector &reaction_list, const vector &Mol, const double t) +{ +// +// double epsilon = 1e-3; +// for (int i = 0; i != N_Mol ; ++i) +// { +// if ( (Mol[i].get_pos()).dot(Mol[i].get_vel()) < - epsilon ) // r.v <0 la molécule descend le potentiel (r diminue), il faut donc la mettre dans le potentiel du bas! +// { +// // file_rate << " MOL " << i << " AU bord " << endl; +// if ( (Mol[i].exc != fond) || (Mol[i].v !=1) || (Mol[i].J != 3) || (Mol[i].M != 3) ) +// { +// // file_rate << " POMPAGE pour Mol " << i << endl; +// +// file_rate << t << " pomp " << Mol[i].get_pos().mag() << " " << i << endl; // position du pompage +// // Sortie_rate(file_rate, rate, reaction_list, Mol, t); +// +// // file_rate << t << " pomp " << (Mol[i].get_pos()).dot(Mol[i].get_vel()) << endl; // position du pompage +// +// +// Mol[i].exc = fond; +// Mol[i].v = vA_ini; +// Mol[i].J = JA_ini; +// Mol[i].M = MJA_ini; +// } +// } +// if ( (Mol[i].get_pos()).dot(Mol[i].get_vel()) > epsilon ) // r.v >0 la molécule monte le potentiel (r augmente), il faut donc la mettre dans le potentiel su haut! +// { +// //file_rate << " MOL " << i << " descend " << endl; +// if ( (Mol[i].exc != fond) || (Mol[i].v !=0) || (Mol[i].J != JX_ini) || (Mol[i].M != MJX_ini) ) +// { +// Mol[i].exc = fond; +// Mol[i].v = vX_ini; +// Mol[i].J = JX_ini; +// Mol[i].M = MJX_ini; +// +// +//// file_rate << " REPOMPAGE pour Mol " << i << endl; +// file_rate << t << " repomp " << Mol[i].get_pos().mag() << " " << i << endl; // position du repompage +// // Sortie_rate(file_rate, rate, reaction_list, Mol, t); +// // file_rate << t << " repomp " << (Mol[i].get_pos()).dot(Mol[i].get_vel()) << endl; // position du pompage +// +// } +// } +// } +// +// return; +} + + diff --git a/Main Code 64bits/Transition_rate_calcul.h b/Main Code 64bits/Transition_rate_calcul.h new file mode 100644 index 0000000..027db9a --- /dev/null +++ b/Main Code 64bits/Transition_rate_calcul.h @@ -0,0 +1,177 @@ +/* + Name: Algorithme de calcul des taux + Author: Daniel Comparat + Date: 16/12/08 + + +REMARQUES: +La prédissociation est traitée comme un parametre phénoménologiue +Les transition a deux photons aussi +la desexcitation dans le continuuum peut être prise en compte car parfois Sum_FC != 1 la partie non 1 est le continuum + + +ATTENTION +Unités des fichier (cm^-1) +Les lasers sont CW. + Dans le cas d'un laser femto il ne faut pas forcément mettre Imoyen cf thèse d'Antoine Monmayrant (IV.5) + +*/ + + +#ifndef Transition_rate_SEEN +#define Transition_rate_SEEN + +#include +using namespace std; + +#include // to include cout, cin +#include // to include sqrt(), etc. +#include "laser.h" // Classe Laser +#include "shift_molecule.h" // Pour le shift en énergie delta +#include "sortie_donnees.h" // Pour le shift en énergie delta +#include "Kinetic_Monte_Carlo.h" // to include the algorithm +#include "algorithmes.h" // to include Is_switch laser +#include // Pour les calculs d'émission spontanée + +#include // For matrix manipulation +using namespace Eigen; + +#include "params.h" // Pour mettre des paramètres dedans + +/************************************************************************/ +/************************** Interaction laser - 2 niveaux *************/ +/************************************************************************/ + +// Taux d'emission spontanée d'une transition (sans prendre en compte l'ordre des états: +double Gamma_spon(const double dip_Debye, const double energie_cm); + + +// Forme gaussienne Gamma = FWHM = 2 \sqrt{2 \ln(2)} \sigma = 2.3548 \sigma +inline double Gauss(const double I_tot, const double delta, const double Gamma); + +// Forme laser plate +// retourne l'intensité (spectrale) au décalage delta souhaité +inline double intensity_flat(const double I_tot, const double delta, const double Gamma); + +// Forme lorentzienne +// I*Gamma/(2.*pi)/(Gamma^2/4 + delta^2) +inline double Lorentz(const double I_tot, const double delta, const double Gamma); + +// Approximation of the Voigt profile [Lorentz*Gaussian](omega) where Lorentz and Gaussian FWHM values of G_L and G_G and centered on 0. +double Pseudo_Voigt(double delta, const double G_L, const double G_G); + + +// comb spectum = gaussian laser but with individual Lorentzian comb lines +// the comb line are positioned at nu_offset + n*nu_repetition +// The intensity is taken at the detuning of the nearest (lorentizian) comb line +// The linewidth is due to the spontaneous emission of the 2 levels system drived by the comb laser +double comb_shape(double I,double delta, const double G_L, const double G_G, const int n_las, const double Energy_transition_cm, FitParams ¶ms); + + +// intensity of a pseudo_BBR (pseudo_Black Body Radiation) that is a BBR spectrum but with a gaussian beam +inline double pseudo_BBR_intensity(const double I, const double Energy_transition_cm, const double T); + + + +// Calcul de l'intensité locale [Lorentz*I](omega) with a natural Cauchy-Lorents linewitdh with FWHM Gamma_atomic. +// delta = omega_Laser - omega_atomic +double intensity_Convolution_linewidth(const double I, const double delta, const double Gamma_atomic, const double Gamma_Laser, const int laser_type, const int n_las, const double Energy_transition_cm, const double Energy_transition_laser_cm, FitParams ¶ms); + +// Taux à deux niveau Gamma' +// is_bound_transition is here to detcte transition (ionization) to continuum (0 = false that is ioniozation ; 1 = true that is bound - bound transition +double rate_two_level(const double I_loc, const double dip_Debye); + +// Rate for (photo-)ionization +double rate_ionization(const double I_loc, const double dip_Debye, const double delta, const double Energy_transition_cm); + +// Field ionization rate +double rate_field_ionization(const Laser& my_laser, const vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE); + +// Calculation of the excitation rate ofr a laser (or a class of coherent laser) for a given transition (bound or ionization) +// Add this rate only is is_rate_calculated is true +double rate_excitation(vector &reaction_list, vector &rate, const int n_las, const vector &Mol, const int n_mol, const Vecteur3D k, const double Itot_loc, const double Itot, + const double dipole_debye, const double delta, const double Energy_transition_cm, const Field &fieldB, const Field &fieldE, const int is_bound_transition, const Internal_state Internal_state_out, const bool is_rate_calculated ); // calculate rate and reaction_list for this transition + +/************************************************************************/ +/************************** Fonctions transition Molecule ***************/ +/************************************************************************/ + +// Calcul de tous les taux d'emission spontanée de la molécule +int rates_molecule_spon(vector &Level, vector &reaction_list, vector &rate, const Molecule &my_mol, const Field &fieldB, const Field &fieldE, const int num_mol, FitParams ¶ms); + + +// Calcul of rate (if no interferece between laser) between level in and out for a given laser and for a given molecule. This add the light shift effect to the dipolar potential (delta_pot_dipolaire) +// update the detuning (delta), the polarization vector also updated), Gamma_spot_total, sqrt of the local intensity of the laser +int rates_single_molecule_laser_level(const int n_las, double dipole, double &delta, double &eps_pol, double &Gamma_spon_tot, double sqrt_intensity_loc[], + vector &Level, Internal_state &Internal_state_in, Internal_state &Internal_state_out, vector &reaction_list, vector &rate, + const vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const Laser &my_laser, const double t, double &delta_pot_dipolaire, + FitParams ¶ms, bool is_rate_calculated, int is_bound_transition=1, const int n_level_in =0, const int n_level_out =1, const double Gamma_in=0., MatrixXd d[]= {}); + + +// Calcul de tous les taux de la molécule pour tous les lasers +// On les ajoutes aux taux des autres +// return nb_rate +// It calculate also the dipole detuning which is just rate * delta/Gamma +// In this last case we do not necessarily to calculate the rate, as for the dipolar shift, so is_rate_calculated would be false +int rates_molecule(vector &Level, vector &reaction_list, vector &rate, + const vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, double &delta_pot_dipolaire, FitParams ¶ms, bool is_rate_calculed = true); + + + + + + +// return the decay rate from Level i = sum_j &Level, MatrixXd d[], const int i); + + + +// Copie tous les taux sauf celui de la molécule numero_mol +// Retourne le nombre de taux de ces molécules +int copie_rates_molecules(vector &reaction_list, vector &rate, const int numero_mol = -1, const int nombre_old_rate = 0); + + +// Calcul de tous les taux de toutes les molécules si numero_mol = aucune (-1) +// Sinon on ne recalcule que celui de la molécule numero_mol +int calcul_rates_molecules(vector &Level, MC_algorithmes Algorithme_MC, vector &reaction_list, vector &rate, const vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, + const double t, const int numero_mol, const int N_Mol, FitParams ¶ms ); + + + +/***********************************************/ +/********** réalisation d'une réaction *********/ +/***********************************************/ + + +// Scan all rates and realize the reaction if the rate*random < dt=0.1/rate_max +// We scan all molecules and make at most one rate per molecule but +// Typically a tens of Molecules will be affected +int do_reaction_FastRoughMethod(const MC_algorithmes Algorithme_MC, const gsl_rng * r, const vector &rate, const vector &reaction_list, vector &Mol, + const int n_reac, const vector &laser, const double dt_KMC, ofstream & file_rate, int &number_photons, FitParams ¶ms); + +// Effectue la réaction. Ne met pas les potentiels à jour ensuite. Il faut le faire à part. +// Retourne le numéro de la molécule affectée +int do_reaction(const MC_algorithmes Algorithme_MC, const gsl_rng * r, const vector &rate, const vector &reaction_list, + vector &Mol, const int n_reac, const vector &my_laser, const double dt_KMC, ofstream & file_rate, bool first_call, int &number_photons, FitParams ¶ms); + +// Gives a random unit vector (in the lab frame) for the spontaneous emission for a transition delta_M=-1,0,+1 and a quantization axis +// Or (if diagonalized) for a polarization vector e_pol: +// e_pol[q] = normalized dipole transition ; q=-1,0,1. So in the quantification axis e_pol = sum_q epol_q E^q +// the probability distribution linked with f(r)= (3/8Ï€)[1-|r.e_pol|^2] +Vecteur3D get_unit_vector_spontaneous_emission(const gsl_rng * r, Vecteur3D e_pol_dipole_transition, Vecteur3D quantization_axis, int delta_M, FitParams ¶ms); + + +/***********************************************/ +/********** taux forcés *********/ +/***********************************************/ + +// Repompage si r < waist laser repompeur +void Repompage( vector &rate, vector &reaction_list, const Molecule &Mol, const double t, const int numero_mol, const vector &laser, const int N_Mol, FitParams ¶ms ); + +// Pompage optique forcé en bord extérieur pour transferer dans le potentiel moins piégeant +// SI la distance diminue on est dans le piège le moins profond +// Si la distance augment afin de perdre de l'énergie on est dans l'autre potentiel +void pompage_rv( vector &rate, vector &reaction_list, const vector &Mol, const double t); + + +#endif diff --git a/Main Code 64bits/Transitions_initialisation.cpp b/Main Code 64bits/Transitions_initialisation.cpp new file mode 100644 index 0000000..3e0f49e --- /dev/null +++ b/Main Code 64bits/Transitions_initialisation.cpp @@ -0,0 +1,477 @@ +/* + +Lecture de +Facteurs de Franck-Condon +Energies des niveaux de vibration (la rotation est ensuite calculée par le Bv) +Calculs de facteurs angulaires liés à la rotation + + +Il y a FC_abs pour l'absorption et FC_em pour l'emission + +On utilise de façon générique le nom +X pour l'état fond +A pour l'état excité +donc vX, vA pour les niveaux vibrationnels et +JX, JA pour la rotation + + + + +Il y a donc des tableaux +FC_abs[vA][vX] // Qui contient un Franck Condon pour l'absorption (Normalisés à 1 pour avoir le bon taux de transition) +proba_abs[JA][MJA][JX][MJX] et proba_em[[JA][MJA][JX][MJX] // Qui contient les facteurs genre Hönl London (Normalisés à 1 pour avoir le bon taux de transition) +// En fait pour eviter des indices <0 on note [JA][MJA+JA][JX][MJX+JX] + +FC_em[vA][vX] // Qui contient un Franck Condon pondéré par un terme en (omega/omega_moyen)^3 pour tenir compte de la durée de vie + +EvX[vX][JX] // Energie des états vX, JX, Pour l'instant très simple avec Bv seul +EvA[vA][JA] // Energie des états vA, JA + + +Les bordures sont absorbantes +i.e. les états de vmax ou Jmax ont des Franck Condon de zéro et restent ainsi piégés + + +LES UNITES ICI SONT CELLES DES FICHIERS (cm^-1 typiquement) + +ATTENTION +La notation [NA][NX] indique qu'il y a +NA lignes et NX colonnes dans les tableaux +Il faut donc bien vérifier que dans les fichiers +vA indice les lignes et vX indice les colonnes + +En effet les boucles sont vA puis vX + + +*/ + +#include "Transitions_initialisation.h" + + +/*** Program to read Line or Energy list from Pgopher ***/ + +// Author: Daniel Comparat +// Date: 12/02/2012 + + + +/** ENERGY LIST **/ +// PGOPHER Gives +// Molecule Manifold M Sym # g Population Label Energy Linear Dipole Err Quadratic Err Two_Level Energy Delta C Dipole2 Err +// WE DO NOT USE IT LIKE THAT BUT USING ORIGIN WE MODIFY AND USE ONLY +// Manifold(1 for upper or 0 for lower typically) M(in Field it is real M) Sym(Parity +/-) #(number to discriminate the levels) Population J N Energy0(in 0 field) Delta C +// Where for fit in Energy in Fields Energy +/- Sqrt(Delta^2/4 + C^2*F^2) where F is field +// C= Linear coefficient is in cm-1/T +// Energy and Delta are in cm-1 + +/*** Program to read Line or Energy list from Pgopher ***/ +// PGOPHER Gives +// Molecule Manifold M Sym # g Population Label Energy Linear Dipole Err Quadratic Err Two_Level Energy Delta C Dipole2 Err +// WE DO NOT USE IT LIKE THAT BUT USING ORIGIN WE MODIFY AND USE ONLY +// Manifold(1 for upper or 0 for lower typically) M(in Field it is real M) Sym(Parity +/-) #(number to discriminate the levels) J N Energy0(in 0 field) Delta C +// Where for fit in Energy in Fields Energy +/- Sqrt(Delta^2/4 + C^2*F^2) where F is field +// C= Linear coefficient is in cm-1/T +// Energy and Delta are in cm-1 + +// Retourne le nb de niveaux (1 si contient seulement Level[0]) +int Pgopher_Level_List(const char *nom_file, vector &Level, FitParams ¶ms) +{ + Level.clear(); + ifstream file(nom_file); + if ( !file ) + { + cerr << "Erreur d'ouverture fichier Level" << nom_file << endl; + return 0; + } + + int i=0; // Compteur du nombre de niveaux + + int type_of_field_for_internal_state_shift = params.LocateParam("type_of_field_for_internal_state_shift")->val; + + while (!file.eof()) + { + Internal_state Current_Level; + if (type_of_field_for_internal_state_shift == 0) // Zeeman effect + Current_Level.read_Level_Pgopher_B(file); // read the new level + if (type_of_field_for_internal_state_shift == 10) // Stark effect + Current_Level.read_Level_Pgopher_E(file); // read the new level + Level.push_back(Current_Level); + i++; + // cout << i << " " << Level[i].Energy0_cm << " " << Level[i].Delta_FieldB << endl; + } + file.close(); + return i; +} + +/*** LINE LIST *****/ +// Read the file containing the position, assignment and intensity of lines in the simulated spectrum. +// Retourne le nb de transitions +// C'est une liste qui depuis l'état de départ pointe vers tous les états d'arrivés possible +int Pgopher_Line_List(const char *nom_file, vector &Level, FitParams ¶ms) +{ + int nb_levels = Level.size(); + + ifstream file(nom_file); + + if ( !file ) + { + cerr << "Erreur d'ouverture fichier Lignes" << nom_file << endl; + return 0; + } + + Internal_state Up_state, Low_state; + double Spol,position,intensity; // Intensité de la raie en Debye^2 + + int i=0; // Compteur du nombre de transitions + + while (!file.eof()) + { + read_Line_Pgopher(file, Up_state, Low_state, Spol,position,intensity); // Transition Up_state --> Low_state avec force Spol +// On ajoute ensuite à la liste des raies le vrai niveau car il contient plus d'informations (en particulier les variations en champ E et B) +// que celui donné dans le fichier de liste des raies + int n_up = -1; + int n_low = -1; + for (int j = 0; j < nb_levels; j++) // Boucle pour voir dans la liste des niveaux où sont Up_state et Low_state + { + if (Level[j].is_equal (Up_state)) + n_up=j; + if (Level[j].is_equal (Low_state)) + n_low=j; + + } + + // cout << " Transition entre niveau num. " << n_up << " et " << n_low << endl; + if ((n_up != -1) && (n_low != -1)) // if we have find the corresponding levels then add the transition + { + Level[n_up].add_transition ( &(Level[n_low]), Spol); // Ajoute la transition Up_state --> Low_state avec force Spol + Level[n_low].add_transition ( &(Level[n_up]), Spol); + i++; + } + } + file.close(); + return i; + +} + + + +/************************************************************************/ +/************************** INITIALISATION FC, Energie, HL **************/ +/************************************************************************/ + +// Initialisation des durées de vies +void initialisation_Gamma( vector &Level, FitParams ¶ms) +{ + int nb_Levels = Level.size(); + for (int i = 0; i < nb_Levels; i++) // Boucle pour voir dans la liste des niveaux où sont Up_state et Low_state + Level[i].one_over_lifetime = Level[i].Einstein_desex_rate(); + + if (( (int) params.LocateParam("if_fixed_lifetime")->val) == ((int) true)) + { + for (int i = 0; i < nb_Levels; i++) + { + if ( Level[i].exc > 0) // Not ground state (0) neither continuum ones (<0) + Level[i].one_over_lifetime = 1./params.LocateParam("duree_vie")->val; + } + } +} + + + +// Initialisation des probabilités de peuplement de départ +void initialisation_proba(const gsl_rng *r, vector &Mol, const int Nb_molecules, const vector &Level) +{ + + int nb_Levels = Level.size(); + + double *proba = new double[nb_Levels]; // We can not use vector proba because of gsl_ran_discrete_preproc + + for (int i=0; i &Level, FitParams ¶ms, DataCards data) +{ + + /*******************************************************/ + /******************** Molecular data (cm-1) ************/ + /*******************************************************/ + + + /** Nom files **/ + + const char *nom_file_FC_vAvX = data.SParam("nom_file_FC_vAvX").c_str(); // File containing FC factors between vA (colonne) and vX (lignes) + const char *nom_file_E_vA = data.SParam("nom_file_E_vA").c_str(); // File containingles energies of the A state (vA, E_vA, Bv) + const char *nom_file_E_vX = data.SParam("nom_file_E_vX").c_str(); // File containingles energies of the A state (vX, E_vX, Bv) + + /*********** Declaration of datas + + BE CAREFUL !!!!!!!!!!!!!!! + ORDER FOR THE NOTATIONS + [A][X] and [v][J] + so: + + EvX[vX][JX] // Energy of vX, JX states + EvA[vA][JA] // Energy of vA, JA states + + *************/ + + + const int NXmax=params.LocateParam("NXmax")->val; // Nb of vibrational levels in X state; 0,1,...,NXmax-1 + const int NAmax=params.LocateParam("NAmax")->val; // Nb of vibrational levels in A state; 0,1,...,NAmax-1 + + const int NX_out=params.LocateParam("NX_out")->val; // Nb of vibrational levels in X state (dans le fichier final) + const int NA_out=params.LocateParam("NA_out")->val; // Nb of vibrational levels in A state (dans le fichier final) + + + + const int N_Two_JX_out_max = params.LocateParam("N_Two_JX_out_max")->val; // Nb of vibrational levels used to calculate X state; 0,1,...,NX-1 + const int N_Two_JA_out_max = params.LocateParam("N_Two_JA_out_max")->val; // Nb of vibrational levels used to calculate A; 0,1,...,NA-1 + + + double **EvX=new double*[NXmax]; + for (int vX=0; vX> FCondon[vA][vX] ; // Read the file FC_vA_vX + // cout << "vX = " << vX << " vA = " << vA << " FC_abs[vA][vX] = " << FCondon[vA][vX] << endl; + } + + file_FC.close(); + + return; +} + + +// Energy of vibrational levels +// The file format is v Ev Bv +void initialisation_energie(double **Ev, const char *nom_file_E_v, const int Nvmax, const int N_Two_J_max, const double E_v0_J0) +{ + + ifstream file_EV(nom_file_E_v); // The file format is v Ev Bv + + for (int vi = 0; vi < Nvmax; vi++) + { + int v; + double Bv; + file_EV >> v; + file_EV >> Ev[v][0]; // We calculate the hypothetic energy of J=0 + file_EV >> Bv; + + + for (int two_J = 0; two_J < N_Two_J_max; two_J++) + { + Ev[v][two_J] = Ev[v][0]+Bv*(two_J/2.)*(two_J/2.+1.); // Rotationel levels Bv J (J+1) + } + } + + double decalage = E_v0_J0 - Ev[0][0]; + for (int v = 0; v < Nvmax; v++) + for (int two_J = 0; two_J < N_Two_J_max; two_J++) + Ev[v][two_J] += decalage; // Dacay of energy in order to get the right origin of energy + + file_EV.close(); + + return; +} + +#include // pour ostringstream +#include // pour steprecision +void New_Pgopher_Level_Line(const char *nom_file_initial_Level, const char *nom_file_initial_Line, vector &Level, double **FC, double **EvX, double **EvA, int NXout, int NAout, int N_Two_JA_out_max, int N_Two_JX_out_max, FitParams ¶ms) +{ + int nb_Levels = Pgopher_Level_List(nom_file_initial_Level, Level, params); + + std::ostringstream oss; + oss << "_vX_" << NXout << "_vA_" << NAout << "_2JX_" << N_Two_JX_out_max-1 << "_2JA_" << N_Two_JA_out_max-1; + std::string num = oss.str(); // num = "[i]" + + string nom_file_short = (string(nom_file_initial_Level)).substr(0,string(nom_file_initial_Level).length() -4); // enlève le .dat + string nom_file_long = nom_file_short + num + ".dat"; + const char *nom_file_new_Level_Out = (nom_file_long).c_str(); // Nom_file[numero_laser].dat + ofstream file_Level_out(nom_file_new_Level_Out); // Fichier contenant les données + file_Level_out << setprecision(8); // POur avoir bien les tous les chiffres significatifs + + + nom_file_short = (string(nom_file_initial_Line)).substr(0,string(nom_file_initial_Line).length() -4); // enlève le .dat + nom_file_long = nom_file_short + num + ".dat"; + const char *nom_file_new_Line_Out = (nom_file_long).c_str(); // Nom_file[numero_laser].dat + ofstream file_Line_out(nom_file_new_Line_Out); // Fichier contenant les données + file_Line_out << setprecision(8); // POur avoir bien les tous les chiffres significatifs + + /********************* LEVELS ***************************/ + + double Bv0X= (EvX[0][2]-EvX[0][0])/2.; // entre J=1 (two_J=2) et J=0 on a Bv J(J+1) = 2 Bv + double Bv0A= (EvA[0][2]-EvA[0][0])/2.; // entre J=1 (two_J=2) et J=0 on a Bv J(J+1) = 2 Bv + + int Max_deg_Number = 10000; // Sécurité pour le max de dégénérescence + for (int i=0; i0 à 0 + if (Level[i].two_J < N_Two_JX_out_max) New_Level.write_Level_PgopherB(file_Level_out); + } + + if (Level[i].exc == 1) // etat A + for (int vA = 0; vA < NAout; vA++) + { + New_Level.v=vA; + New_Level.deg_number = Level[i].deg_number + Max_deg_Number*vA; // Nouvelle dégénérescence (on met une sécurité avec Nb_niveau qui est le max possible de la dégénéréscence) + New_Level.Energy0_cm = Level[i].Energy0_cm + EvA[vA][Level[i].two_J] - Bv0A* (Level[i].two_J/2.)*( Level[i].two_J/2.+1.); + if (vA != 0) New_Level.population = 0.; + if (Level[i].two_J < N_Two_JA_out_max) New_Level.write_Level_PgopherB(file_Level_out); + } + } + + file_Level_out.close(); + + /********************* LIGNES ***************************/ + + Internal_state Up_state, Low_state, New_Up, New_Low; + double Spol, New_Spol; + double position, New_position, Intensity, New_Intensity; + + ifstream file(nom_file_initial_Line); + + while (true) + { + read_Line_Pgopher(file, Up_state, Low_state, Spol, position, Intensity); + +// On cherche le vrai niveau en parcourant la liste des niveaux car il contient plus d'informations (en particulier J) +// que celui donné dans le fichier de liste des raies + int n_up=0; + int n_low=0; + for (int j = 0; j < nb_Levels; j++) // Boucle pour voir dans la liste des niveaux où sont Up_state et Low_state + { + if (Level[j].is_equal (Up_state)) + n_up=j; + if (Level[j].is_equal (Low_state)) + n_low=j; + } + + Up_state = Level[n_up]; // Copie toutes les infos du niveau + Low_state = Level[n_low]; + + for (int vX = 0; vX < NXout; vX++) + for (int vA = 0; vA < NAout; vA++) + { + New_Low = Low_state; + New_Low.v=vX; + New_Low.deg_number = Low_state.deg_number + Max_deg_Number*vX; // Nouvelle dégénérescence (on met une sécurité avec LARGE_NUMBER qui est le max possible de la dégénéréscence) + New_Low.Energy0_cm = Low_state.Energy0_cm + EvX[vX][Low_state.two_J] - Bv0X* (Low_state.two_J/2.)*( Low_state.two_J/2.+1.); // Rotationel levels Bv J (J+1). Permet de conserver la vrai progression pour v=0. Ensuite c'est le Bv théorique + if (Low_state.two_J >= N_Two_JX_out_max) continue; // Si pas le bon niveau on sort + + New_Up = Up_state; + New_Up.v=vA; + New_Up.deg_number = Up_state.deg_number + Max_deg_Number*vA; // Nouvelle dégénérescence (on met une sécurité avec Nb_niveau qui est le max possible de la dégénéréscence) + New_Up.Energy0_cm = Up_state.Energy0_cm + EvA[vA][Up_state.two_J] - Bv0A* (Up_state.two_J/2.)*( Up_state.two_J/2.+1.); + if (Up_state.two_J >= N_Two_JA_out_max) continue; + + New_Spol = Spol*FC[vA][vX]/FC[0][0]; + New_position = New_Up.Energy0_cm- New_Low.Energy0_cm; + New_Intensity = Intensity * FC[vA][vX]/FC[0][0]; + + if (New_Spol < sqrt(SMALL_NUMBER)) continue; // On ne prend que les transition importantes dipole ~ sqrt(Spol) + + write_Line_Pgopher(file_Line_out, New_Up, New_Low, New_Spol, New_position, New_Intensity); + } + if ( file.eof() ) + { + break; // test de fin de fichier + } + } + file_Line_out.close(); + file.close(); +} + diff --git a/Main Code 64bits/Transitions_initialisation.h b/Main Code 64bits/Transitions_initialisation.h new file mode 100644 index 0000000..8c75892 --- /dev/null +++ b/Main Code 64bits/Transitions_initialisation.h @@ -0,0 +1,96 @@ +/* + +Program to read Line or Energy list from Pgopher + + +LES UNITES ICI SONT CELLES DES FICHIERS (cm^-1 typiquement) + +Avant j'utilisaait des fichiers Franck-Condon et Hönl-London +Je les laisse ici mais il ne servent plus +La notation [NA][NX] indique qu'il y a +NA lignes et NX colonnes dans les tableaux +Il faut donc bien vérifier que dans les fichiers +vA indice les lignes et vX indice les colonnes + +En effet les boucles sont vA puis vX + + +*/ + + +#ifndef Transition_init_SEEN +#define Transition_init_SEEN + +#include +using namespace std; + +#include "Internal_state.h" +#include // for random generator +#include // for gaussian random generator + +#include "Molecule.h" // Classe molecule +#include "params.h" +#include "datacards.h" // Pour lire le fichier de paramètres + +#include // POUR les 3j de Wigner +// double gsl_sf_coupling_3j (int two_ja, int two_jb, int two_jc, int two_ma, int two_mb, int two_mc) +// gsl_sf_coupling_3j (2*ja,2*jb,2*jc,2*ma,2*mb,2*mc); +// compute the Wigner 3-j coefficient, + +// ja jb jc +// ma mb mc + +// where the arguments are given in half-integer units, ja = two ja/2, ma = two ma/2 +// Gives 0 in wrong cases + + +/*** Program to read Line or Energy list from Pgopher ***/ +// Manifold(1 for upper or 0 for lower typically) M(in Field it is real M) Sym(Parity +/-) #(number to discriminate the levels) Population J N Energy0(in 0 field) Delta C +// Where for fit in Energy in Fields Energy +/- Sqrt(Delta^2/4 + C^2*F^2) where F is field +// C= Linear coefficient is in cm-1/T +// Energy and Delta are in cm-1 +// Retourne le nb de niveaux (1 si contient seulement Level[0]) + int Pgopher_Level_List(const char *nom_file, vector &Level, FitParams ¶ms); + + +/*** LINE LIST *****/ +// Les fichiers contiennent + // UpperManifold M' Sym' #' LowerManifold M" Sym" #" Position Intensity Eupper Elower Spol +// Read the file containing the position, assignment and intensity of lines in the simulated spectrum. +// Retourne le nb de transitions +int Pgopher_Line_List(const char *nom_file, vector &Level, FitParams ¶ms); + + +// initalisation des probabilités de peuplement de départ +void initialisation_proba(const gsl_rng *r, vector &Mol, const int Nb_molecules, const vector &Level); + + + +/************************************************************************/ +/************************** INITIALISATION FC, Energie, HL **************/ +/************************************************************************/ + +// Initialisation des durées de vies +void initialisation_Gamma( vector &Level, FitParams ¶ms); + + +// Modification des fichiers de niveaux et de transitions en fonction des FC et des Energies +void Modification_FC_trans_mol(const char *nom_file_Levels, const char *nom_file_Lines , vector &Level, FitParams ¶ms, DataCards data); + + +// Initialization Of FC factors for absorption and emission +void initialisation_FC(double **FCondon, const char *nom_file_FC, const int NvAmax, const int NvXmax); + + +// Energy of vibrational levels +// The file format is v Ev Bv (en cm-1) +void initialisation_energie(double **Ev, const char *nom_file_E_v, const int Nvmax, const int NJmax, const double E_v0_J0 = 0.); + +// Crée le nouveau fichier de données à partir des FC. +// On lit un fichier de base contenant juste vX=0 et vA=0. Ensuite des FC et des Energie Ev et Bv des niveaux et on forme le nouveau ficheir +void New_Pgopher_Level_Line(const char *nom_file_initial_Level, const char *nom_file_initial_Line, vector &Level, double **FC, double **EvX, double **EvA, int NXout, int NAout, int N_Two_JA_out_max, int N_Two_JX_out_max, FitParams ¶ms); + + + +// Initi +#endif diff --git a/Main Code 64bits/TricubicInterpolation_module.cpp b/Main Code 64bits/TricubicInterpolation_module.cpp new file mode 100644 index 0000000..81b4f77 --- /dev/null +++ b/Main Code 64bits/TricubicInterpolation_module.cpp @@ -0,0 +1,384 @@ +#include "TricubicInterpolation_module.h" +#include "LekienMarsdenMatrix.h" + +using namespace std; + +//Costructor #0 +LM_Interpolator::LM_Interpolator() {}; + + +//Costructor #1 +LM_Interpolator::LM_Interpolator(int NewXDimension, int NewYDimension, int NewZDimension, double* Xvalues, double* Yvalues, double* Zvalues) +{ + Init(NewXDimension, NewYDimension, NewZDimension, Xvalues, Yvalues, Zvalues); +}; + +//Costructor #2 +LM_Interpolator::LM_Interpolator(int NewXDimension, int NewYDimension, int NewZDimension, double delta_x, double delta_y, double delta_z, double X0, double Y0, double Z0) +{ + Init(NewXDimension, NewYDimension, NewZDimension, delta_x, delta_y, delta_z, X0, Y0, Z0); +}; + + +void LM_Interpolator::Init(int NewXDimension, int NewYDimension, int NewZDimension, double* Xvalues, double* Yvalues, double* Zvalues) +{ + m_xdimension = NewXDimension; + m_ydimension = NewYDimension; + m_zdimension = NewZDimension; + // Prepare X positions array + m_xvalues = new double[m_xdimension]; + for(int i = 0; i< m_xdimension; i++) + { + m_xvalues[i] = Xvalues[i]; + } + // Prepare Y positions array + m_yvalues = new double[m_ydimension]; + for(int i = 0; i< m_ydimension; i++) + { + m_yvalues[i] = Yvalues[i]; + } + // Prepare Z positions array + m_zvalues = new double[m_zdimension]; + for(int i = 0; i< m_zdimension; i++) + { + m_zvalues[i] = Zvalues[i]; + } + // Prepare array for coefficients + m_coefficients = new double[64]; + // Assume that points are equipartitioned + m_delta_x = m_xvalues[1]-m_xvalues[0]; + m_delta_y = m_yvalues[1]-m_yvalues[0]; + m_delta_z = m_zvalues[1]-m_zvalues[0]; + //Allocate nonzero indices + PrepareLMIndicesArray(); +}; + +void LM_Interpolator::Init(int NewXDimension, int NewYDimension, int NewZDimension, double delta_x, double delta_y, double delta_z, double X0, double Y0, double Z0) +{ + m_xdimension = NewXDimension; + m_ydimension = NewYDimension; + m_zdimension = NewZDimension; + //Prepare X positions array + m_xvalues = new double[m_xdimension]; + for(int i = 0; i< m_xdimension; i++) + { + m_xvalues[i] = X0 + i*delta_x; + } + //Prepare Y positions array + m_yvalues = new double[m_ydimension]; + for(int i = 0; i< m_ydimension; i++) + { + m_yvalues[i] = Y0 + i*delta_y; + } + //Prepare Z positions array + m_zvalues = new double[m_zdimension]; + for(int i = 0; i< m_zdimension; i++) + { + m_zvalues[i] = Z0 + i*delta_z; + } + //Prepare array for coefficients + m_coefficients = new double[64]; + //Assume that points are equipartitioned + m_delta_x = delta_x; + m_delta_y = delta_y; + m_delta_z = delta_z; + + /* + cout<(floor((X-m_xvalues[0])/m_delta_x)); + m_yindex = static_cast(floor((Y-m_yvalues[0])/m_delta_y)); + m_zindex = static_cast(floor((Z-m_zvalues[0])/m_delta_z)); + //cout<= m_xdimension || m_xindex < 0 || m_yindex >= m_ydimension || m_yindex < 0 || m_zindex >= m_zdimension || m_zindex < 0) + { + //cout<= m_xdimension || m_xindex < 0 || m_yindex >= m_ydimension || m_yindex < 0 || m_zindex >= m_zdimension || m_zindex < 0) + { + cout< +and commented by Daniel Comparat using the commented code by + https://github.com/deepzot/likely/tree/master/likely + and + https://github.com/nbigaouette/libtricubic + + + + The headers required for the tricubic interpolation are + "TricubicInterpolation_module.h" and "LekienMarsden_matrix.h". + + You have to instantiate an object of class LM_Interpolator and give it the required input values. + + +**/ + +#ifndef TRICUBIC_LM_INTERPOLATION +#define TRICUBIC_LM_INTERPOLATION + +#include +#include +#include + + +/** +Map x,y,z to a point dx,dy,dz in the cube [0,n1) x [0,n2) x [0,n3) +**/ + +class LM_Interpolator +{ +public: + LM_Interpolator(); + LM_Interpolator(int NewXDimension, int NewYDimension, int NewZDimension, double* Xvalues, double* Yvalues, double* Zvalues); + LM_Interpolator(int NewXDimension, int NewYDimension, int NewZDimension, double delta_x, double delta_y, double delta_z, double X0 = 0, double Y0 = 0, double Z0 = 0); + void Init(int NewXDimension, int NewYDimension, int NewZDimension, double* Xvalues, double* Yvalues, double* Zvalues); + void Init(int NewXDimension, int NewYDimension, int NewZDimension, double delta_x, double delta_y, double delta_z, double X0 = 0, double Y0 = 0, double Z0 = 0); + ~LM_Interpolator(); + bool GetValue(double*** matrix, const double &x, const double &y, const double &z, double &ans, double &dervx, double &dervy, double &dervz); + bool EvaluateIndices(const double &x, const double &y, const double &z); + double GetValue(double*** matrix, const double &x, const double &y, const double &z); + const char* GetInterpolationType(); +protected: + int ijk_to_index(int i, int j, int k); + void PrepareLMIndicesArray(); + void GetLMIndices(int index, int& i, int& j); + void GetIndex(const double &x, const double &y, const double &z); + void Prepare_Coefficients(double*** matrix); + double PartialXDerivative(double ***matrix, int IndexX, int IndexY, int IndexZ); + double PartialYDerivative(double ***matrix, int IndexX, int IndexY, int IndexZ); + double PartialZDerivative(double ***matrix, int IndexX, int IndexY, int IndexZ); + double PartialXYDerivative(double ***matrix, int IndexX, int IndexY, int IndexZ); + double PartialXZDerivative(double ***matrix, int IndexX, int IndexY, int IndexZ); + double PartialYZDerivative(double ***matrix, int IndexX, int IndexY, int IndexZ); + double PartialXYZDerivative(double ***matrix, int IndexX, int IndexY, int IndexZ); +private: + double *m_coefficients; + double *m_xvalues, *m_yvalues, *m_zvalues; + int m_xdimension, m_ydimension, m_zdimension; + int m_xindex, m_yindex, m_zindex; + double m_delta_x, m_delta_y, m_delta_z; + int *m_nonzero_indices; + int m_nonzero_counter; +}; + +#endif diff --git a/Main Code 64bits/Vecteur3D.cpp b/Main Code 64bits/Vecteur3D.cpp new file mode 100644 index 0000000..5ef0d59 --- /dev/null +++ b/Main Code 64bits/Vecteur3D.cpp @@ -0,0 +1,142 @@ +// Classe Vecteur à 3 dimensions +// Basée sur ThreeVector.h, +// as part of the CLHEP - a Class Library for High Energy Physics. +// http://wwwinfo.cern.ch/asd/lhc++/clhep/index.html* + +// Cette classe était assez incomplète par exemple l'operator / qui manque ... +// Je l'ai en partie completée +// Il y a en fait beaucoup de fonction en ligne qui ne sont pas définie ensuite + + +// Voir aussi la classe « vecteur_ » (exemple du cours C++) +// Patrick TRAU ULP-IPST Strasbourg novembre 04 +// Pour les stream + + +// En gros +// Une fois défini un Vecteur3D point=Vecteur3D(0,1,2); ou +// Vecteur3D point(0,1,2); +// point.x() pour prendre la coordonnée X + +#include "Vecteur3D.h" + + +extern const Vecteur3D HepXHat, HepYHat, HepZHat; + +ostream& operator << (ostream &f,Vecteur3D v) +{ + v.affiche(f); + return(f); +} + +istream& operator >> (istream &f,Vecteur3D &v) //v est modifié! +{ + v.saisie(f); + return(f); +} + +typedef Vecteur3D HepThreeVectorD; +typedef Vecteur3D HepThreeVectorF; + + +// -------------- +// Global methods +// -------------- + +Vecteur3D operator / (const Vecteur3D & p, double a) +{ + return Vecteur3D(p.x()/a, p.y()/a, p.z()/a); +} + +Vecteur3D operator + (const Vecteur3D & a, const Vecteur3D & b) +{ + return Vecteur3D(a.x() + b.x(), a.y() + b.y(), a.z() + b.z()); +} + +Vecteur3D operator - (const Vecteur3D & a, const Vecteur3D & b) +{ + return Vecteur3D(a.x() - b.x(), a.y() - b.y(), a.z() - b.z()); +} + +Vecteur3D operator * (const Vecteur3D & p, double a) +{ + return Vecteur3D(a*p.x(), a*p.y(), a*p.z()); +} + +Vecteur3D operator * (double a, const Vecteur3D & p) +{ + return Vecteur3D(a*p.x(), a*p.y(), a*p.z()); +} + +double operator * (const Vecteur3D & a, const Vecteur3D & b) +{ + return a.dot(b); +} + + + +//Add by PAULINE 26/03/2015 + +Vecteur3D operator / (const Vecteur3D & a, const Vecteur3D & b) +{ + return Vecteur3D(a.x()/b.x(), a.y()/b.y(), a.z()/b.z()); +} + +Vecteur3D operator - ( const Vecteur3D & p, double a) +{ + return Vecteur3D(p.x() - a, p.y()-a, p.z()-a); +} + +Vecteur3D operator + ( const Vecteur3D & p, double a) +{ + return Vecteur3D(p.x() + a, p.y()+ a, p.z()+ a); +} + + Vecteur3D racine(const Vecteur3D & a) // function square root of a 3D vector +{ + return Vecteur3D(sqrt(a.x()),sqrt(a.y()),sqrt(a.z())); +} + Vecteur3D Hadamard(const Vecteur3D & a, const Vecteur3D & b) // special multiplication: component by component. Multiplication d'Hadamard +{ + return Vecteur3D(a.x()*b.x(), a.y()*b.y(),a.z()*b.z()); +} + + + Vecteur3D abso(const Vecteur3D & a) //absolute value +{ + return Vecteur3D(abs(a.x()), abs(a.y()),abs(a.z())); +} + + +// -------------------------- +// Set in various coordinates +// -------------------------- + + + +void Vecteur3D::gaussian_initialisation (const gsl_rng * r, const Vecteur3D sigma) +{ + dx = gsl_ran_gaussian (r,sigma.getX()); + dy = gsl_ran_gaussian (r,sigma.getY()); + dz = gsl_ran_gaussian (r,sigma.getZ()); +} + + +// Laplace initilisation utilise +// This function returns a random variate from the Laplace distribution with width a. +// p(x)dx = (1/2a)exp(−|x/a|)dx. +void Vecteur3D::laplace_initialisation (const gsl_rng * r, const Vecteur3D sigma) +{ + dx = gsl_ran_laplace (r,sigma.getX()); + dy = gsl_ran_laplace (r,sigma.getY()); + dz = gsl_ran_laplace (r,sigma.getZ()); +} + +// x in Laplace, y in Laplace and z in gaussian +void Vecteur3D::laplace_laplace_gauss_initialisation (const gsl_rng * r, const Vecteur3D sigma) +{ + dx = gsl_ran_laplace (r,sigma.getX()); + dy = gsl_ran_laplace (r,sigma.getY()); + dz = gsl_ran_gaussian (r,sigma.getZ()); +} + diff --git a/Main Code 64bits/Vecteur3D.h b/Main Code 64bits/Vecteur3D.h new file mode 100644 index 0000000..691c1c4 --- /dev/null +++ b/Main Code 64bits/Vecteur3D.h @@ -0,0 +1,929 @@ +// Classe Vecteur à 3 dimensions +// Basée sur ThreeVector.h, +// as part of the CLHEP - a Class Library for High Energy Physics. +// http://wwwinfo.cern.ch/asd/lhc++/clhep/index.html* + +// Cette classe était assez incomplète par exemple l'operator / qui manque ... +// Je l'ai en partie completée +// Il y a en fait beaucoup de fonction en ligne qui ne sont pas définie ensuite + + +// Voir aussi la classe « vecteur_ » (exemple du cours C++) +// Patrick TRAU ULP-IPST Strasbourg novembre 04 +// Pour les stream + + +// En gros +// Une fois défini un Vecteur3D point=Vecteur3D(0,1,2); ou +// Vecteur3D point(0,1,2); +// point.x() pour prendre la coordonnée X + +#ifndef VECTOR3D_SEEN +#define VECTOR3D_SEEN + +#include +#include +#include // to read the data and put them in files +#include // To have random_number generator +#include + +#include +using namespace std; + +class Vecteur3D +{ + +public: + + // Basic properties and operations on 3-vectors: + + enum + { + X=0, Y=1, Z=2, NUM_COORDINATES=3, SIZE=NUM_COORDINATES + }; + // Safe indexing of the coordinates when using with matrices, arrays, etc. + // (BaBar) + + inline Vecteur3D(double x = 0.0, double y = 0.0, double z = 0.0); + // The constructor. + + inline Vecteur3D(const Vecteur3D &); + // The copy constructor. + + inline ~Vecteur3D(); + // The destructor. Not virtual - inheritance from this class is dangerous. + + void affiche(ostream & pr) + { + // pr<<"["<>dx; + if (&f==&cin) + cout<<"entrez y : "; + f>>dy; + if (&f==&cin) + cout<<"entrez z : "; + f>>dz; + return; + } + + double operator () (int i) const +// Get components by index -- 0-based (Geant4) + { + if (i == 0) + { + return dx; + } + else if (i == 1) + { + return dy; + } + else if (i == 2) + { + return dz; + } + else + { + // cerr << "Vector3D::operator(): bad index" << endl; + return 0.0; + } + } + + inline double operator [] (int) const; + // Get components by index -- 0-based (Geant4) + + double & operator () (int i) + // Get components by index. 0-based. + { + if (i == 0) + { + return dx; + } + else if (i == 1) + { + return dy; + } + else if (i == 2) + { + return dz; + } + } + + + + + inline double & operator [] (int); + // Get components by index. 0-based. + + inline double x() const; + inline double y() const; + inline double z() const; + // The components in cartesian coordinate system. Same as getX() etc. + + // Get by each coordinate int =0 for x, 1 for y and 2 for z + inline double get(int); + + + inline void setX(double); + inline void setY(double); + inline void setZ(double); + // Set the components in cartesian coordinate system. + + // set by each coordinate int =0 for x, 1 for y and 2 for z + inline void set(int,double); + + inline void set( double x, double y, double z); + // Set all three components in cartesian coordinate system. + + inline double phi() const; + // The azimuth angle. + + inline double theta() const; + // The polar angle. + + inline double cosTheta() const; + // Cosine of the polar angle. + + inline double cos2Theta() const; + // Cosine squared of the polar angle - faster than cosTheta(). (ZOOM) + + inline double mag2() const; + // The magnitude squared (r^2 in spherical coordinate system). + + inline Vecteur3D square() const; + // The squared (x^2,y^2,z^2) of each component . + + inline double mag() const; + // The magnitude (r in spherical coordinate system). + + inline void setPhi(double); + // Set phi keeping mag and theta constant (BaBar). + + inline void setTheta(double); + // Set theta keeping mag and phi constant (BaBar). + + void setMag(double); + // Set magnitude keeping theta and phi constant (BaBar). + + inline double perp2() const; + // The transverse component squared (rho^2 in cylindrical coordinate system). + + inline double perp() const; + // The transverse component (rho in cylindrical coordinate system). + + inline void setPerp(double); + // Set the transverse component keeping phi and z constant. + + void setCylTheta(double); + // Set theta while keeping transvers component and phi fixed + + inline double perp2(const Vecteur3D &) const; + // The transverse component w.r.t. given axis squared. + + inline double perp(const Vecteur3D &) const; + // The transverse component w.r.t. given axis. + + inline Vecteur3D & operator = (const Vecteur3D &); + // Assignment. + + inline bool operator == (const Vecteur3D &) const; + inline bool operator != (const Vecteur3D &) const; + // Comparisons (Geant4). + + bool isNear (const Vecteur3D &, double epsilon=tolerance) const; + // Check for equality within RELATIVE tolerance (default 2.2E-14). (ZOOM) + // |v1 - v2|**2 <= epsilon**2 * |v1.dot(v2)| + + double howNear(const Vecteur3D & v ) const; + // sqrt ( |v1-v2|**2 / v1.dot(v2) ) with a maximum of 1. + // If v1.dot(v2) is negative, will return 1. + + double deltaR(const Vecteur3D & v) const; + // sqrt( pseudorapity_difference**2 + deltaPhi **2 ) + + inline Vecteur3D & operator += (const Vecteur3D &); + // Addition. + + inline Vecteur3D & operator -= (const Vecteur3D &); + // Subtraction. + + inline Vecteur3D operator - () const; + // Unary minus. + + inline Vecteur3D & operator *= (double); + // Scaling with real numbers. + + inline Vecteur3D & operator /= (double); + // Division by (non-zero) real number. + + inline Vecteur3D unit() const; + // Vector parallel to this, but of length 1. + + inline Vecteur3D orthogonal() const; + // Vector orthogonal to this (Geant4). + + inline double dot(const Vecteur3D &) const; + // double product. + + inline Vecteur3D cross(const Vecteur3D &) const; + // Cross product. + + double angle(const Vecteur3D &) const; + // The angle w.r.t. another 3-vector. + + double pseudoRapidity() const; + // Returns the pseudo-rapidity, i.e. -ln(tan(theta/2)) + + void setEta ( double p ); + // Set pseudo-rapidity, keeping magnitude and phi fixed. (ZOOM) + + void setCylEta ( double p ); + // Set pseudo-rapidity, keeping transverse component and phi fixed. (ZOOM) + + + // = = = = = = = = = = = = = = = = = = = = = = = = + // + // Esoteric properties and operations on 3-vectors: + // + // 1 - Set vectors in various coordinate systems + // 2 - Synonyms for accessing coordinates and properties + // 3 - Comparisions (dictionary, near-ness, and geometric) + // 4 - Intrinsic properties + // 5 - Properties releative to z axis and arbitrary directions + // 6 - Polar and azimuthal angle decomposition and deltaPhi + // + // = = = = = = = = = = = = = = = = = = = = = = = = + + // 1 - Set vectors in various coordinate systems + + inline void setRThetaPhi (double r, double theta, double phi); + // Set in spherical coordinates: Angles are measured in RADIANS + + inline void setREtaPhi ( double r, double eta, double phi ); + // Set in spherical coordinates, but specify peudorapidiy to determine theta. + + inline void setRhoPhiZ (double rho, double phi, double z); + // Set in cylindrical coordinates: Phi angle is measured in RADIANS + + void setRhoPhiTheta ( double rho, double phi, double theta); + // Set in cylindrical coordinates, but specify theta to determine z. + + void setRhoPhiEta ( double rho, double phi, double eta); + // Set in cylindrical coordinates, but specify pseudorapidity to determine z. + + // 2 - Synonyms for accessing coordinates and properties + + inline double getX() const; + inline double getY() const; + inline double getZ() const; + // x(), y(), and z() + + inline double getR () const; + inline double getTheta() const; + inline double getPhi () const; + // mag(), theta(), and phi() + + inline double r () const; + // mag() + + inline double rho () const; + inline double getRho () const; + // perp() + + double eta () const; + double getEta () const; + // pseudoRapidity() + + inline void setR ( double s ); + // setMag() + + inline void setRho ( double s ); + // setPerp() + + // 3 - Comparisions (dictionary, near-ness, and geometric) + + int compare (const Vecteur3D & v) const; + bool operator > (const Vecteur3D & v) const; + bool operator < (const Vecteur3D & v) const; + bool operator>= (const Vecteur3D & v) const; + bool operator<= (const Vecteur3D & v) const; + // dictionary ordering according to z, then y, then x component + + inline double diff2 (const Vecteur3D & v) const; + // |v1-v2|**2 + + static double setTolerance (double tol); + static inline double getTolerance (); + // Set the tolerance used in isNear() for Vecteur3Ds + + bool isParallel (const Vecteur3D & v, double epsilon=tolerance) const; + // Are the vectors parallel, within the given tolerance? + + bool isOrthogonal (const Vecteur3D & v, double epsilon=tolerance) const; + // Are the vectors orthogonal, within the given tolerance? + + double howParallel (const Vecteur3D & v) const; + // | v1.cross(v2) / v1.dot(v2) |, to a maximum of 1. + + double howOrthogonal (const Vecteur3D & v) const; + // | v1.dot(v2) / v1.cross(v2) |, to a maximum of 1. + + enum + { + ToleranceTicks = 100 + }; + + // 4 - Intrinsic properties + + double beta () const; + // relativistic beta (considering v as a velocity vector with c=1) + // Same as mag() but will object if >= 1 + + double gamma() const; + // relativistic gamma (considering v as a velocity vector with c=1) + + double coLinearRapidity() const; + // inverse tanh (beta) + + // 5 - Properties relative to Z axis and to an arbitrary direction + + // Note that the non-esoteric CLHEP provides + // theta(), cosTheta(), cos2Theta, and angle(const Vecteur3D&) + + inline double angle() const; + // angle against the Z axis -- synonym for theta() + + inline double theta(const Vecteur3D & v2) const; + // synonym for angle(v2) + + inline double cosTheta (const Vecteur3D & v2) const; + inline double cos2Theta(const Vecteur3D & v2) const; + // cos and cos^2 of the angle between two vectors + + inline Vecteur3D project () const; + Vecteur3D project (const Vecteur3D & v2) const; + // projection of a vector along a direction. + + inline Vecteur3D perpPart() const; + inline Vecteur3D perpPart (const Vecteur3D & v2) const; + // vector minus its projection along a direction. + + double rapidity () const; + // inverse tanh(v.z()) + + double rapidity (const Vecteur3D & v2) const; + // rapidity with respect to specified direction: + // inverse tanh (v.dot(u)) where u is a unit in the direction of v2 + + double eta(const Vecteur3D & v2) const; + // - ln tan of the angle beween the vector and the ref direction. + + // 6 - Polar and azimuthal angle decomposition and deltaPhi + + // Decomposition of an angle within reference defined by a direction: + + double polarAngle (const Vecteur3D & v2) const; + // The reference direction is Z: the polarAngle is abs(v.theta()-v2.theta()). + + double deltaPhi (const Vecteur3D & v2) const; + // v.phi()-v2.phi(), brought into the range (-PI,PI] + + double azimAngle (const Vecteur3D & v2) const; + // The reference direction is Z: the azimAngle is the same as deltaPhi + + double polarAngle (const Vecteur3D & v2, + const Vecteur3D & ref) const; + // For arbitrary reference direction, + // polarAngle is abs(v.angle(ref) - v2.angle(ref)). + + double azimAngle (const Vecteur3D & v2, + const Vecteur3D & ref) const; + // To compute azimangle, project v and v2 into the plane normal to + // the reference direction. Then in that plane take the angle going + // clockwise around the direction from projection of v to that of v2. + + +// Random initiliastion + + void gaussian_initialisation (const gsl_rng * r, const Vecteur3D sigma); + + void laplace_initialisation (const gsl_rng * r, const Vecteur3D sigma); + + void laplace_laplace_gauss_initialisation (const gsl_rng * r, const Vecteur3D sigma); + + +protected: + void setSpherical (double r, double theta, double phi); + void setCylindrical (double r, double phi, double z); + double negativeInfinity() const; + +protected: + + double dx; + double dy; + double dz; + // The components. + + static double tolerance; + // default tolerance criterion for isNear() to return true. +} +; // Vecteur3D + + +extern const Vecteur3D HepXHat, HepYHat, HepZHat; + +ostream& operator << (ostream &f,Vecteur3D v); + +istream& operator >> (istream &f,Vecteur3D &v); //v est modifié! + +typedef Vecteur3D HepThreeVectorD; +typedef Vecteur3D HepThreeVectorF; + +Vecteur3D operator / (const Vecteur3D &, double a); +// Division of 3-vectors by non-zero real number + +Vecteur3D operator + (const Vecteur3D &, const Vecteur3D &); +// Addition of 3-vectors. + +Vecteur3D operator - (const Vecteur3D &, const Vecteur3D &); +// Subtraction of 3-vectors. + +double operator * (const Vecteur3D &, const Vecteur3D &); +// double product of 3-vectors. + +Vecteur3D operator * (const Vecteur3D &, double a); +Vecteur3D operator * (double a, const Vecteur3D &); +// Scaling of 3-vectors with a real number + + +//ADD by PAULINE 26/03/2015 +Vecteur3D operator / (const Vecteur3D & a, const Vecteur3D & b); +Vecteur3D operator - ( const Vecteur3D & p, double a); +Vecteur3D operator + ( const Vecteur3D & p, double a); + +Vecteur3D racine(const Vecteur3D & a); // sqrt of a 3D vector +Vecteur3D Hadamard(const Vecteur3D & a, const Vecteur3D & b); +//modi pauline 8/04 +Vecteur3D abso(const Vecteur3D & a); //absolute value +//Vecteur3D operator racine(const Vecteur3D & a); +// Scaling of 3-vectors with a real number + + + +// ------------------ +// Access to elements +// ------------------ + +// x, y, z + +inline double & Vecteur3D::operator[] (int i) +{ + return operator()(i); +} + +inline double Vecteur3D::operator[] (int i) const +{ + return operator()(i); +} + +inline double Vecteur3D::x() const +{ + return dx; +} +inline double Vecteur3D::y() const +{ + return dy; +} +inline double Vecteur3D::z() const +{ + return dz; +} + +inline double Vecteur3D::getX() const +{ + return dx; +} +inline double Vecteur3D::getY() const +{ + return dy; +} +inline double Vecteur3D::getZ() const +{ + return dz; +} + + +// Get by each coordinate int =0 for x, 1 for y and 2 for zz +inline double Vecteur3D::get(int i) +{ + if (i == 0) + { + return dx; + } + else if (i == 1) + { + return dy; + } + else if (i == 2) + { + return dz; + } + return 0.; +} + + + +inline void Vecteur3D::setX(double x) +{ + dx = x; +} +inline void Vecteur3D::setY(double y) +{ + dy = y; +} +inline void Vecteur3D::setZ(double z) +{ + dz = z; +} + + +// set by each coordinate int =0 for x, 1 for y and 2 for z +inline void Vecteur3D::set(int i,double value) +{ + if (i == 0) + { + dx = value; + } + else if (i == 1) + { + dy = value; + } + else if (i == 2) + { + dz = value; + } +} + + +inline void Vecteur3D::set(double x, double y, double z) +{ + dx = x; + dy = y; + dz = z; +} + +// -------------- +// Global methods +// -------------- + +// -------------------------- +// Set in various coordinates +// -------------------------- + +inline void Vecteur3D::setRThetaPhi +( double r, double theta, double phi ) +{ + setSpherical(r, theta, phi); +} + +inline void Vecteur3D::setREtaPhi +( double r, double eta, double phi ) +{ + setSpherical(r, 2*atan(exp(-eta)), phi); +} + +inline void Vecteur3D::setRhoPhiZ +( double rho, double phi, double z) +{ + setCylindrical(rho, phi, z); +} + +// ------------ +// Constructors +// ------------ + +inline Vecteur3D::Vecteur3D(double x, double y, double z) + : dx(x), dy(y), dz(z) +{} + +inline Vecteur3D::Vecteur3D(const Vecteur3D & p) + : dx(p.dx), dy(p.dy), dz(p.dz) +{} + +inline Vecteur3D::~Vecteur3D() +{} + +inline Vecteur3D & Vecteur3D::operator = (const Vecteur3D & p) +{ + dx = p.dx; + dy = p.dy; + dz = p.dz; + return *this; +} + +// ------------------ +// Access to elements +// ------------------ + +// r, theta, phi + +inline double Vecteur3D::mag2() const +{ + return dx*dx + dy*dy + dz*dz; +} +inline double Vecteur3D::mag() const +{ + return sqrt(mag2()); +} +inline double Vecteur3D::r() const +{ + return mag(); +} + +inline double Vecteur3D::theta() const +{ + return dx == 0.0 && dy == 0.0 && dz == 0.0 ? 0.0 : atan2(perp(),dz); +} +inline double Vecteur3D::phi() const +{ + return dx == 0.0 && dy == 0.0 ? 0.0 : atan2(dy,dx); +} + +inline double Vecteur3D::getR() const +{ + return mag(); +} +inline double Vecteur3D::getTheta() const +{ + return theta(); +} +inline double Vecteur3D::getPhi() const +{ + return phi(); +} +inline double Vecteur3D::angle() const +{ + return theta(); +} + +inline double Vecteur3D::cosTheta() const +{ + double ptot = mag(); + return ptot == 0.0 ? 1.0 : dz/ptot; +} + +inline double Vecteur3D::cos2Theta() const +{ + double ptot2 = mag2(); + return ptot2 == 0.0 ? 1.0 : dz*dz/ptot2; +} + +inline void Vecteur3D::setR(double r) +{ + setMag(r); +} + +inline void Vecteur3D::setTheta(double th) +{ + double ma = mag(); + double ph = phi(); + setX(ma*sin(th)*cos(ph)); + setY(ma*sin(th)*sin(ph)); + setZ(ma*cos(th)); +} + +inline void Vecteur3D::setPhi(double ph) +{ + double xy = perp(); + setX(xy*cos(ph)); + setY(xy*sin(ph)); +} + +// perp, eta, + +inline double Vecteur3D::perp2() const +{ + return dx*dx + dy*dy; +} +inline double Vecteur3D::perp() const +{ + return sqrt(perp2()); +} +inline double Vecteur3D::rho() const +{ + return perp(); +} +inline double Vecteur3D::eta() const +{ + return pseudoRapidity(); +} + +inline double Vecteur3D::getRho() const +{ + return perp(); +} +inline double Vecteur3D::getEta() const +{ + return pseudoRapidity(); +} + +inline void Vecteur3D::setPerp(double r) +{ + double p = perp(); + if (p != 0.0) + { + dx *= r/p; + dy *= r/p; + } +} +inline void Vecteur3D::setRho(double rho) +{ + setPerp (rho); +} + + +// ---------- +// Comparison +// ---------- + +inline bool Vecteur3D::operator == (const Vecteur3D& v) const +{ + return (v.x()==x() && v.y()==y() && v.z()==z()) ? true : false; +} + +inline bool Vecteur3D::operator != (const Vecteur3D& v) const +{ + return (v.x()!=x() || v.y()!=y() || v.z()!=z()) ? true : false; +} + +inline double Vecteur3D::getTolerance () +{ + return tolerance; +} + +// ---------- +// Arithmetic +// ---------- + +inline Vecteur3D& Vecteur3D::operator += (const Vecteur3D & p) +{ + dx += p.x(); + dy += p.y(); + dz += p.z(); + return *this; +} + +inline Vecteur3D& Vecteur3D::operator -= (const Vecteur3D & p) +{ + dx -= p.x(); + dy -= p.y(); + dz -= p.z(); + return *this; +} + +inline Vecteur3D Vecteur3D::operator - () const +{ + return Vecteur3D(-dx, -dy, -dz); +} + +inline Vecteur3D& Vecteur3D::operator *= (double a) +{ + dx *= a; + dy *= a; + dz *= a; + return *this; +} + +inline Vecteur3D & Vecteur3D::operator /= (double a) +{ + dx /= a; + dy /= a; + dz /= a; + return *this; +} + +// ------------------- +// Combine two Vectors +// ------------------- + +inline Vecteur3D Vecteur3D::square() const +{ + return Vecteur3D(dx*dx, dy*dy, dz*dz); // The squared (x^2,y^2,z^2) of each component . +} + + +inline double Vecteur3D::diff2(const Vecteur3D & p) const +{ + return (*this-p).mag2(); +} + +inline double Vecteur3D::dot(const Vecteur3D & p) const +{ + return dx*p.x() + dy*p.y() + dz*p.z(); +} + +inline Vecteur3D Vecteur3D::cross(const Vecteur3D & p) const +{ + return Vecteur3D(dy*p.z()-p.y()*dz, dz*p.x()-p.z()*dx, dx*p.y()-p.x()*dy); +} + +inline double Vecteur3D::perp2(const Vecteur3D & p) const +{ + double tot = p.mag2(); + double ss = dot(p); + return tot > 0.0 ? mag2()-ss*ss/tot : mag2(); +} + +inline double Vecteur3D::perp(const Vecteur3D & p) const +{ + return sqrt(perp2(p)); +} + +inline Vecteur3D Vecteur3D::perpPart () const +{ + return Vecteur3D (dx, dy, 0); +} +inline Vecteur3D Vecteur3D::project () const +{ + return Vecteur3D (0, 0, dz); +} + +inline Vecteur3D Vecteur3D::perpPart (const Vecteur3D & v2) const +{ + return ( *this - project(v2) ); +} + + +// angle entre les 2 vecteurs // FAUX car c'est l'angle entre Oz et q!! +// A MON AVIS TOUTES LES FORMULES CI-DESSOUS SONT FAUSSES +inline double Vecteur3D::angle(const Vecteur3D & q) const +{ + return acos(cosTheta(q)); +} +// +//inline double Vecteur3D::angle_2_vec(const Vecteur3D & v2) const +//{ +// return acos(v2.dot(*this)/(mag(v2)*(mag(*this))); // v1 v2 cos(theta) = v1.v2 +//} + + +inline double Vecteur3D::azimAngle(const Vecteur3D & v2) const +{ + return deltaPhi(v2); +} + +inline double Vecteur3D::cosTheta(const Vecteur3D & v2) const +{ + return((*this-v2).cosTheta()); +} +inline double Vecteur3D::cos2Theta(const Vecteur3D & v2) const +{ + return((*this-v2).cos2Theta()); +} +// cos and cos^2 of the angle between MM2 and axe Oz (axe Oz est theta=0). + +inline double Vecteur3D::theta(const Vecteur3D & v2) const +{ + return((*this-v2).theta()); +} + + + + + +// ---------- +// Properties +// ---------- + +inline Vecteur3D Vecteur3D::unit() const +{ + double tot = mag2(); + Vecteur3D p(x(),y(),z()); + return tot > 0.0 ? p *= (1.0/sqrt(tot)) : p; +} + +inline Vecteur3D Vecteur3D::orthogonal() const +{ + double x = dx < 0.0 ? -dx : dx; + double y = dy < 0.0 ? -dy : dy; + double z = dz < 0.0 ? -dz : dz; + if (x < y) + { + return x < z ? Vecteur3D(0,dz,-dy) : Vecteur3D(dy,-dx,0); + } + else + { + return y < z ? Vecteur3D(-dz,0,dx) : Vecteur3D(dy,-dx,0); + } +} + + + +#endif diff --git a/Main Code 64bits/algorithmes.cpp b/Main Code 64bits/algorithmes.cpp new file mode 100644 index 0000000..5b180c9 --- /dev/null +++ b/Main Code 64bits/algorithmes.cpp @@ -0,0 +1,111 @@ +/********************* +Modulo +binary searchr +File number of line +wait en seconde +*********************/ + +#include "algorithmes.h" + + + +// Macro to Switch laser (based on the rule 0 = false ; 1 = true) Gives +// 0 if t is between 0 and T1 (modulo T1+T2) +// 1 if t is between T1, T1+T2 (modulo T1+T2) +// Thus we can switch between lasers by nlas + Nb_laser * Is_Switch +int Is_Switch(double T1, double T2, double t) +{ + double reste = t - (T1 + T2) * floor(t/(T1 + T2)); // is t modulo T1+T2 + if (reste < T1) + return 0; + else + return 1; +} + + + +/* +Fonction de recherche binaire par dichotomie +Retourne position tel que sortedArray[position] < key <= sortedArray[position+1] +-1 si rien n'est trouvé + +Provient de http://www.fredosaurus.com/notes-cpp/algorithms/searching/binarysearch.html +Voir aussi #include // Pour le binary search +Existe aussi dans gsl c'est gsl_histogram_find +lower_bound existe aussi +*/ +int binarySearch(double sortedArray[], int first, int last, double key) +{ + int llast = last ; + int ffirst = first; + int mid; + while (ffirst <= llast) + { + mid = (int) (ffirst + llast) / 2; // compute mid point. + if (key > sortedArray[mid]) + ffirst = mid + 1; // repeat search in top half. + else if (key < sortedArray[mid]) + llast = mid - 1; // repeat search in bottom half. + else + return mid; // Trouver la position exacte key = sortedArray[mid] + } + return llast; // sortedArray[llast] < key < sortedArray[first] = sortedArray[llast+1] +} + + + +// Retourne le nb de lignes d'un fichier +int number_line_file(const char *nom_file) +{ + ifstream file(nom_file); + int n = 0; + string s; + while( getline( file, s ) ) + { + n++; + } + file.close(); + return n; +} + + + +// Attend le nb de seconds (précis à la milliseconde) +void wait(double sec) +{ + clock_t start; + start = clock(); + + + while ((clock()-start)/double(CLOCKS_PER_SEC) < sec) + { + } +} + + +// Compare des doubles pour qsort +// if they match in ranking, the function shall return zero; if elem1 goes before elem2, it shall return a negative value; and if it goes after, a positive value. +int compare_doubles (const void *x, const void *y) +{ + + // x and y are pointers to doubles. + + // Returns -1 if x < y + // 0 if x == y + // +1 if x > y + + double dx, dy; + + dx = *(double *)x; + dy = *(double *)y; + + if (dx < dy) + { + return -1; + } + else if (dx > dy) + { + return +1; + } + return 0; +} diff --git a/Main Code 64bits/algorithmes.h b/Main Code 64bits/algorithmes.h new file mode 100644 index 0000000..997ea18 --- /dev/null +++ b/Main Code 64bits/algorithmes.h @@ -0,0 +1,57 @@ +/********************* +fonction signe +binary search +wait en seconde +*********************/ + +#ifndef Algorithmes_SEEN +#define Algorithmes_SEEN + +#include // For clock() +#include // to read the data and put them in files +#include +#include /* floor */ +using namespace std; + + +// Fonction signe +template inline int sgn(T t) +{ + return t > 0 ? 1 : t < 0 ? -1 : 0; +} + + +// Macro to Switch laser (based on the rule 0 = false ; 1 = true) Gives +// 0 if t is between 0 and T1 (modulo T1+T2) +// 1 if t is between T1, T1+T2 (modulo T1+T2) +// Thus we can switch between lasers by nlas + Nb_laser * Is_Switch +int Is_Switch(double T1, double T2, double t); + + +/* +Fonction de recherche binaire par dichotomie +Retourne position tel que sortedArray[position] < key <= sortedArray[position+1] +-1 si rien n'est trouvé + +Provient de http://www.fredosaurus.com/notes-cpp/algorithms/searching/binarysearch.html +Voir aussi #include // Pour le binary search +Existe aussi dans gsl c'est gsl_histogram_find +lower_bound existe aussi +*/ + +int binarySearch(double sortedArray[], int first, int last, double key); + +// Retourne le nb de lignes d'un fichier +int number_line_file(const char *nom_file); + +// Attend le nb de seconds (précis à la milliseconde) +void wait(double sec); + +// Compare des doubles pour qsort +// if they match in ranking, the function shall return zero; if elem1 goes before elem2, it shall return a negative value; and if it goes after, a positive value. +int compare_doubles(const void *x, const void *y); + + +#endif + + diff --git a/Main Code 64bits/atome.cpp b/Main Code 64bits/atome.cpp new file mode 100644 index 0000000..ff1cac1 --- /dev/null +++ b/Main Code 64bits/atome.cpp @@ -0,0 +1,148 @@ +#include "atome.h" +// ------------ +// Constructors +// ------------ + + +Atome::Atome() // Constructeur par défaut +{ + pos.set(0.,0.,0.); + vel.set(0.,0.,0.); + acc.set(0.,0.,0.); + mass = 0.; + charge = 0.; + name =""; +}; + +//Atome::~Atome() +//{} +//; // Destructeur + +Atome::Atome(const Atome & at) // Constructeur de (re)copie +{ + pos = at.pos; + vel = at.vel; + acc = at.acc; + mass = at.mass; + charge = at.charge; + name = at.name; +}; + +Atome & Atome::operator = (const Atome & at) // Affectation par recopie +{ + if (this != &at) // On vérifie que les objets ne sont pas les mêmes ! + { + pos = at.pos; + vel = at.vel; + acc = at.acc; + mass = at.mass; + charge = at.charge; + name = at.name; + } + return *this; +} + +//-------------------------------------------- +// Surcharge des opérateurs +,-,*,/ +// + (-) = addition (soustraction) membre à membre. +// * (/) = multiplication (division) membre à membre (et même sous membres à sous membre. pos_x*pos_x +// On peut aussi le faire avec un réel +//-------------------------------------------- + +Atome operator +(const Atome at1, const Atome at2) +{ + Atome sum; + + sum.set_pos(at1.get_pos()+at2.get_pos()); + sum.set_vel(at1.get_vel()+at2.get_vel()); + sum.set_acc(at1.get_acc()+at2.get_acc()); + sum.set_mass(at1.get_mass()+at2.get_mass()); + sum.set_charge(at1.get_charge()+at2.get_charge()); + sum.set_name(at1.get_name()+at2.get_name()); + + return sum; +} + + + + +// ---------- +// Comparison +// ---------- + +bool Atome::operator == (const Atome & at) const +{ + return (at.pos==pos && at.vel==vel && at.acc==acc && at.mass==mass && at.charge==charge && at.name == name) ? true : false; +} + +bool Atome::operator != (const Atome & at) const +{ + return (at.pos!=pos || at.vel!=vel || at.acc!=acc || at.mass!=mass || at.charge!=charge || at.name != name) ? true : false; +} + +//---------------------------------- +// Surdéfinition des entrées sorties +//---------------------------------- + +ostream& operator << (ostream &flux,Atome at) +{ + at.write(flux); + return(flux); +} + +istream& operator >> (istream &flux,Atome & at) //at est modifié! +{ + at.read(flux); + return(flux); +} +//---------- +// Distances, angles +//---------- + +// Distance carrée entre deux Atomes +inline double Atome::dist2(const Atome & at) const +{ + double R2 = (pos - at.get_pos()).mag2(); + return(R2); +} + +// Distance entre deux Atomes +inline double Atome::dist(const Atome & at) const +{ + return(sqrt(this->dist2(at))); // ou return(sqrt(*this.dist2(at))); +} + +// Distance carrée entre deux vitesses d'Atomes +inline double Atome::dist2_vel(const Atome & at) const +{ + double R2 = (vel - at.get_vel()).mag2(); + return(R2); +} + +// Distance entre deux deux vitesses d'Atomes +inline double Atome::dist_vel(const Atome & at) const +{ + return(sqrt(this->dist2_vel(at))); +} + +inline double Atome::cosTheta (const Atome & at) const +{ + return((pos-at.get_pos()).Vecteur3D::cosTheta()); +} +inline double Atome::cos2Theta(const Atome & at) const +{ + return((pos-at.get_pos()).Vecteur3D::cos2Theta()); +} +// cos and cos^2 of the angle between the two points and axe Oz (axe Oz est theta=0). + +inline double Atome::theta(const Atome & at) const +{ + return((pos-at.get_pos()).Vecteur3D::theta()); +} + + +// ---------------------------------- +// FIN DES FONCTIONS EN LIGNES +// ---------------------------------- + + diff --git a/Main Code 64bits/atome.h b/Main Code 64bits/atome.h new file mode 100644 index 0000000..2232ab8 --- /dev/null +++ b/Main Code 64bits/atome.h @@ -0,0 +1,235 @@ +/* + Name: classe « Atome » + Copyright: + Author: Daniel Comparat + Date: 15/10/06 11:01 + Description: + + +EN FAIT C'EST L'ETAT EXTERNE D'UNE PARTICULE + Classe Atome at contenant un vecteur3D pos, vel, acc and mass + charge + name + * Elles sont initialisée à 0. + * On peut leur mettre des valeurs par (exemple) at.set_pos(new_pos) + * On peut lire les valeurs par (exemple) at.get_pos() + * On peut incrémenter les valeurs par at.inc_pos(d_pos) + * == et != sont surdéfinis ATTENTION ILS COMPARENT DES DOUBLES (avec les erreurs d'arrondis cela doit être faux) + * write et read permettent d'écrire et de lire dans un flux (cout (pas cerr ou clog) ou fichier) + * FONCTIONS + at1.dist2(at2) est distance carrée entre at1 et at2 + at1.dist(at2) est distance entre at1 et at2 + at1.cosTheta(at2) + at1.cos2Theta(at2) cos and cos^2 of the angle between MM2 and axe Oz (axe Oz est theta=0). + + */ + + + + +#ifndef Atom_SEEN +#define Atom_SEEN + +#include +using namespace std; + +#include "Vecteur3D.h" + +class Atome +{ +protected: + Vecteur3D pos; // (X,Y,Z) position + Vecteur3D vel; // (X,Y,Z) velocity + Vecteur3D acc; // (X,Y,Z) acceleration + double mass; // mass + double charge; // coulombian charge + string name; + +public: // Forme canonique d'une classe + Atome(); //constructeur + Atome(const Atome&); // Constructeur de copie + Atome& operator = (const Atome&); // Affectation par recopie + virtual ~Atome() {}; // Destructeur par defaut + +//-------------------------------------------- +// Surcharge des opérateurs +,-,*,/ +// + = addition membre à membre. +// * = multiplication membre à membre (et même sous membres à sous membre. pos_x*pos_x +// On peut aussi le faire avec un réel +//-------------------------------------------- + + + friend Atome operator +(const Atome , const Atome); // surcharge de l'opérateur + + + // Get components + Vecteur3D get_pos() const + { + return pos; + } + Vecteur3D get_vel() const + { + return vel; + } + Vecteur3D get_acc() const + { + return acc; + } + double get_mass() const + { + return mass; + } + double get_charge() const + { + return charge; + } + string get_name() const + { + return name; + } + + + // Set components + void set_pos(const Vecteur3D& new_pos) + { + pos = new_pos; + } + void set_vel(const Vecteur3D& new_vel) + { + vel = new_vel; + } + void set_acc(const Vecteur3D& new_acc) + { + acc = new_acc; + } + void set_mass(const double& new_mass) + { + mass = new_mass; + } + void set_charge(const double& new_charge) + { + charge = new_charge; + } + void set_name(const string& new_name) + { + name = new_name; + } + + // Clear components + void clear_pos() + { + pos = Vecteur3D(0.,0.,0.); + } + void clear_vel() + { + vel = Vecteur3D(0.,0.,0.); + } + void clear_acc() + { + acc = Vecteur3D(0.,0.,0.); + } + void clear_mass() + { + mass = 0.; + } + void clear_charge() + { + charge = 0.; + } +// I did not put for name it is useless + + void inc_pos(const Vecteur3D& d_pos) + { + pos += d_pos; + } + void inc_vel(const Vecteur3D& d_vel) + { + vel += d_vel; + } + void inc_acc(const Vecteur3D& d_acc) + { + acc += d_acc; + } +// I did not put for mass, charge, name it is useless + + // Comparison + bool operator == (const Atome & at) const; + bool operator != (const Atome & at) const; + + + // Affichage + + virtual void write(ostream & flux) + { + if (&flux == &cout) + cout << "masse : " << mass << "\t"; + else + flux << mass << "\t"; + if (&flux == &cout) + cout << "charge : " << charge << "\t"; + else + flux << charge << "\t"; + if (&flux == &cout) + cout << "position : " << pos << "\t"; + else + flux << pos << "\t"; + if (&flux == &cout) + cout << "vitesse : " << vel << "\t"; + else + flux << vel<< "\t"; + if (&flux == &cout) + cout << "acceleration : " << acc << "\t"; + else + flux << acc << "\t"; + if (&flux == &cout) + cout << "name : " << name << "\t"; + else + flux << name << "\t"; + } + + // read des données + + virtual void read(istream & flux) + { + if (&flux == &cin) + cout << "enter mass : "; + flux >> mass; + if (&flux == &cin) + cout << "enter charge : "; + flux >> charge; + if (&flux == &cin) + cout << "enter position : "; + flux >> pos; + if (&flux == &cin) + cout << "enter vitesse : "; + flux >> vel; + if (&flux == &cin) + cout << "enter acceleration : "; + flux >> acc; + if (&flux == &cin) + cout << "enter name : "; + flux >> name; + } + + + // Distance carrée entre deux Atomes + inline double dist2(const Atome & at) const; + + // Distance entre deux Atomes + inline double dist(const Atome & at) const; + + // Distance carrée entre deux vitesses d'Atomes + inline double dist2_vel(const Atome & at) const; + + // Distance entre deux deux vitesses d' Atomes + inline double dist_vel(const Atome & at) const; + + inline double cosTheta (const Atome & at) const; + + inline double cos2Theta(const Atome & at) const; + + // cos and cos^2 of the angle between MM2 and axe Oz (axe Oz est theta=0). + + inline double theta(const Atome & at) const; + +}; + + +#endif diff --git a/Main Code 64bits/constantes_SI.h b/Main Code 64bits/constantes_SI.h new file mode 100644 index 0000000..ecf14ad --- /dev/null +++ b/Main Code 64bits/constantes_SI.h @@ -0,0 +1,427 @@ +/* + Name: Constantes physiques du système d'unité international + Copyright: + Author: Daniel COMPARAT + Date: 23/10/06 09:10 + Description: + Basé sur CLHEP - a Class Library for High Energy Physics. + http://wwwinfo.cern.ch/asd/lhc++/clhep/index.html + +// HEP coherent Physical Constants +// Below is a non exhaustive list of Physical CONSTANTS, +// +// The basic units are : +// meter (not millimeter as in CLHEP) +// second (not nanosecond ) +// electron Volt (not Mev) +// degree Kelvin +// amount of substance (mole) +// luminous intensity (candela) +// radian +// steradian + +*/ + + +#ifndef constantes_SI_SEEN +#define constantes_SI_SEEN + + + #include + #include "Vecteur3D.h" + +using namespace std; + + +const double VERY_LARGE_NUMBER = 1.e90; +const double VERY_SMALL_NUMBER = 1./VERY_LARGE_NUMBER; +const double SMALL_NUMBER = 1.e-10; // Utile pour les différences finies (pour éviter les erreurs d'arrondis) +const double LARGE_NUMBER = 1./SMALL_NUMBER; +const double SMALL_NUMBER_RATE = 1.; // Rate smaller than this (1 second) will not be considered +const double SMALL_DIPOLE_DEBYE = 1.e-8; // Rate smaller than this (1 second) will not be considered + + +const int aucune = -1; // numéro pour indiquer aucune molécule +const int all = -1; // numéro pour indiquer toute les molécule + +static const double pi = 3.14159265358979323846; +static const double twopi = 2*pi; +static const double halfpi = pi/2; +static const double pi2 = pi*pi; +static const double SQRT2 = sqrt(2.); + +static const double g_grav = 9.80665; // Gravité standard +static const Vecteur3D gravity(0.,0.,-g_grav); + +static const double EAU = 219474.63137032; // Energy atomic units -> cm^(-1) +static const double hartree = EAU; // Energy atomic units -> cm^(-1) +static const double hartreeJ = 4.35974417*1e-18; // Hartree en J +static const double BAU = 2.35051809*1e5; +static const double ME = 9.1093697*1e-31; +static const double FAU = 5.1422082*1e11; +static const double ASO = 2*554.0406*hartree/3; +static const double MAU = 1.6605402*1e-27; +static const double Mproton = 1.67262178*1e-27; +static const double mau = 1.6605402*1e-27; +static const double MCs = 132.905442*MAU; +static const double MRb87 = 86.90918052*MAU; +static const double MRb85 = 84.911789732*MAU; +static const double MNa = 22.98976928*MAU; +static const double MH = 1.00794*MAU; +static const double MCs2 = 2.*132.905442*MAU; +static const double MCO = 28.*MAU; +static const double MNH = 15.0146*MAU; +static const double MBaF = 156.325*MAU; +static const double MLi7Cs = (7+133)*MAU; +static const double MLi6Cs = (6+133)*MAU; +static const double MRb85Cs = (85+133)*MAU; +static const double MRb87Cs = (87+133)*MAU; +static const double MPs = 2.*ME; +static const double MRb = 87.*mau; +static const double MC2moins = 24.*MAU; +static const double kCoulomb = 8.9875517873681764*1e9; // 1/(4 pi epsilon_0) + +static const double H = 6.6260755*1e-34; +static const double hPlanck = 6.6260755*1e-34; +static const double HBAR = H/(2*pi); +static const double C = 299792458; +static const double QE = -1.60217733*1e-19; +static const double QION = -QE; +static const double A0 = 0.529177249*1e-10; +static const double a0 = 0.529177249*1e-10; +static const double MU0 = 4*pi*1e-7; +static const double EPSILON0 = 1/(MU0*C*C); +static const double e2 = QE*QE*C*C*1e-7; // e2 = q_e^2/(4 Pi Epsilon0) +static const double ALPHA = e2/(HBAR*C); +static const double MUBOHR = -QE*HBAR/(2*ME); // ATTENTION POSITIF!! +static const double MHz = 1e6 ; +static const double MHzcm = C/10000 ;// cm^(-1) -> MHz +static const double VparcmMHz = -QE*ALPHA*C/hartreeJ/1e6; // champ électrique V/cm -> MHz +static const double CenCm =QE*A0*A0/(ALPHA*C); // MHz -> C*m +static const double kB = 1.380658*1e-23; +static const double MUKMHZ = 1e-6*kB/(1e6*H); +static const double mW = 1e-3; +static const double nW = 1e-9; +static const double MICRON = 1e-6; +static const double Mus = MICRON; // microseconde +// static const double conversionUAEnergieMHz=pow(QE*A0,2)/(H*pow(MICRON,3)*MHz);// utilisé dans les calculs de potentiels +static const double Debye = 1.e-21/C; +static const double Spol_Debye_A_s = (8e6*pi*pi*C*C*C*Debye*Debye)/(3.*EPSILON0*C*C*C*HBAR); // 3.13618932*10^-7 = Conversion HonlLondon (en Debye) en A Einstein (s^-1) si energie en cm^-1 +static const double Conv_Ecm_delta = 2.*pi*MHz*MHzcm ;// cm^(-1) -> s^-1; +static const double sigmaSB = 5.670367e-8 ; // Stefan–Boltzmann + + + +// Conversion entre l'unité des énergie dans les fichiers et celle des calcul de taux + +// +// Length [L] +// +static const double millimeter = 0.001; +static const double millimeter2 = millimeter*millimeter; +static const double millimeter3 = millimeter*millimeter*millimeter; + +static const double centimeter = 10.*millimeter; +static const double centimeter2 = centimeter*centimeter; +static const double centimeter3 = centimeter*centimeter*centimeter; + +static const double meter = 1000.*millimeter; +static const double meter2 = meter*meter; +static const double meter3 = meter*meter*meter; + +static const double kilometer = 1000.*meter; +static const double kilometer2 = kilometer*kilometer; +static const double kilometer3 = kilometer*kilometer*kilometer; + +static const double parsec = 3.0856775807e+16*meter; + +static const double micrometer = 1.e-6 *meter; +static const double nanometer = 1.e-9 *meter; +static const double angstrom = 1.e-10*meter; +static const double fermi = 1.e-15*meter; + +static const double barn = 1.e-28*meter2; +static const double millibarn = 1.e-3 *barn; +static const double microbarn = 1.e-6 *barn; +static const double nanobarn = 1.e-9 *barn; +static const double picobarn = 1.e-12*barn; + +// symbols +static const double nm = nanometer; +static const double um = micrometer; + +static const double mm = millimeter; +static const double mm2 = millimeter2; +static const double mm3 = millimeter3; + +static const double cm = centimeter; +static const double cm2 = centimeter2; +static const double cm3 = centimeter3; + +static const double m = meter; +static const double m2 = meter2; +static const double m3 = meter3; + +static const double km = kilometer; +static const double km2 = kilometer2; +static const double km3 = kilometer3; + +static const double pc = parsec; + +// +// Angle +// +static const double radian = 1.; +static const double milliradian = 1.e-3*radian; +static const double degree = (3.14159265358979323846/180.0)*radian; + +static const double steradian = 1.; + +// symbols +static const double rad = radian; +static const double mrad = milliradian; +static const double sr = steradian; +static const double deg = degree; + +// +// Time [T] +// +static const double nanosecond = 1.e-9; +static const double second = 1.e+9 *nanosecond; +static const double millisecond = 1.e-3 *second; +static const double microsecond = 1.e-6 *second; +static const double picosecond = 1.e-12*second; + +static const double hertz = 1./second; +static const double kilohertz = 1.e+3*hertz; +static const double megahertz = 1.e+6*hertz; + +// symbols +static const double ns = nanosecond; +static const double s = second; +static const double ms = millisecond; + +// +// Electric charge [Q] +// +// static const double eplus = 1. ;// positron charge +static const double eplus = 1.60217733e-19 ;// positron charge +static const double e_SI = 1.60217733e-19;// positron charge in coulomb +static const double coulomb = eplus/e_SI;// coulomb = 6.24150 e+18 * eplus + + + +// +// Energy [E] +// +//static const double megaelectronvolt = 1.e6 ; // CERN value +static const double megaelectronvolt = 1.e6*e_SI ; // SI_value +static const double electronvolt = 1.e-6*megaelectronvolt; +static const double kiloelectronvolt = 1.e-3*megaelectronvolt; +static const double gigaelectronvolt = 1.e+3*megaelectronvolt; +static const double teraelectronvolt = 1.e+6*megaelectronvolt; +//static const double petaelectronvolt = 1.e+9*megaelectronvolt; +// + +// Joule ici 1 ! +static const double joule = electronvolt/e_SI;// joule = 6.24150 e+12 * MeV + + + + +// symbols +static const double MeV = megaelectronvolt; +static const double eV = electronvolt; +static const double keV = kiloelectronvolt; +static const double GeV = gigaelectronvolt; +static const double TeV = teraelectronvolt; + +// +// Mass [E][T^2][L^-2] +// +static const double kilogram = joule*second*second/(meter*meter); +static const double gram = 1.e-3*kilogram; +static const double milligram = 1.e-3*gram; + +// symbols +static const double kg = kilogram; +static const double g = gram; +static const double mg = milligram; + +// +// Power [E][T^-1] +// +static const double watt = joule/second;// watt = 6.24150 e+3 * MeV/ns + +// +// Force [E][L^-1] +// +static const double newton = joule/meter;// newton = 6.24150 e+9 * MeV/mm + +// +// Pressure [E][L^-3] +// + +static const double hep_pascal = newton/m2; // pascal = 6.24150 e+3 * MeV/mm3 +static const double bar = 100000*hep_pascal; // bar = 6.24150 e+8 * MeV/mm3 +static const double atmosphere = 101325*hep_pascal; // atm = 6.32420 e+8 * MeV/mm3 + +// +// Electric current [Q][T^-1] +// +static const double ampere = coulomb/second; // ampere = 6.24150 e+9 * eplus/ns +static const double milliampere = 1.e-3*ampere; +static const double microampere = 1.e-6*ampere; +static const double nanoampere = 1.e-9*ampere; + +// +// Electric potential [E][Q^-1] +// +//static const double megavolt = megaelectronvolt/eplus; +static const double megavolt = 1.e6; +static const double kilovolt = 1.e-3*megavolt; +static const double volt = 1.e-6*megavolt; + +// +// Electric resistance [E][T][Q^-2] +// +static const double ohm = volt/ampere;// ohm = 1.60217e-16*(MeV/eplus)/(eplus/ns) + +// +// Electric capacitance [Q^2][E^-1] +// +static const double farad = coulomb/volt;// farad = 6.24150e+24 * eplus/Megavolt +static const double millifarad = 1.e-3*farad; +static const double microfarad = 1.e-6*farad; +static const double nanofarad = 1.e-9*farad; +static const double picofarad = 1.e-12*farad; + +// +// Magnetic Flux [T][E][Q^-1] +// +static const double weber = volt*second;// weber = 1000*megavolt*ns + +// +// Magnetic Field [T][E][Q^-1][L^-2] +// +static const double tesla = volt*second/meter2;// tesla =0.001*megavolt*ns/mm2 +static const double milli_tesla = 0.001;// tesla =0.001*megavolt*ns/mm2 + +static const double gauss = 1.e-4*tesla; +static const double kilogauss = 1.e-1*tesla; + +// +// Inductance [T^2][E][Q^-2] +// +static const double henry = weber/ampere;// henry = 1.60217e-7*MeV*(ns/eplus)**2 + +// +// Temperature +// +static const double kelvin = 1.; +static const double mK = 1e-3*kelvin; +static const double muK = 1e-6*kelvin; + +// +// Amount of substance +// +static const double mole = 1.; + +// +// Activity [T^-1] +// +static const double becquerel = 1./second ; +static const double curie = 3.7e+10 * becquerel; + +// +// Absorbed dose [L^2][T^-2] +// +static const double gray = joule/kilogram ; +static const double kilogray = 1.e+3*gray; +static const double milligray = 1.e-3*gray; +static const double microgray = 1.e-6*gray; + +// +// Luminous intensity [I] +// +static const double candela = 1.; + +// +// Luminous flux [I] +// +static const double lumen = candela*steradian; + +// +// Illuminance [I][L^-2] +// +static const double lux = lumen/meter2; + +// +// Miscellaneous +// +static const double perCent = 0.01 ; +static const double perThousand = 0.001; +static const double perMillion = 0.000001; + + + +// +// +// +static const double Avogadro = 6.0221367e+23/mole; + +// +// c = 299.792458 mm/ns +// c^2 = 898.7404 (mm/ns)^2 +// +static const double c_light = 2.99792458e+8 * m/s; +static const double c_squared = c_light * c_light; + +// +// h = 4.13566e-12 MeV*ns +// hbar = 6.58212e-13 MeV*ns +// hbarc = 197.32705e-12 MeV*mm +// +static const double h_Planck = 6.6260755e-34 * joule*s; +static const double hbar_Planck = h_Planck/twopi; +static const double hbarc = hbar_Planck * c_light; +static const double hbarc_squared = hbarc * hbarc; + +// +// +// +static const double electron_charge = - eplus; // see SystemOfUnits.h +static const double e_squared = eplus * eplus; + +// +// amu_c2 - atomic equivalent mass unit +// amu - atomic mass unit +// +static const double electron_mass_c2 = 0.51099906 * MeV; +static const double proton_mass_c2 = 938.27231 * MeV; +static const double neutron_mass_c2 = 939.56563 * MeV; +static const double amu_c2 = 931.49432 * MeV; +static const double amu = amu_c2/c_squared; + +// +// permeability of free space mu0 = 2.01334e-16 Mev*(ns*eplus)^2/mm +// permittivity of free space epsil0 = 5.52636e+10 eplus^2/(MeV*mm) +// +static const double mu0 = 4*pi*1.e-7 * henry/m; +static const double epsilon0 = 1./(c_squared*mu0); + +// +// electromagnetic coupling = 1.43996e-12 MeV*mm/(eplus^2) +// +static const double elm_coupling = e_squared/(4*pi*epsilon0); +static const double fine_structure_const = elm_coupling/hbarc; +static const double classic_electr_radius = elm_coupling/electron_mass_c2; +static const double electron_Compton_length = hbarc/electron_mass_c2; +static const double Bohr_radius = electron_Compton_length/fine_structure_const; + + +// +// static const double k_Boltzmann = 8.617385e-11 * MeV/kelvin; +static const double k_Boltzmann = 1.3806504e-23; + +#endif diff --git a/Main Code 64bits/datacards.cpp b/Main Code 64bits/datacards.cpp new file mode 100644 index 0000000..0bf88cf --- /dev/null +++ b/Main Code 64bits/datacards.cpp @@ -0,0 +1,291 @@ +// $Id: datacards.cc,v 1.4 2009/12/05 08:33:15 astier Exp $ +// +// Datacards, acquisition EROS II +// +// +// Eric Aubourg, Decembre 95 +// +// DAPNIA/SPP (Saclay) / CEA + +#include "datacards.h" +#include +#include +#include +#include +#include // for strlen, strcmp, ... + +//++ +// Class DataCards +// Lib Outils++ +// include datacards.h +// +// Cette classe permet la gestion des parametres d'un programme a partir +// de mot-cle (lecture d'un fichier par exemple) +//-- + +//++ +// Titre Constructeurs +//-- +//++ +// +// DataCards() +// DataCards(string const& fn) +// Createur avec lecture des parametres ds le fichier de nom "fn" +//-- + +DataCards::DataCards() +{ +} + +DataCards::DataCards(string const& fn) +{ + ReadFile(fn); +} + +// AddProcF(ProcCard f, string const& mtch="*") +// Ajoute une fonction de traitement a la liste pour les mots cle +// compatibles avec la chaine "mtch" ("mtch" peut contenir "*" en debut +// fin de mot) +// +// Clear() +// Supprime les cartes existantes +// +// ReadFile(string const& fn) +// Lit le contenu du fichiers "fn" et ajoute les cartes a la liste +// +// AppendCard(string const& line) +// Rajoute la carte "line" a la liste +//-- + +void +DataCards::AddProcF(ProcCard f, string const& mtch) +{ +CrdPF mpf; +if (f == NULL) return; +mpf.pf = f; +if (mtch.length() <= 0) mpf.patt = "*"; +else mpf.patt = mtch; +cpfs.push_back(mpf); + + +// On applique cette nouvelle fonction aux cartes existantes +CardList::iterator ic; +for(ic = cards.begin(); ic != cards.end(); ic ++) + { + vector::iterator ik; + string tks; + for(ik = (*ic).tokens.begin(); ik != (*ic).tokens.end(); ik++) + tks = tks + " " + (*ik); + ApplyPF(mpf, (*ic).kw, tks); + } +} + +void +DataCards::Clear() +{ +cards.erase(cards.begin(), cards.end()); +} + +void +DataCards::ReadFile(string const& fn) +{ + /* was used in Peida to read default datacards files. + senseless in our case */ + DoReadFile(fn); +} + +void +DataCards::AppendCard(string const& crd) +{ +Card c; +size_t p = 1; +size_t q = crd.find_first_of(" \t"); +size_t l = crd.length(); + +string toks; +if (l < 2) return; +if (crd[0] != '@') return; + +if (q < l) + { c.kw = crd.substr(p,q-p); toks = crd.substr(q, l-q); } +else { c.kw = crd.substr(p,l-p); toks = ""; } +// On applique les ProcFunc's +ApplyPFL(c.kw, toks); +while (q < l) + { + p = crd.find_first_not_of(" \t",q+1); // au debut d'un token + if (p>=l) break; + q = crd.find_first_of(" \t",p); // la fin du token; + string token = crd.substr(p,q-p); + c.tokens.push_back(token); + } +// On supprime la carte de la liste, si elle existe deja ... +RemoveCard(c.kw); +cards.push_back(c); +} + +void +DataCards::DoReadFile(string const& fn) +{ +char line_buff[512]; +FILE *fip; + +if ( (fip = fopen(fn.c_str(),"r")) == NULL ) + { + cerr << " DataCards::DoReadFile cannot open file " << fn << endl; + return; + } +while (fgets(line_buff,511,fip) != NULL) + { + char *last = line_buff+strlen(line_buff) -1; + if (*last == '\n') *last = '\0'; /* CR at end of line : remove it */ + string line(line_buff); + AppendCard(line); + } +fclose(fip); +} + +int +DataCards::ApplyPF(CrdPF & cpf, string const& key, string const& toks) +{ +size_t l,lk; +int rc = 0; +// On verifie si le "pattern" correspond +bool mtch = false; +l = cpf.patt.length(); +if (cpf.patt == "*") mtch = true; +else if (cpf.patt[0] == '*') + { + lk = key.length(); + if (cpf.patt[l-1] != '*') + { + if (strcmp(key.c_str()+(lk-l+1), cpf.patt.c_str()+1) == 0) mtch = true; + } + else if (key.find(cpf.patt.substr(1,l-2)) < lk) mtch = true; + } +else if (cpf.patt[l-1] == '*') + { + if ( strncmp(key.c_str(), cpf.patt.c_str(),l-1) == 0) mtch = true; + } +else if (key == cpf.patt) mtch = true; + +// Si oui, on appelle la fonction correspondante +if (mtch) rc = cpf.pf(key, toks); + +return(rc); +} + + +int +DataCards::ApplyPFL(string const& key, string const& toks) +{ +int rc = 0; +CrdPFList::iterator icf; +for(icf = cpfs.begin(); icf != cpfs.end(); icf++) + rc += ApplyPF((*icf), key, toks); +return(rc); +} + +void +DataCards::RemoveCard(string const& key) +{ +CardList::iterator i; +for(i=cards.begin(); i != cards.end(); i++) + if ((*i).kw == key) { cards.erase(i); break; } +} + +DataCards::Card * +DataCards::FindKey(string const& key) +{ +/* + CardList::iterator i = find_if(cards.begin(), cards.end(), bind2nd(KeyEq(),key)); + if (i == cards.end() ) return NULL; +*/ + CardList::iterator i; + for(i=cards.begin(); i != cards.end(); i++) + if ((*i).kw == key) return &*i; + + return NULL; +} + + +// int NbCards() +// Renvoie le nombre de cartes data +// bool HasKey(string const& key) +// Indique l'existence d'une carte avec la cle "key" +// int NbParam(string const& key) +// Indique le nombre de parametres (separes par des espaces) pour la cle "key" +// string SParam(string const& key, int num = 0, string def="") +// Renvoie la valeur du parametre numero "num" ( 0..(NbParam()-1) ) sous forme de +// chaine de caracteres ("string") +// long IParam(string const& key, int numero = 0, long def = 0) +// Renvoie la valeur du parametre numero "num" ( 0..(NbParam()-1) ) convertie +// en entier ("long") +// double DParam(string const& key, int numero = 0, double def = 0) +// Renvoie la valeur du parametre numero "num" ( 0..(NbParam()-1) ) convertie +// en flottant ("double") +//-- + + +bool +DataCards::HasKey(string const& key) +{ + return FindKey(key) != NULL; +} + +int +DataCards::NbCards() +{ +return(cards.size()); +} + +int +DataCards::NbParam(string const& key) +{ + DataCards::Card * p = FindKey(key); + if (!p) return(-1); + else return(p->tokens.size()); +} + +string +DataCards::SParam(string const& key, int numero, string def) +{ + DataCards::Card * p = FindKey(key); + if (!p) return def; + if ( (numero < 0) || (numero >= int(p->tokens.size())) ) return def; + return p->tokens[numero]; +} + +long +DataCards::IParam(string const& key, int numero, long def) +{ + string p = SParam(key, numero, ""); + if (p == "") return def; + long i; + //istrstream(p.c_str(), p.length()) >> i; + sscanf(p.c_str(),"%ld",&i); + return i; +} + +double +DataCards::DParam(string const& key, int numero, double def) +{ + string p = SParam(key, numero, ""); + if (p == "") return def; + double i; + //istrstream(p.c_str(), p.length()) >> i; + sscanf(p.c_str(),"%lg",&i); + return i; +} + + +ostream& operator << (ostream& s, DataCards c) +{ + for (DataCards::CardList::iterator i = c.cards.begin(); i != c.cards.end(); i++) { + s << setw(10) << "@"+(*i).kw << " "; + for (vector::iterator j = (*i).tokens.begin(); j != (*i).tokens.end(); j++) + s << (*j) << " "; + s << endl; + } + return s; +} diff --git a/Main Code 64bits/datacards.h b/Main Code 64bits/datacards.h new file mode 100644 index 0000000..a5e2973 --- /dev/null +++ b/Main Code 64bits/datacards.h @@ -0,0 +1,132 @@ +// PERMET DE LIRE DES DATA A PARTIR D'UN FICHIER. +// Ecrit par: +// Eric Aubourg, Decembre 95 // DAPNIA/SPP (Saclay) / CEA LAL - IN2P3/CNRS (Orsay) +// Reza Ansari, Aout 96 +// Daniel Comparat Sept 2012 + + +// Cette classe permet la gestion des parametres d'un programme a partir +// de mot-cle (lecture d'un fichier par exemple) + + +// Les "card" sont les variables, ce sont les noms en début de ligne commençant par @ suivit ensuite une liste de valeurs séparées par des blancs (ou tab) et ceux jusqu'a un saut de ligne + +/*** Example de fichier datacard ********** + +# +@SEEING_PRCTAGE 0.9 +@TRUC_ENTIER 15 17 23 +@TRUC_STRING udchdjkzbcz +# + +*************************/ + +// La 1ère valeur peut être int (appelée par: data.IParam("nom_de_la_variable")) ou double (de même avec D) où string (S); +// De même si on veux la troisième valeur data.IParam("nom_de_la_variable",2) +// Toute autre mot ou ligne est ignorée + + +// int NbCards() +// Renvoie le nombre de cartes data +// bool HasKey(string const& key) +// Indique l'existence d'une carte avec la cle "key" +// int NbParam(string const& key) +// Indique le nombre de parametres (separes par des espaces) pour la cle "key" + + + +/****************** Exemple Utilisation datacard ****************** + + +string nomdat = "ma_data_card" ; +DataCards data(nomdat.c_str()); +double prctage = data.DParam("SEEING_PRCTAGE") ; +int itruc = data.IParam("TRUC_ENTIER") ; +string struc = data.SParam("TRUC_STRING") ; + + +***************************/ + +#ifndef DATACARDS_SEEN +#define DATACARDS_SEEN + +#include +#include +#include +#include +#include + +using namespace std; + + +typedef int (*ProcCard)(string const& key, string const& toks); + +class DataCards { +public: + DataCards(); + DataCards(string const& fn); + + virtual ~DataCards() {} + +// AddProcF(ProcCard f, string const& mtch="*") +// Ajoute une fonction de traitement a la liste pour les mots cle +// compatibles avec la chaine "mtch" ("mtch" peut contenir "*" en debut +// fin de mot) +// + + +// Rajoute la carte "line" a la liste + void AddProcF(ProcCard f, string const& mtch="*"); + + +// Supprime les cartes existantes + void Clear(); + +// Lit le contenu du fichiers "fn" et ajoute les cartes a la liste + void ReadFile(string const& fn); + void AppendCard(string const& line); + + int NbCards(); + bool HasKey(string const& key); + int NbParam(string const& key); + string SParam(string const& key, int numero = 0, string def=""); + long IParam(string const& key, int numero = 0, long def = 0); + double DParam(string const& key, int numero = 0, double def = 0); + + friend ostream& operator << (ostream& s, DataCards c); + +public: + struct Card { + string kw; + vector tokens; + // STRUCTCOMPF(Card,kw) + }; + typedef list CardList; + struct CrdPF { + ProcCard pf; + string patt; + // STRUCTCOMPF(CrdPF,pf) + }; + typedef list CrdPFList; +public: + CardList cards; + CrdPFList cpfs; + + void DoReadFile(string const& fn); + + int ApplyPF(CrdPF & cpf, string const& key, string const& toks); + int ApplyPFL(string const& key, string const& toks); + + void RemoveCard(string const& key); + + Card* FindKey(string const& key); + +#ifndef SWIG + struct KeyEq : binary_function { + bool operator()(const Card& x, const string& y) const + { return x.kw == y; } + }; +#endif + +}; +#endif diff --git a/Main Code 64bits/diagonalization.cpp b/Main Code 64bits/diagonalization.cpp new file mode 100644 index 0000000..572be80 --- /dev/null +++ b/Main Code 64bits/diagonalization.cpp @@ -0,0 +1,406 @@ +#include "diagonalization.h" + +#include // to include cout, cin + +// diagonalized the Hamiltionian for B field and v velocity (orthogonal to B) and give the eigenvectors and eigenvalues and update all Level[n].Energy_cm +void Diagonalization_Energy(vector &Level, double B, double v, SelfAdjointEigenSolver &es) +{ + // Manifold 2M Sym #=1..21 + // population v=n 2J=2Spin 2N=2L 2Ω Ecm Δ C + + int nb_levels=21; // Level.size() + + + /******* ORDER OF LEVELS (the n=0 and n=1 manifold, the one for spontaneous emission, should be order in Energy) **************** + + + + The matrix are calculated using a Mathematica code which use n S L J M_J ordering that is the most natural orderning. So we use it here. + + Dead Level 1S00 3S1-1 3S10 3S11, 1S00 3S1-1 3S10 3S11, 1P1-1 1P10 1P11 3P00 3P1-1 3P10 3P11 3P2-2 3P2-1 3P20 3P21 3P22 + + number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 + in C++ [i] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 + + + However the diagonalization then gives an ordering in energy that is + + Dead Level 1S00 3S1-1 3S11 3S10, 1S00 3P00 3P1-1 3P10 3P11 1P1-1 1P10 1P11 3P2-2 3P2-1 3P20 3P21 3P22 3S1-1 3S10 3S11 + + correspond: 1 2 3 5 4 6 13 14 15 16 10 11 12 17 18 19 20 21 7 8 9 + in C++ [i] 0 1 2 4 3 5 12 13 14 15 9 10 11 16 17 18 19 20 6 7 8 + +new number C++[i]0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 + + + Indeed the block ordered in energy are: + + DEAD LEVEL M=0 + n=1 1S00 + + 3S1-1 3S11 3S10 + + 1S00 + + 3P00 + + 3P1-1 3P10 3P11 + + 1P1-1 1P10 1P11 + + 3P2-2 3P2-1 3P20 3P21 3P22 + + 3S1-1 3S10 3S11 + + + + + BUT in the following the order in only ordered in Energy in the ground state + DEAD LEVEL M=0 + n=1 1S00 3S1-1 3S11 3S10 + n=2S 1S00 3S1-1 3S10 3S11 + n=2P 1P1-1 1P10 1P11 3P00 3P1-1 3P10 3P11 3P2-2 3P2-1 3P20 3P21 3P22 + + + + + + + *************************************/ + + + +// I add a small shift to ensure the energy orderning in the ground state + double E0_cm[nb_levels][nb_levels] = + { + {-10000.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,-6.817589266,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,-0.000000000001,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.000000000001,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,41147.81261,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,41148.66481,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,41148.66481,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,41148.66481,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.29958,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.29958,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.29958,0.,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.0561,0.,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.23871,0.,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.23871,0.,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.23871,0.,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.3848,0.,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.3848,0.,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.3848,0.,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.3848,0.}, + {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,41148.3848} + }; + + double Zeeman_cm_B[nb_levels][nb_levels] = + { + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0.9337307964640151,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0.9337307964640151,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0.9337307964640151,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0.9337307964640151,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0.6602473779824211,0,0,0,0.6602473779824211,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,-0.5390897266891428,0,0,0,0,0,0.7623880028197907,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-0.6602473779824211,0,0,0,0.6602473779824211,0}, + {0,0,0,0,0,0,0,0,0,0,-0.5390897266891428,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0.6602473779824211,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,-0.6602473779824211,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0.6602473779824211,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0.7623880028197907,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0.6602473779824211,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0} + }; + + double Stark_cm_Bv[nb_levels][nb_levels] = + { + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,1.8108016266147785e-6,0,-1.8108016266147785e-6,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,-1.0454668065750543e-6,0,1.2804301095629403e-6,0,1.8108016266147785e-6,0,-7.392566684346655e-7,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,1.2804301095629403e-6,0,1.2804301095629403e-6,0,1.2804301095629403e-6,0,-1.2804301095629403e-6,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,1.0454668065750543e-6,0,1.2804301095629403e-6,0,0,0,7.392566684346655e-7,0,-1.8108016266147785e-6}, + {0,0,0,0,0,1.8108016266147785e-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,-1.8108016266147785e-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,-1.0454668065750543e-6,0,1.0454668065750543e-6,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,1.2804301095629403e-6,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,1.2804301095629403e-6,0,1.2804301095629403e-6,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,1.2804301095629403e-6,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,1.8108016266147785e-6,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,1.2804301095629403e-6,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,-7.392566684346655e-7,0,7.392566684346655e-7,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,-1.2804301095629403e-6,0,0,0,0,0,0,0,0,0,0,0,0,0}, + {0,0,0,0,0,0,0,0,-1.8108016266147785e-6,0,0,0,0,0,0,0,0,0,0,0,0} + }; + +// For small sizes, especially for sizes smaller than (roughly) 16, using fixed sizes is hugely beneficial to performance, as it allows Eigen to avoid dynamic +// So here I use dynamical size +// But I use double and not flat to increase the precision but this is double size so slower ! + + + MatrixXd H(nb_levels,nb_levels); // Hamiltonian Matrix + + // data Allocation + for (int i=0; i_0 = 0__0 +// cout << " i,j " << i << " " << j << " " << E0_cm[i][j] << " " << Zeeman_cm_B[i][j] << " " << Stark_cm_Bv[i][j] << endl; + } + + es.compute(H); // calculate the new eigenvectors |i> (i start from 0) and new eingen_Energies + // E_i = es.eigenvalues()(i) (in incresing order) + // es.eigenvectors()(i,j) = 0 gives (i=line, j = column index) the new (column) vector |j> in function of the old |i>_0 + + for( int n = 0; n < nb_levels; n++ ) + { + Level[n].Energy_cm = es.eigenvalues()(n); + } +} + + +// diagonalized the Hamiltionian for B field and v velocity (orthogonal to B) and give the eigenvectors and eigenvalues and dipoles (in Debye)update all Level[n].Energy_cm +void Diagonalization_Energy_dipole(vector &Level, double B, double v, SelfAdjointEigenSolver &es, MatrixXd d[]) +{ + int nb_levels=21; // Level.size(); 21 in our case + + /******* ORDER OF LEVELS (ordered in energy for the stable states n=1) ***************************** + + DEAD LEVEL M=0 + n=1 1S00 3S1-1 3S11 3S10 + n=2S 1S00 3S1-1 3S10 3S11 + n=2P 1P1-1 1P10 1P11 3P00 3P1-1 3P10 3P11 3P2-2 3P2-1 3P20 3P21 3P22 + + ***************************************************************************************************/ + +// E_laser=E' + E'^dag +// for absorption (that is for E_j> E_i and a transition i --> j) the Rabi frequency comes from d_{ji} = +// so for a laser with polarization vector E' along e_q the dipole is = E' with m_j = q+ m_i +// so the dipole is that is coded here as d[q+1][j][i] +// +// q=-1 for sigma- +// q=0 for pi +// q= +1 for sigma+. +// So be CAREFUL m_i - m_j = q (polar) ONLY for E_j> E_i +// +// For (spontaneous or) stimulated emission with the same laser, that is j-->i for E_j> E_i, the transition is = ()* +// that is if the dipoles (in Debye)are REAL (THAT IS OUR CASE). + +/*** is coded here as d[q+1][i][j] (real), i = line, j = column ; that is for a i<-->j transition (with E_i> E_j) ****/ + + double dipole[3][nb_levels][nb_levels]= + { + { + {0, 0, 0, 4.722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, // this is d[-1][0][j] = <0|d_-1|j> + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0}, // this is d[-1][1][j] = <1|d_-1|j> + {4.722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.18635, 0, 2.67773, 0, 0, 0, 1.54599, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.78688}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.67773, 0, 0, 0, 2.67773, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 2.18635, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, -2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, -2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 1.54599, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} + }, + { + {0, 159.878, 0, 0, 4.722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {159.878, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.67773, 0, 0, 0, -2.67773, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.67773, 0, 0, 0, -2.67773, 0}, + {4.722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.18635, 0, 0, 0, 0, 0, -3.09197, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, -3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 2.18635, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, -2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, -2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, -3.09197, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, -2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} + }, + { + {0, 0, 4.722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, // this is d[+1][0][j] = <0|d_+1|j> + {0, 0, 0, 0, 0, 0, 0, 0, 0, 3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, // this is d[+1][1][j] = <1|d_+1|j> + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.78688, 0, 0, 0, 0}, + {4.722, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2.18635, 0, -2.67773, 0, 0, 0, 1.54599, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.67773, 0, 0, 0, 2.67773, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 2.18635, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 1.54599, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 2.67773, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 3.78688, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} + } + }; + + + + MatrixXd d0[3]; // d0 = matrix dipole in zero field + + d0[0] = MatrixXd(nb_levels,nb_levels); + d0[1] = MatrixXd(nb_levels,nb_levels); + d0[2] = MatrixXd(nb_levels,nb_levels); + + +// dipole matrix element + for (int i=0; i_0 (i = out and j = in) + // cout << "polar " << n_polar << " i " << i << " j " << j << " d " << d0[n_polar+1](i,j) << endl; + } + } + + + /*** diagonalization ***/ + +// diagonalized the Hamiltionian for B field and v velocity and give the eigenvectors and eigenvalues + Diagonalization_Energy(Level, B, v, es); + + + /**** calcul of the new dipoles (in Debye) ***/ + + for(int n_polar = -1; n_polar <= 1; n_polar++) + { + d[n_polar+1] = (es.eigenvectors().adjoint())*d0[n_polar+1]*(es.eigenvectors()); + + // evec = es.eigenvectors() verifie evec(j0,j) = 0 gives (j0=line, j = column index) the new (column) vector |j> in function of the old |j0>_0 + // d0[q+1]_i0 j0 = 0__0 . So d[q+1]_ij = = Sum i0,j0 0 00 0 = Sum i0,j0 evec^dag (i,i0) d_q(i0,j0) evec(j0,j) + // The new dipole are given by d[polar] = evec^dag.d0[polar].evec = with evec_j = |j> = sum_|j>_0 0_. + } + + +} + + +// A partir de la matrice des dipole qui contient en première ligne les M_in et dernière colonne les M_out +int Create_dipole_Lines_from_Matrices(const char *nom_file) +{ + int nb_levels=21; + + double matrice[nb_levels+1][nb_levels+1]; + double dipole[3][nb_levels][nb_levels]; + + string filename = "Data/matrice_dipole.dat"; + // ifstream file(nom_file); + ifstream file(filename.c_str()); + if ( !file ) + { + cerr << "Erreur d'ouverture fichier Level" << nom_file << endl; + return 0; + } + + for (int i=0; i_0 + } + } + + + while (!file.eof()) + { + for (int i=0; i> matrice[i][j] ; + } + } + + for (int i=0; i_0 + } + } + + for(int n_polar = -1; n_polar <= 1; n_polar++) + { + dipole_file << "{"; + for (int i=0; i +#include "Internal_state.h" + +using namespace Eigen; +using namespace std; + +// diagonalized the Hamiltionian for B field and v velocity (orthogonal to B) and give the eigenvectors and eigenvalues and update all Level[n].Energy_cm +void Diagonalization_Energy(vector &Level, double B, double v, SelfAdjointEigenSolver &es); + +// diagonalized the Hamiltionian for B field and v velocity (orthogonal to B) and give the eigenvectors and eigenvalues and dipoles (in Debye) update all Level[n].Energy_cm +void Diagonalization_Energy_dipole(vector &Level, double B, double v, SelfAdjointEigenSolver &es, MatrixXd d[]); + +// A partir de la matrice des dipole qui contien en première ligne et dernière colonne les M +int Create_dipole_Lines_from_Matrices(const char *nom_file); diff --git a/Main Code 64bits/laser.cpp b/Main Code 64bits/laser.cpp new file mode 100644 index 0000000..7a79d79 --- /dev/null +++ b/Main Code 64bits/laser.cpp @@ -0,0 +1,424 @@ +#include "laser.h" +#include + + + + +// ------------ +// Constructors +// ------------ + +Laser::Laser() // Constructeur par défaut +{ + waist_pos.set(0.,0.,0.); + direction.set(0.,0.,1.); + waist.set(1.,1.,0.); + lambda = 1.; + Gamma_Laser = 1.; + Power = 0.; + polarisation.set(0.,0.,0.); + polar_angle_degree = 0.; + type_laser = CW; + coherent_avec_laser_num = -1; + spectre_Ecm_attenuation.clear(); // spectre_Ecm_attenuation = map < double, double > (); + spectre_Ecm_attenuation.insert ( pair(0.,1.) ); // Par défaut le spectre est non façonné. On écrit spectre_Ecm_attenuation[0.] = 1.; + +}; + + +Laser::~Laser() +{} +; // Destructeur + +Laser::Laser(const Laser & my_laser) // Constructeur de (re)copie +{ + waist_pos = my_laser.waist_pos; + direction = my_laser.direction; + waist = my_laser.waist; + lambda = my_laser.lambda; + Gamma_Laser = my_laser.Gamma_Laser; + Power = my_laser.Power; + polarisation = my_laser.polarisation; + polar_angle_degree = my_laser.polar_angle_degree; + type_laser = my_laser.type_laser; + coherent_avec_laser_num = my_laser.coherent_avec_laser_num; + // map < double, double > spectre_Ecm_attenuation; // In order to create properly the object (cf Guarreta course p22) + spectre_Ecm_attenuation = my_laser.spectre_Ecm_attenuation; +}; + +Laser & Laser::operator = (const Laser& my_laser) // Affectation par recopie +{ + if (this != &my_laser) // On vérifie que les objets ne sont pas les mêmes ! + { + waist_pos = my_laser.waist_pos; + direction = my_laser.direction; + waist = my_laser.waist; + lambda = my_laser.lambda; + Gamma_Laser = my_laser.Gamma_Laser; + Power = my_laser.Power; + polarisation = my_laser.polarisation; + polar_angle_degree = my_laser.polar_angle_degree; + type_laser = my_laser.type_laser; + coherent_avec_laser_num = my_laser.coherent_avec_laser_num; + spectre_Ecm_attenuation = my_laser.spectre_Ecm_attenuation; // Attention ne recopie pas la map seulement l'adresse. + } + return *this; +} + + + +// ---------- +// Comparison +// ---------- + +// On ne test pas le spectre (inutile car cette fonction est inutile en fait) +bool Laser::operator == (const Laser& my_laser) const +{ + return ( waist_pos == my_laser.waist_pos && + direction == my_laser.direction && + waist == my_laser.waist && + lambda == my_laser.lambda && + Gamma_Laser == my_laser.Gamma_Laser && + Power == my_laser.Power && + polarisation == my_laser.polarisation && + polar_angle_degree == my_laser.polar_angle_degree && + type_laser == my_laser.type_laser && + coherent_avec_laser_num == my_laser.coherent_avec_laser_num) ? true : false; +} + +bool Laser::operator != (const Laser& my_laser) const +{ + return (waist_pos != my_laser.waist_pos || + direction != my_laser.direction || + waist != my_laser.waist || + lambda != my_laser.lambda || + Gamma_Laser != my_laser.Gamma_Laser || + Power != my_laser.Power || + polarisation != my_laser.polarisation || + polar_angle_degree != my_laser.polar_angle_degree || + type_laser != my_laser.type_laser || + coherent_avec_laser_num != my_laser.coherent_avec_laser_num) ? true : false; +} + +//---------------------------------- +// Surdéfinition des entrées sorties +//---------------------------------- + +// Sortie des paramètre sauf le spectre +ostream& operator << (ostream &flux, Laser my_laser) +{ + my_laser.write(flux); + return(flux); +} + +istream& operator >> (istream &flux, Laser & my_laser) //my_laser est modifié! +{ + my_laser.read(flux); + return(flux); +} + + +void Laser::read_Spectrum(istream & flux) +{ + double energy_cm, attenuation; + flux >> energy_cm; + flux >> attenuation; + spectre_Ecm_attenuation.insert ( pair(energy_cm,attenuation) ); // spectre_Ecm_attenuation[energy_cm] = attenuation; Mais je préfère ainsi car as modifier un std::map dans une boucle for basée sur ses iterators. Même le fait d'accéder à une clé via l'opérateur [ ] insère cette clé (avec la donnée T()) dans la map. +} + +int Laser::read_Spectrum(const char *nom_file) +{ + ifstream file(nom_file); + + if ( !file || nom_file== NULL) + { + // cerr << "No able to open the file " << nom_file << endl; // Better to not put because sometimes their is no file (and so if this line is here, we will have all the time a message) and we just as the defautl values + file.close(); + return 0; // So spectre_Ecm_attenuation is unchanged and thus compose by the default file + } + + int i=0; + spectre_Ecm_attenuation.clear(); // To avoid to insert the default file at the begining + + while (!file.eof()) + { + this->read_Spectrum(file); + i++; + } + + file.close(); + return i; +} + + +void Laser::write_Spectrum(ostream & flux) +{ + if (spectre_Ecm_attenuation.size() ==0) + cout << " FICHIER VIDE " << endl; + map < double, double >::const_iterator itr; + + if (&flux == &cout) + for(itr = spectre_Ecm_attenuation.begin(); itr != spectre_Ecm_attenuation.end(); ++itr) + cout << "Energie(cm^-1) " << (*itr).first << " Value attenuation: " << (*itr).second << endl; + else + for(itr = spectre_Ecm_attenuation.begin(); itr != spectre_Ecm_attenuation.end(); ++itr) + flux << itr->first << itr->second << endl; + +} + + +// ---------------------------------- +// FONCTIONS EN LIGNES +// ---------------------------------- + +// intensité au waist +double Laser::intensity() const +{ + double intensity = 2.*Power/(pi*(waist.x())*(waist.y())); + // I=2P/(pi*w^2) lorsque w=wX=wY + // Rappel w.Z=0; + + return intensity; + +} + + +// intensité au waist prenant en compte le spectre +double Laser::transmission_spectrum(const double energie_trans_cm) const +{ + map < double, double >::const_iterator itr; + + itr = spectre_Ecm_attenuation.upper_bound (energie_trans_cm); // itr pointe sur l'élément juste après energie_trans_c + itr--; + + return (itr->second); +} + + + + +// Zone de Rayleigh Vecteur3D +// ZRZ est la zone de Railieh moyenne +Vecteur3D Laser::Rayleigh_range() const +{ + + double ZRX=pi*waist.x()*waist.x()/lambda; + double ZRY=pi*waist.y()*waist.y()/lambda; //ZR = pi wo^2/lambda + double ZRZ=sqrt(ZRX*ZRX+ZRY*ZRY); + return Vecteur3D(ZRX,ZRY,ZRZ); +} + +// waist au point (X,Y,Z) +Vecteur3D Laser::waist_size(const Vecteur3D& point) const +{ + + double ZRX=pi*waist.x()*waist.x()/lambda; + double ZRY=pi*waist.y()*waist.y()/lambda; //ZR = pi wo^2/lambda + + double wX = (waist.x())*sqrt(1+(point.z()/ZRX)*(point.z()/ZRX)); // w(z)^2=w0^2(1+(z/zr)^2) + double wY = (waist.y())*sqrt(1+(point.z()/ZRY)*(point.z()/ZRY)); // w(z)^2=w0^2(1+(z/zr)^2) + + return Vecteur3D(wX,wY,sqrt(ZRX*ZRX+ZRY*ZRY)); // waist selon zone de Rayleigh +} + + +// intensité au point (X,Y,Z) dans le repère laser centré sur le waist +double Laser::intensity_repere_sur_waist(const Vecteur3D& point) const +{ + double wX = (this->waist_size(point)).x(); + double wY = (this->waist_size(point)).y(); + double I0 = (this->intensity())*waist.x()*waist.y()/(wX*wY); + + + return I0*exp (-2*point.x()*point.x()/(wX*wX)) * exp (-2*point.y()*point.y()/(wY*wY)); // I=I0 exp(-2r^2/w^2) + // Plus généralement I= P * exp(-2 (x^2/wx^2))/(sqrt(2pi(wx/2)^2) * exp(-2 (y^2/wy^2))/(sqrt(2pi(wy/2)^2) +} + + + +// intensité au point (x,y,z) +// I.E. lié au repère du labo +// Pour le calculer on le remet dans le repère du laser +double Laser::intensity_lab_axis(const Vecteur3D& point) const +{ + return this->intensity_repere_sur_waist(rotation_lab_axis(point - this->get_waist_pos(), (Euler_angles(direction)).x(), (Euler_angles(direction)).y(), (Euler_angles(direction)).z()) ); +} + + +// wave_vector k +// h c / \lambda = h c \sigma(m-1) = \hbar c k +Vecteur3D Laser::wave_vector() const +{ + double k = 2*pi/lambda ; // k = 2pi/lambda + return k*direction.unit(); +} + + + + +// Energie de la transition laser en cm^-1 +double Laser::Energy_transition_laser_cm() const +{ + return 0.01/lambda ; +} + +//---------------------------------- +// AUTRES fonctions +//-------------------------------- + +// I = ε0 c E^2 /2. +double champ_E(const double irradiance) +{ + return sqrt(2*irradiance/(C*EPSILON0)); +} + + + +// (absolute value of the) effectif dipole d.e_laser = sum_p d_p epsilon^p +// where the dipole transition vector d= sum_p d_p e^p is given in the local quantification axis +// and the polarisation vector e_laser= sum_p' epsilon^p' e_p' is given in the laser axis +double effectif_dipole_local(const Vecteur3D& dipole, const Vecteur3D& axe_quant, const Laser& my_laser) +{ + double dp,d0,dm; + dm = dipole(0); + d0 = dipole(1); + dp = dipole(2); + + Vecteur3D Euler_angles_axe_quant = Euler_angles(axe_quant); + Vecteur3D Euler_angles_axe_laser = Euler_angles(my_laser.get_direction()); + +// The link between the polar angles (theta, phi) and the Euler angle (alpha, beta, gamma) in ZXZ convention as we used them (Wikipedia) are + // alpha= phi +pi/2; beta = theta; gamma = -pi/2 + double phi_F = Euler_angles_axe_quant(0) - pi/2.; // polar angle for the quantization axis (along the field F) + double theta_F = Euler_angles_axe_quant(1); // polar angle for the quantization axis (along the field F) + double phi_k = Euler_angles_axe_laser(0) - pi/2.; // polar angle for the laser axis (along the vector k) + double theta_k = Euler_angles_axe_laser(1); // polar angle for the laser axis (along the vector k) + + + // The polarization vector = am exp(i psi) e'_-1 + ap exp(-i psi) e'_+1 is given in the list param by ap (for sigma+), am for sigma- and the polar_angle psi + // So epsilon_-1 = am exp(-i psi) and epsilon_+1 = ap exp(i psi) + Vecteur3D polarization = my_laser.get_polarisation(); + double am = polarization(0); + double ap = polarization(2); + double psi = my_laser.get_polar_angle_degree()*pi/180.; +// TODO (dc#4#): We assume real dipole transition in -1,0,+1 polarizaion basis (sigma+, pi, sigma-). ... +//If different be careful + + + + complex dip_eff; + const complex i(0., 1.); + + /*** We try to optimize the calcul so to reduce at maximmum the numebr of operations ****/ + + double sin_theta_k = sin(theta_k); + double sin_theta_F = sin(theta_F); + double cos_theta_k = cos(theta_k); + double cos_theta_F = cos(theta_F); + double sqrt2 = sqrt(2.); + + double dp_minus_dm = (dp-dm); + + double d1F = -dp_minus_dm*cos_theta_F + sqrt2*d0*sin_theta_F; + double d2F = dp_minus_dm*sin_theta_F + sqrt2*d0*cos_theta_F; + + double dp_plus_dm = dp+dm; + + complex am_psi_minus_ap = am*exp(2.*i*psi) - ap; + complex am_psi_plus_ap = am*exp(2.*i*psi) + ap; + complex exp_F_plus_k = exp(2.*i*phi_F) + exp(2.*i*phi_k) ; + complex exp_F_minus_k = exp(2.*i*phi_F) - exp(2.*i*phi_k) ; + + dip_eff = am_psi_plus_ap*(dp_plus_dm*exp_F_plus_k - exp_F_minus_k*d1F)+ + am_psi_minus_ap*cos_theta_k*(-dp_plus_dm*exp_F_minus_k + exp_F_plus_k*d1F) + -2.*exp(i*(phi_F+phi_k))*am_psi_minus_ap*d2F*sin_theta_k; + + return abs(dip_eff/4.); // Only the absolute value is needed +} + + +/*** +Compare to the PRA 2014 we change notation now to be like Wikipedia in ZXZ concention (BE CAREFUL MATHEMATICA and Varshalovitch are in ZYZ convention) + repère x,y,z du labo et X,Y,Z de l'axe de quantification donné par le champ extérieur local +On utilise les angles d'Euler pour faire les rotations de repère +http://en.wikipedia.org/wiki/Euler_angles qui note (alpha,beta,gamma) + + +1. the first rotation is by an angle alpha (modulo 2pi, we chooose (-pi,pi] to use atan2 ) about the z-axis (even if we are going to use acos in 0 pi !) + +2. the second rotation is by an angle beta in [0,pi] about the former (new) x-axis (now x') + +3. the third rotation is by an angle gamma in (modulo 2pi, we chooose (-pi,pi] to use atan2 ) about the former z-axis (now z'). +***/ + +// Calcul des angles d'EULER. Pour un repère donné uniquement par son vecteur OZ=direction +// Il reste donc un arbitraire pour choisir l'angle de rotation autour de cet axe pour son repère +// Nous choissons les angles tel que le repère soit le repère polaire dont OZ est la direction et OX selon le méridien +Vecteur3D Euler_angles( Vecteur3D direction) +{ + double norm = direction.mag(); + direction = direction/norm; + double alpha; + + if (direction.x()==0 && direction.y()==0) + alpha = pi/2.; + else + alpha = atan2(direction.x(), - direction.y()); // alpha = atan2(Z_1,-Z2); where Z1 is the x coordinate of Z, Z2 is the y, Z3 is the z . atan2 (y,x) is defined as the angle between the positive x-axis and the ray to the point of coordinate (x,y) + // The other formula does nt depends on Z1 so is wrong for instance for direction = (-1,0,0) along -Ox : cos(alpha) = -Z_2 / \sqrt{1 - Z_3^2}. acos( - direction.y() / sqrt(1.00000000000001 -direction.z()*direction.z()) ) to avoid 1-1=0 + + double beta = acos(direction.z()); // ArcCos(Z3) + return Vecteur3D(alpha,beta,-pi/2.); + // Le lien entre les angles sphériques (polaires) (phi,theta,psi) et les angles d'Euler sont alpha=phi+pi/2; beta=theta; gamma = psi-pi/2 +} + + +/** +With the Euler angle alpha, beta, gamma that goes from the x,y,z, frame to the X,Y,Z one + +we have for the coordinates R=Ar (Z1 X2 Z3 convention) +A is the matrix + +a_(11) a_(12) a_(13) +a_(21) a_(22) a_(23) +a_(31) a_(32) a_(33) + + +a_(11) = cos(gamma)*cos(alpha) - cos(beta)*sin(alpha)*sin(gamma) +a_(12) = cos(gamma)*sin(alpha) + cos(beta)*cos(alpha)*sin(gamma) +a_(13) = sin(gamma)*sin(beta) +a_(21) = -sin(gamma)*cos(alpha) - cos(beta)*sin(alpha)*cos(gamma) +a_(22) = -sin(gamma)*sin(alpha) + cos(beta)*cos(alpha)*cos(gamma) +a_(23) = cos(gamma)*sin(beta) +a_(31) = sin(beta)*sin(alpha) +a_(32) = -sin(beta)*cos(alpha) +a_(33) = cos(beta) + + +**/ + +// Passage des coordonnées point(x,y,z) (labo) à (X,Y,Z): R=Ar donné par les angles d'Euler alpha beta et gamma +// cf http://mathworld.wolfram.com/EulerAngles.html +//Laser coordinates where point=(x,y,z) is lab coordinate +Vecteur3D rotation_lab_axis(const Vecteur3D& point, double alpha, double beta, double gamma) +{ + Vecteur3D A1,A2,A3; // A Rotation Matrix + + A1=Vecteur3D(cos(gamma)*cos(alpha)-cos(beta)*sin(alpha)*sin(gamma),cos(gamma)*sin(alpha)+cos(beta)*cos(alpha)*sin(gamma), sin(gamma)*sin(beta)); // A1=(a11,a12,a13) + A2=Vecteur3D(-sin(gamma)*cos(alpha)-cos(beta)*sin(alpha)*cos(gamma), -sin(gamma)*sin(alpha)+cos(beta)*cos(alpha)*cos(gamma),cos(gamma)*sin(beta) ); + A3=Vecteur3D(sin(beta)*sin(alpha), -sin(beta)*cos(alpha), cos(beta)); + + double X,Y,Z; //Laser coordinates where point=(x,y,z) is lab coordinate + X=A1.dot(point); + Y=A2.dot(point); + Z=A3.dot(point); + + return Vecteur3D(X,Y,Z); +} + + +// Passage des coordonnées point (X,Y,Z) donné dans le REPERE à labo (x,y,z) (repère labo). +// Le repère XYZ est donnée donné par les angles d'Euler alpha beta et gamma par rapport à xyz +Vecteur3D rotation_axis_lab(const Vecteur3D& point, double alpha, double beta, double gamma) +{ + return rotation_lab_axis(point, -gamma, - beta, -alpha); +} diff --git a/Main Code 64bits/laser.h b/Main Code 64bits/laser.h new file mode 100644 index 0000000..80f6c82 --- /dev/null +++ b/Main Code 64bits/laser.h @@ -0,0 +1,460 @@ +/* + Name: classe « Laser » + Copyright: + Author: Daniel Comparat + Date: 15/12/08 + Description: + + Classe Laser + Laser supposé gaussien + contenant +waist_pos : vecteur3D position du waist dans le repère fixe du labo, +direction : du vecteur d'onde, non nécessairement normalisé, +waist : Le waist est w_kx, w_ky, w_kz où kz est l'axe selon k. +lambda : longueur d'onde lambda moyenne (en SI, i.e. en metre) DANS LE VIDE. +Gamma_Laser : largeur spectrale FWHM en s^-1. +Power : puissance, +Polarisation est un vecteur normé qui contient epsilon^-1 (codé sur x), espilon^0 (sur y) et epsilon^+1 (sur z) +où -1 (pour sigma- = circulaire right car l'axe de quanti est k),0 (pour pi), 1 (pour sigma+ = circulaire left car l'axe de quanti est k) +polar_angle_degree gives the polarization angle (cf User Guide) +type_laser : le type (CW, pulsé femto, gaussien, lorentzien, comb, black body...) +coherent_avec_laser_num: pour les interférences est le numéro du premier laser avec lequel il est cohérent. + + +On met aussi (surtout pour le cas façonné) un spectre en énergie spectrale (cm^-1) du laser. +C'est un tableau Energie_cm, I_attenuation (1= non atténué, 0= éteind). +L'intensité sera donc celle du laser multiplié par I_attenuation à l'énergie (immédiatement supérieure) de la transition (1 par défaut). + + + +Il y a aussi les fonctions donnant (ATTENTION LES X,Y,Z réfèrent au repère lié au laser !) +Donc pas dans le repère du labo! + +Mais il y a une fonction qui donne les angles d'Euler: Euler_angles + +intensité (irradiance) au waist: intensity() +Zone de Rayleigh: Rayleigh_range() +waist au point (X,Y,Z): waist_size(point) +intensité (irradiance) au point (X,Y,Z): intensity(point) +wave_vector: wave_vector() + +RAPPEL: E =h\nu = \hbar \omega= h c / \lambda_{\rm vide} = h c \sigma(m-1) = \hbar c k = 100 h c sigma(cm^-1) + + * Les éléments de la classe sont initialisée à 0. Sauf le waist, direction, lambda, Gamma_Laser à (1,1,0); (0,0,1), 1, 1 pour éviter des divisions par zéros + * On peut leur mettre des valeurs par (exemple) my_laser.set_waist_pos(new_pos) + * On peut lire les valeurs par (exemple) my_laser.get_waist_pos() + * == et != sont surdéfinis ATTENTION ILS COMPARENT PARFOIS DES DOUBLES (avec les erreurs d'arrondis cela doit être faux) + * write et read permettent d'écrire et de lire dans un flux (cout (pas cerr ou clog) ou fichier) + + + + */ + + + + +#ifndef my_laser_SEEN +#define my_laser_SEEN + +#include // Pour le spectre du laser Energy, Intensité relative +#include +using namespace std; + +#include "Vecteur3D.h" +#include "constantes_SI.h" // SI Constantes pour pi, cm, MHz ou autre + +/* +Forme canonique d'une classe T (Claude Delannoy, Programmer en C++) + +class T +{ + public: + T(...); // constructeur de T, autres que par recopie + T(const T &); // constructeur de recopie de T + ~T(); // destructeur + T & T::operator = (const T &); // opérateur d'affectation + ..... +}; +*/ + + +enum // Différents types de lasers +{ + spon_emission = -1, // no_laser + CW = 0, + femto =1, + multi_mode=2, + pulse=3, + faconne = 4, // Obsolete car il y a le spectre maintenant + gaussien = 5, + lorentzien = 6, + comb = 7, + pseudo_BBR =8, + field_ionization =9 +}; + + + +class Laser +{ +protected: + Vecteur3D waist_pos; // (X,Y,Z) position + Vecteur3D direction; // (X,Y,Z) direction du vecteur d'onde k + Vecteur3D waist; // Le waist est w_kx, w_ky, w_kz où kz est l'axe selon k. + double lambda; // longueur d'onde lambda moyenne (en SI, i.e. en metre), DANS LE VIDE + double Gamma_Laser; // largeur spectrale (Delta lambda) + double Power; // puissance, + Vecteur3D polarisation; // Polarisation -1,0,+1: sigma-,pi,sigma+ + double polar_angle_degree; // angle of the polarizaiton vector versus X axis + int type_laser; // CW, faconne , femto, pulsé , ... + int coherent_avec_laser_num; // numéro du premier laser avec lequel il est cohérent -1 ou lui même si pas cohérent + +public: + map < double, double > spectre_Ecm_attenuation ; //La liste du spectre laser atténué +// C'est un tableau Energie_cm, I_attenuation (1= non atténué, 0= éteind). + + + + +public: // Forme canonique d'une classe + Laser(); //constructeur + Laser(const Laser&); // Constructeur de copie + Laser& operator = (const Laser&); // Affectation par recopie + virtual ~Laser(); // Destructeur par defaut + + // Get components + Vecteur3D get_waist_pos() const + { + return waist_pos; + } + Vecteur3D get_direction() const + { + return direction.unit(); // vecteur directeur normalisé + } + Vecteur3D get_waist() const + { + return waist; + } + double get_lambda() const + { + return lambda; + } + double get_omega() const // Pulsation + { + return 2*pi*C/lambda; + } + double get_Gamma_Laser() const + { + return Gamma_Laser; + } + double get_Power() const + { + return Power; + } + Vecteur3D get_polarisation() const + { + return polarisation; + } + double get_polar_angle_degree() const + { + return polar_angle_degree; + } + int get_type_laser() const + { + return type_laser; + } + int get_coherent_avec_laser_num() const + { + return coherent_avec_laser_num; + } + + + + // Set components + void set_waist_pos(const Vecteur3D& new_pos) + { + waist_pos = new_pos; + } + void set_direction(const Vecteur3D& new_dir) + { + direction = new_dir; + } + void set_waist(const Vecteur3D& new_waist) + { + waist = new_waist; + } + void set_lambda(const double& new_lambda) + { + lambda = new_lambda; + } + void set_energy_cm(const double& new_energy_cm) + { + lambda = 1./(100.*new_energy_cm); + } + void set_Gamma_Laser(const double& new_Gamma_Laser) + { + Gamma_Laser = new_Gamma_Laser; + } + void set_Gamma_Laser_MHz(const double& new_Gamma_Laser_MHz) + { + Gamma_Laser = 2*pi*new_Gamma_Laser_MHz*1e6; + } + void set_Power(const double& new_Power) + { + Power = new_Power; + } + void set_polarisation(const Vecteur3D& new_pol) + { + polarisation = new_pol; + } + + void set_polar_angle(const double& new_polar_angle_degree) + { + polar_angle_degree = new_polar_angle_degree; + } + + void set_type_laser(const int& new_type) + { + type_laser = new_type; + } + void set_coherent_avec_laser_num(const int& new_type) + { + coherent_avec_laser_num = new_type; + } + + +// Lit les fichiers Energy_cm atténuation +// Si le fichier est inconnu cela ne rajoute rien à la liste + void read_Spectrum(istream & flux); + + int read_Spectrum(const char *nom_file); + +// Ecrit le spectre + void write_Spectrum(ostream & flux); + + // Clear components + void clear_waist_pos() + { + waist_pos = Vecteur3D(0.,0.,0.); + } + void clear_direction() + { + direction = Vecteur3D(0.,0.,1.); + } + void clear_waist() + { + waist = Vecteur3D(1.,1.,0.); + } + void clear_lambda() + { + lambda = 1.; + } + void clear_Gamma_Laser() + { + Gamma_Laser = 1.; + } + void clear_Power() + { + Power = 0.; + } + void clear_polarisation() + { + polarisation = Vecteur3D(0.,0.,0.); + } + void clear_polar_angle() + { + polar_angle_degree = 0.; + } + + void clear_type_laser() + { + type_laser = CW; + } + void clear_coherent_avec_laser_num() + { + coherent_avec_laser_num = -1; + } + + + + // Comparison + bool operator == (const Laser & Laser) const; + bool operator != (const Laser & Laser) const; + + + // Affichage + + virtual void write(ostream & flux) const + { + if (&flux == &cout) + cout << "waist position : " << waist_pos << "\t"; + else + flux << waist_pos << "\t"; + if (&flux == &cout) + cout << "direction : " << direction << "\t"; + else + flux << direction << "\t"; + if (&flux == &cout) + cout << "waist : " << waist << "\t"; + else + flux << waist<< "\t"; + if (&flux == &cout) + cout << "lambda : " << lambda << "\t"; + else + flux << lambda << "\t"; + if (&flux == &cout) + cout << "Gamma_Laser : " << Gamma_Laser << "\t"; + else + flux << Gamma_Laser << "\t"; + if (&flux == &cout) + cout << "Power : " << Power << "\t"; + else + flux << Power << "\t"; + if (&flux == &cout) + cout << "polarisation : " << polarisation << "\t"; + else + flux << polarisation << "\t"; + if (&flux == &cout) + cout << "polar_angle_degree : " << polar_angle_degree << "\t"; + else + flux << polar_angle_degree << "\t"; + if (&flux == &cout) + cout << "type_laser : " << type_laser << "\t"; + else + flux << type_laser << "\t"; + if (&flux == &cout) + cout << "coherent_avec_laser_num : " << coherent_avec_laser_num << "\t"; + else + flux << coherent_avec_laser_num << "\t"; + + } + + + + // read des données + + virtual void read(istream & flux) + { + if (&flux == &cin) + cout << "entrez waist position : "; + flux >> waist_pos; + if (&flux == &cin) + cout << "entrez direction : "; + flux >> direction; + if (&flux == &cin) + cout << "entrez waist : "; + flux >> waist; + if (&flux == &cin) + cout << "entrez lambda : "; + flux >> lambda; + if (&flux == &cin) + cout << "entrez Gamma_Laser : "; + flux >> Gamma_Laser; + if (&flux == &cin) + cout << "entrez Power : "; + flux >> Power; + if (&flux == &cin) + cout << "entrez polarisation : "; + flux >> polarisation; + if (&flux == &cin) + cout << "entrez polar_angle_degree : "; + flux >> polar_angle_degree; + if (&flux == &cin) + cout << "entrez type_laser : "; + flux >> type_laser; + if (&flux == &cin) + cout << "entrez coherent_avec_laser_num : "; + flux >> coherent_avec_laser_num; + + } + +// ---------------------------------- +// FONCTIONS EN LIGNES +// ---------------------------------- + +// intensité au waist + double intensity() const; + + // transmission (1 = 100%, 0 = 0) prenant en compte le spectre à l'énergie de la transition + double transmission_spectrum(const double energie_trans_cm) const; + +// Zone de Rayleigh Vecteur3D +// ZRZ est la zone de Railieh moyenne + Vecteur3D Rayleigh_range() const; + +// waist au point (X,Y,Z) + Vecteur3D waist_size(const Vecteur3D& point) const; + +// intensité au point (X,Y,Z) dans le repère laser centré sur le waist + double intensity_repere_sur_waist(const Vecteur3D& point) const; + + +// intensité au point (x,y,z) +// I.E. lié au repère du labo + double intensity_lab_axis(const Vecteur3D& point) const; + + +// wave_vector k +// h c / \lambda = h c \sigma(m-1) = \hbar c k + Vecteur3D wave_vector() const; + + + // Energie de la transition laser en cm^-1 + double Energy_transition_laser_cm() const; + + +// ---------------------------------- +// FIN DES FONCTIONS EN LIGNES +// ---------------------------------- + +} +; + + + +//---------------------------------- +// AUTRES fonctions +//-------------------------------- + +// I = ε0 c E^2 /2. +double champ_E(const double irradiance); + + +// (absolute value of the) effectif dipole d.e_laser = sum_p d_p epsilon^p +// where the dipole transition vector d= sum_p d_p e^p is given in the local quantification axis +// and the polarisation vector e_laser= sum_p' epsilon^p' e_p' is given in the laser axis +double effectif_dipole_local(const Vecteur3D& dipole, const Vecteur3D& axe_quant, const Laser& my_laser); + + + +/*** + +Compare to the PRA 2014 we change notation now to be like Wikipedia in ZXZ convention(BE CAREFUL MATHEMATICA and Varshalovitch are in ZYZ convention) + repère x,y,z du labo et X,Y,Z de l'axe de quantification donné par le champ extérieur local +On utilise les angles d'Euler pour faire les rotations de repère +http://en.wikipedia.org/wiki/Euler_angles qui note (alpha,beta,gamma) + + +1. the first rotation is by an angle alpha (modulo 2pi, we chooose (-pi,pi] to use atan2 ) about the z-axis, + +2. the second rotation is by an angle beta in [0,pi] about the former (new) x-axis (now x') + +3. the third rotation is by an angle gamma in (modulo 2pi, we chooose (-pi,pi] to use atan2 ) about the former z-axis (now z'). + +***/ + +// Calcul des angles d'EULER. Pour un repère donné uniquement par son vecteur OZ=direction +// Il reste donc un arbitraire pour choisir l'angle de rotation autour de cet axe pour son repère +// Nous choissons les angles tel que le repère soit le repère polaire dont OZ est la direction et OX selon le méridien +Vecteur3D Euler_angles( Vecteur3D direction); + +// Passage des coordonnées point(x,y,z) (labo) à (X,Y,Z): donné par les angles d'Euler alpha beta et gamma (qui font passer de e_x,e_y,e_z à e_X e_Y e_Z) +// cf http://mathworld.wolfram.com/EulerAngles.html +//Laser coordinates where point=(x,y,z) is lab coordinate +Vecteur3D rotation_lab_axis(const Vecteur3D& point, double alpha, double beta, double gamma=0.); + +// Passage des coordonnées point (X,Y,Z) donné dans le REPERE à labo (x,y,z) (repère labo). +// Le repère XYZ est donnée donné par les angles d'Euler alpha beta et gamma par rapport à xyz +Vecteur3D rotation_axis_lab(const Vecteur3D& point, double alpha, double beta, double gamma=0.); + +#endif diff --git a/Main Code 64bits/main_Laser_Cooling.cpp b/Main Code 64bits/main_Laser_Cooling.cpp new file mode 100644 index 0000000..ecb9138 --- /dev/null +++ b/Main Code 64bits/main_Laser_Cooling.cpp @@ -0,0 +1,493 @@ +/* + Name: Laser cooling of translational degree of freedom of a molecule. + + + Author: Daniel Comparat + Date: 17/12/08 (mise à jour 25/4/2012) + + Compilateur : Code::Blocks + Librairy Math: GSL (GNU) + Affichage: OPEN GL + GLUT + + +les molécules sont décrites par une classe Molecule +leur paramètres (nb, vitesse, etc.. sont dans le fichier Liste_Param.h) (ce n'est pas un fichier C++ le .h est là juste pour avoir un bon éditeur)) +Les transtions moléculaires niveaux, transitions (Franck-COndon, Hönl London,...) sont lus +dans Initialisation_programme qui appelle les fichiers dans Transitions_initialisation + +Les taux de transitions proviennent d'une liste qui souvent vient du programme PGOPHER +Ainsi les unités sont +DEBYE^2 pour force de raie (dipole^2) et +CM^-1 pour énergie + +Elles sont excité par laser (classe Laser) +qui excite le nuage gaussien (taille sigma_SAMPLEx,y,z) via plusieurs +laser eux aussi supposés gaussiens (waist_x,y,z). Voir détail dans chaque .h des classes) + +Il y a un mouvement dans un champ (électrique ou magnétique) décrit par une classe Field + +Le programme Transitions_rate_calcul calcul les taux de transition (pas d'équations de Bloch seulement de taux). +Il est basé sur l'interaction avec un laser de largeur fini. +La saturation est (un peu) prise en compte. + + +l'évolution temporelle (de l'état interne) est basée sur une équation de taux bien adapté +à l'évolution cinétique Monte Carlo faite dans le programme Kinetic_Monte_Carlo + +Plus précisement on calcul un temps dt_KMC pour l'évolution de l'état interne +il faut évidemment qu'il soit petit devant le temps dt_dyn caractéristique d'une petite évolution des taux +(par exemple le temps de transit dans le laser qui modifie les taux d'excitation) +Dans le cas contraire on fait évoluer les positions des particules d'une fraction de dt_dyn +sous l'effets des forces Zeeman, Stark et dipolaires selon un algorithme "Vélocity Verlet" dans "one_body" +et on recommence. + +La mise à jours des états des molécules et de leur énergie ce fait dans "shift_molecule". + +La sortie est graphique dans "Affichage" et dans des fichiers de données dans "sortie_donnees" + +Des statistiques peuvent être faites sur les vitesses et positions (températures, énergie) dans "Stat_Molecule" + +Il y a des +TODO: là où il faut faire des choses mieux +DEBUG là où je met des fonctions utilisées pour le débuggage actuel + +*/ + +#include // to include cout, cin +#include // to include sqrt(), etc. +#include // for atoi() and atof() +#include +#include +#include // for getopt() +#include // to read the data and put them in files +#include // Pour le binary search +#include // Pour accumulate +#include +#include // for list + + +#include +#ifdef __APPLE__ +#include +#else +#include +#endif + +#include // GLUT bibliotheque +#include // OPENGL (GLU) +#include // OPENGL +#include + +//#include "GltZpr/zpr.h" //Pour zoomer, translater et tourner avec la souris +// Ne marche pas actuelement +//#include "GltZpr/zpr.c" //Pour zoomer, translater et tourner avec la souris + + +#include // for random generator +#include // for gaussian random generator + + +#include "algorithmes.h" // Pour le binary search et le wait +#include "Internal_state.h" // Classe état interne +#include "constantes_SI.h" // SI Constantes +#include "Kinetic_Monte_Carlo.h" // Algorithme MC cinétique +#include "Laser.h" // Classe Laser +#include "Molecule.h" // Classe molecule +#include "Field.h" // Classe molecule +#include "datacards.h" // Pour lire le fichier de paramètres +#include "params.h" // Pour faire varier des paramètres + +#include "Transitions_initialisation.h" // Initialisation du programme +#include "Initialisation_programme.h" // Initialisation du programme +#include "shift_molecule.h" // Pour le shift en énergie delta +#include "diagonalization.h" // Pour le shift en énergie delta +#include "Transition_rate_calcul.h" // Sauvegarde des données (+ sortie diverses) +#include "Stat_Molecule.h" // Classe molecule +#include "Affichage.h" // Affichage écran +#include "Affichage_Mol.h" // Affichage des molécules +#include "sortie_donnees.h" // Sauvegarde des données (+ sortie diverses) +#include "one_body.h" // Algorithme pour calculer les déplacements +#include "scaling_velocities.h" + +using namespace std; + + +// fonction appelée en cas de dépassement de mémoire +void deborde () +{ + cerr << "mémoire insuffisante - arrêt de l'exécution " << endl; + exit (1); +} + + +/************************************************************************/ +/************************** Programme Principal *************************/ +/******** main appelle RePaint () dans OPENGL + GLUT *******************/ +/************************************************************************/ + + +// fonction générale: initialisation + boucle KMC et N-corps +void RePaint () +{ + /*****************************************************************/ + /** Création des variables utiles (paramètres à scanner ou pas) **/ + /*****************************************************************/ + + string nomdat = "Data/Liste_Param.h" ; // nom du fichier de paramètres + DataCards data(nomdat.c_str()); // Lit le fichier et crée les datacards. + + bool Graphics = (bool) data.IParam("Graphics"); // affichage graphique ou non. + const double SIZE_affichage = data.DParam("SIZE_affichage"); // Taille de la zone d'affichage + MC_algorithmes Algorithme_MC = (MC_algorithmes) data.IParam("Choix_algorithme_Monte_Carlo"); // Choix de l'algorithme Monté Carlo + N_Body_algorithmes Algorithme_N_body = (N_Body_algorithmes) data.IParam("Choix_algorithme_N_corps"); // Choix de l'alogithme N coprs + + /*** NOM DES FICHIERS ***/ + string nom_sortie_temp_string, nom_sortie_scal_string, nom_file_Levels_string, nom_file_Lines_string, nom_sortie_donnees_string, nom_sortie_rate_string, nom_fichier_random_gen_string, + nom_file_Laser_Spectrum_string, nom_file_Magn_Field_3D_string, nom_file_Elec_Field_3D_string; + + const char *nom_sortie_temp, *nom_sortie_scal, *nom_file_Levels, *nom_file_Lines, *nom_sortie_donnees, *nom_sortie_rate, *nom_fichier_random_gen, *nom_file_Laser_Spectrum, *nom_file_Magn_Field_3D, *nom_file_Elec_Field_3D; + + nom_file_Levels_string = data.SParam("nom_file_Levels"); // Fichier contenant les Levels (etat, energie, ...) + nom_file_Lines_string = data.SParam("nom_file_Lines"); // Fichier contenant les transitions + nom_sortie_donnees_string = data.SParam("nom_sortie_donnees"); + nom_sortie_rate_string = data.SParam("nom_sortie_rate"); + nom_fichier_random_gen_string = data.SParam("nom_fichier_random_gen"); + nom_file_Laser_Spectrum_string = data.SParam("nom_file_Laser_Spectrum"); // Fichier contenant les transitions + nom_sortie_temp_string = data.SParam("nom_sortie_temp"); + nom_sortie_scal_string = data.SParam("nom_sortie_scal"); + nom_file_Magn_Field_3D_string = data.SParam("nom_file_Magn_Field_3D"); + nom_file_Elec_Field_3D_string = data.SParam("nom_file_Elec_Field_3D"); + +// We need to do this fro codeblock 17_12 beacuse nom_file_Levels = data.SParam("nom_file").c_str(); create a Bug !! + + nom_file_Levels = nom_file_Levels_string.c_str(); // Fichier contenant les Levels (etat, energie, ...) + nom_file_Lines = nom_file_Lines_string.c_str(); // Fichier contenant les transitions + nom_sortie_donnees = nom_sortie_donnees_string.c_str(); + nom_sortie_rate = nom_sortie_rate_string.c_str(); + nom_fichier_random_gen = nom_fichier_random_gen_string.c_str(); + nom_file_Laser_Spectrum = nom_file_Laser_Spectrum_string.c_str(); // Fichier contenant les transitions + nom_sortie_temp = nom_sortie_temp_string.c_str(); + nom_sortie_scal = nom_sortie_scal_string.c_str(); + nom_file_Magn_Field_3D = nom_file_Magn_Field_3D_string.c_str(); + nom_file_Elec_Field_3D = nom_file_Elec_Field_3D_string.c_str(); + + + + FitParams params; // this is a vector + params.read(nomdat); // Lit le ficher des paramètres entre "BEGIN_OF_FITPARAMS" et "END_OF_FITPARAMS". + params.init_value(nomdat); // Initialise les paramètres selon la valeur non scannée de la dataCard (cf datacards.h) ou à la valeur min si scannée + + // cout << data << endl; + // params.dump(); + + /******************************************************************/ + /** création abstraite des objets (champs, molécules, laser ...) **/ + /******************************************************************/ + + vector Level; // Level is a list of Internal_state + vector lasers; //Lasers utilisés pour le refroidissement + + Field champB, champE; //champs magnétique et électrique + + const int Nb_type_of_Mol = data.IParam("Nb_type_of_Mol"); + int N_Mol[1]; + N_Mol[0] = (int) params.LocateParam("N_Mol[0]")->val; // The number of laser cooled molecules + vector Mol; + + vector rate; // Taux (intégré en temps) des transitions. + vector reaction_list; // liste des réactions selon le format donné par type_codage_react souvent (n° du système, état final du système) + + ofstream file_out(nom_sortie_donnees); // ajouter ", ios::app" si on veux écrire à la fin du fichier. Sinon efface le fichier à la réecriture + file_out<< setprecision(8); // 8 décimales dans les fichiers de sortie + ofstream file_rate(nom_sortie_rate); + ofstream file_temp(nom_sortie_temp); + ofstream file_scal(nom_sortie_scal);// for scaling velocities + + clock_t t_start,t_end; // Pour mesurer le temps de déroulement du programme + t_start = clock(); + + const int NX_out = params.LocateParam("NX_out")->val; + const int N_Two_JX_out_max = params.LocateParam("N_Two_JX_out_max")->val; + + /*****************************************************************/ + /********************** Initialisation du GSL ********************/ + /*****************************************************************/ + + gsl_rng * r; // Générateur de nb aléatoire + // set_random_generator(r, (int) params.LocateParam("Seed_Init_Random_Number_Generator")->val, nom_fichier_random_gen); // Initialize the random_generator (Mersenne Twister here)// Corriger car NE MARCHE PAS + const gsl_rng_type * T; + gsl_rng_env_setup(); + T = gsl_rng_default; // "Mersenne Twister" generator by default. Plus rapide que RANLUX. cf. chapitre 17.12 de gsl_ref. + r = gsl_rng_alloc (T); + initialisation_trans_mol(nom_file_Levels, nom_file_Lines, Level, params); // Lecture des fichiers de niveaux et de transitions + + + if (data.SParam("is_File_FC") == "true") + { + Modification_FC_trans_mol(nom_file_Levels, nom_file_Lines, Level, params, data); // Modification des fichiers de niveaux et de transitions en fonction des FC et des Energies + exit(1); // Sortie. + } + + bool test_fin_boucle_param; // Paramètre de fin de boucle sur les paramètres à scanner + + + + if (data.IParam("is_DataCard_out") == 1) + { + file_out << " Nb card " << data.NbCards() << endl << "DATA " << endl << data << endl; + } + // AU DEBUT SORT TOUTES LES DONNEES du fichier de donnée initiale + if (data.IParam("is_DataCard_out") == 2) + { + ofstream file_out_datacard(data.SParam("nom_sortie_donnees_Data").c_str()); // ajouter ", ios::app" si on veux écrire à la fin du fichier. Sinon efface le fichier à la réecriture + file_out_datacard << " Nb card " << data.NbCards() << endl << "DATA " << endl << data << endl; // AU DEBUT SORT TOUTES LES DONNEES du fichier de donnée initiale + file_out_datacard.close(); + } + + do // boucle sur les paramètres à scannés (voir fonction Modif_Param) + { + double t=0.; //temps de début de la simulation en µs + double t_mise_a_jour=0.; //temps de faire la mise a jour (potentiels, accélération, N corps ..) de toutes les molécules + /** On ne met à jour les potentiels que de la molécule dont l'état interne à été modifié ou lorsque le pas temporel du N-corps est atteind on les modifie toutes **/ + double t_dia=0.; //temps de sortie fichier + double t_out=0.; //temps d'affichage + double t_fin = params.LocateParam("t_fin")->val; // temps final + double dt_KMC; // Temps pour qu'une réaction apparaisse + double dt_dyn = 0; // temps dynamique + double dt_dia = params.LocateParam("dt_dia")->val; // time interval between diagnostics (in cout) output + double dt_out = params.LocateParam("dt_out")->val; // time interval between output of snapshots (draw particles) + + double t_max_vel_scaling=params.LocateParam("time_max_vel_scaling")->val; //duration of the velocity scaling + double dt_scal = params.LocateParam("dt_scal")->val; + double t_scal=0.; + double coupling_efficiency = params.LocateParam("coupling_efficiency")->val; + + + /*****************************************************************/ + /********************** Initialisation du GSL ********************/ + /*****************************************************************/ + + gsl_rng_set(r,(int) params.LocateParam("Seed_Init_Random_Number_Generator")->val); + save_random_generator(r, nom_fichier_random_gen); + + /*****************************************************************/ + /********************** Initialisation des molécules *************/ + /*****************************************************************/ + + + Init_Field(champB, champE, params, nom_file_Magn_Field_3D, nom_file_Elec_Field_3D); // Initialise les champs. + // Create the list of molecules (create the vector Mol here) its size will not be modified then + Init_Molecule(r, Mol, champB, champE, Nb_type_of_Mol, params, data); // Position, vitesse + initialisation_proba(r, Mol, N_Mol[0], Level); // Etat des populations de molécules au départ en fonction de la population voulue + + + const int Nb_laser = data.IParam("Nb_laser"); // number of used laser (we could have more in the Liste_Param file, but this will be the number used in this run) + + Init_Laser(lasers,Nb_laser, params, nom_file_Laser_Spectrum); // Initialise les lasers + // Sortie_laser_spectrum(file_out, lasers[0], params); + + /** + on calcul un temps dt_KMC pour l'évolution de l'état interne. + Si dt_KMC < temps dt_evol_ext_typ caractéristique de l'évolution des taux (par exemple le temps de transit dans le laser qui modifie les taux d'excitation) on effectue la transition et on bouge les particules + Dans le cas contraire on fait évoluer les particules durant dt_dyn qui est d'une fraction de dt_evol_ext_typ et on recommence. + **/ + + int number_mol = aucune; // numéro de la molécule affectée par une modification (aucune au début d'où la valeur -1) + int nb_repet = (int) params.LocateParam("nb_repet")->val; // nb de répétition du processus. A t_repet on remet à zéro et on recommence + double t_repet = params.LocateParam("t_repet")->val; + int number_photons = 0; // nombre de photons en jeu (absorption, emission spontanée ou stimulé ... + + bool velocity_scaling= (bool) data.IParam("velocity_scaling"); // affichage graphique ou non. + + int i=0; + + while(velocity_scaling == true) // scaling velocities ON. i.e thermalisation of the cloud + { + + Init_Field(champB, champE, params); // Re-Initialise les champs. Important si scan des paramètres car ils ont changés. + + if(t>=t_max_vel_scaling) + { + velocity_scaling=false; + t=0; // remise à zéro du temps + break; + } + + + if(t>=t_scal) + { + //scaling_velocities( t, Mol, Mol.size(),Level, champB,champE, params, coupling_efficiency, file_scal); + //(saling_velocities calculates v'(t)=v(t)*Lambda(t). We want to apply: v'(t+dt)=v(t+dt)*Lambda(t). + Vecteur3D Lambda; + Lambda= calcul_lambda( t, Mol, Mol.size(),Level, champB,champE, params, coupling_efficiency, file_scal); //Lambda(t) + t_scal+=dt_scal; //t=t+dt + i++; + cout << "scaling in progress n " << i << endl; + evolve_step(Algorithme_N_body, Mol, champB, champE, lasers, Mol.size(), t, dt_scal, params); + rescaling_velocities_after_dt ( t, Mol, Mol.size(),Level, champB,champE, params, coupling_efficiency, file_scal, Lambda); + //calculates v'(t+dt)=v(t+dt)*Lambda(t) + } + evolve_step(Algorithme_N_body, Mol, champB, champE, lasers, Mol.size(), t, dt_dyn, params); + if (Graphics ) + { + Draw(Mol, Level, champB, champE, lasers, SIZE_affichage, t, Mol.size(), Nb_type_of_Mol, params); // Affichage des point + wait(params.LocateParam("t_wait_affichage")->val); // Permet de ne pas avoir un affichage trop rapide + } + } + + cerr << "GRAVITY ON z-AXIS" << endl; + + //Create_dipole_Lines_from_Matrices("matrice_dipole.dat"); + + while(velocity_scaling == false) //once the rescaling is done. Infinit llop untill t_end is reached + { + Init_Field(champB, champE, params); // Re0-Initialise les champs. Important si scan des paramètres car ils ont changés. We do not add the files because we do not modify them + Init_Laser(lasers, Nb_laser, params, nom_file_Laser_Spectrum); // Initialise les lasers. // On pourait ne pas remetre à jour le fichier des niveaux + + //Sortie_test_debug(file_out, Mol,Level, champB, champE, lasers, t, Mol.size() ,params, data, number_photons); // sortie de toutes les données moléculaires + //exit(1); + + // t_evol_ext_typ = temps d'évolution typique des forces (ou potentiels) ~ 0.1 waist/vitesse et au max 1 ms + // dt_dyn = (params.LocateParam("epsilon_param")->val) * t_evol_ext(Mol, champB, champE, lasers, params.LocateParam("Temp_ini")->val); // Temps d'évolution pour le N_corps. Modifier epsilon_param jusqu'a convergence! + dt_dyn = (params.LocateParam("dt_dyn_epsilon_param")->val); + + calcul_rates_molecules(Level, Algorithme_MC, reaction_list, rate, Mol, champB, champE, lasers, t, number_mol, N_Mol[0], params); // Calcul les taux de transition de toutes les molécules si numero_mol = aucune. + // Sinon on ne recalcule que celui de la molécule numero_mol + // Sortie_rate(file_rate, rate, Level, reaction_list, Mol, champB, champE, lasers, N_Mol[0], t, params); + + // Sortie_donnee_etat_int_simple(file_out , Mol, lasers, t, params); + + // Sortie_debug(file_rate, rate, reaction_list, Mol, champB, champE, lasers, 0, t,params); // sortie de toutes les données moléculaires + + + if (t >= t_dia) + { + // Sortie_laser_spectrum(file_out, lasers, params, 0); + Sortie_rate(file_rate, rate, Level, reaction_list, Mol, champB, champE, lasers, N_Mol[0], t, params); + // Sortie_donnee_pop_v(file_out, Mol, N_Mol[0], t, NX_out, params, number_photons); + // Sortie_donnee_pop_vJ(file_out, Mol, N_Mol[0], t, NX_out, N_Two_JX_out_max, params); + // Sortie_donnee(file_out, Mol, Level, champB, champE, lasers, t, (int) Mol.size(),params, data, number_photons); // sortie de toutes les données moléculaires + t_dia += dt_dia; + } + + int n_reac = find_reaction(Algorithme_MC, r, rate, dt_KMC); // Trouve la réaction KMC + + if (dt_KMC < dt_dyn || Algorithme_MC == Fast_Rough_Method) // L'évolution se fera durant un temps dt_KMC or if Fast_Rough_Method in order to be sure to evolve the internal states (because it is not random) + { + evolve_step(Algorithme_N_body, Mol, champB, champE, lasers, Mol.size(), t, dt_KMC, params); // Evolution N corps (avant le changement de vitesse). Cela change aussi le temps; + number_mol = do_reaction(Algorithme_MC, r, rate, reaction_list, Mol, n_reac, lasers, dt_KMC, file_rate, true, number_photons, params); // On fait l'évolution de l'état interne + // if (Mol[number_mol].exc == photoionized) + // Sortie_donnee_electrons(file_out, Mol,Level, champB, champE, lasers, t, number_mol,params, data, number_photons); // sortie de toutes les données moléculaires + } + else // L'évolution se fera sans réaction durant un temps dt_dyn + { + evolve_step(Algorithme_N_body, Mol, champB, champE, lasers, Mol.size(), t, dt_dyn, params); // Evolution N corps (avant le changement de vitesse) + } + +// On peut peut être améliorer. Ne faut'il pas mettre à jour toujours la molécule modifée surtout dans le cas dipolaire ? + if (t >= t_mise_a_jour || Algorithme_MC == Fast_Rough_Method) + { + number_mol = aucune; // Il faudra faire une mise a jour totale (cf calcul rate) donc que toutes les molécules ont été affectées + // set_pot_all_mol(Mol, champB, champE, lasers, t, N_Mol[0], params); //Met à jour (pour recalculer les bonnes transitions) de tous les potentiels (gravité, dipolaire, magnétique, electrique, ...) avec la nouvelle position + t_mise_a_jour += dt_dyn; + } +// On pourrait penser accélerer, en faisant évoluer le N_corps jusqu'a dt_KMC sans recalculer dt_KMC à chaque fois. Mais cela est risqué comme on le voit avec un molécule loin d'un waist --> tKMC immense mais qui va diminuer vite et si on ne recalcule pas on va faire une erreur + + if (t >= t_repet) // Remise à zéro au bout d'une seconde. On recommence la séquence temporelle mais avec les molécules comme elles sont + { + t=0.; + t_dia = dt_dia; + t_out = dt_out; + nb_repet --; + } + + if (Graphics && t >= t_out) + { + Draw(Mol, Level, champB, champE, lasers, SIZE_affichage, t, Mol.size(), Nb_type_of_Mol, params); // Affichage des point + t_out += dt_out; + // cout << "time " << (double) t << endl; + wait(params.LocateParam("t_wait_affichage")->val); // Permet de ne pas avoir un affichage trop rapide + } + + + if (t > t_fin || nb_repet < 0) // FIN DE LA BOUCLE + { + //cout << " time final " << t << " fin loop " << endl; + + for (ParamIterator i=params.begin(); i != params.end(); ++i) + { + Param &p = **i; + if( p.is_scanned == true ) + cout << " " << p.val_t0 ; + } + cout << endl; + break; + } + + Modif_Param(t, params); // On modifie en dynamique la longueur d'onde le waist etc... des lasers en fonction du temps + } + + + if (data.SParam("is_Scan_Random") == "true") + test_fin_boucle_param = params.Scan_Param_aleatoire(r); // Modification des paramètres + else + test_fin_boucle_param = params.Scan_Param(); + } + + while (!test_fin_boucle_param); // test de fin des boucles sur les paramètres + + file_out.close(); + file_rate.close(); + file_temp.close(); + t_end = clock(); + + cout << "durée du programme (s) = " << (t_end - t_start)/double(CLOCKS_PER_SEC) << endl; + + +// FIN du programme + + + exit(1); + system("PAUSE"); + return; + +} + + + + +// fonction main appellant RePaint (). +// C'est ainsi que fonctionne OPENGL + GLUT +int main(int argc, char** argv) +{ + + + string nomdat = "Data/Liste_Param.h" ; // nom du fichier de paramètres + DataCards data(nomdat.c_str()); // Lit le fichier et crée les datacards. + bool Graphics = (bool) data.IParam("Graphics"); // affichage graphique ou non. + + if (Graphics) + { + int size_screen =600; + glutInit(&argc, argv); //Initialisation de la GLUT + glutInitDisplayMode(GLUT_DEPTH| //On active la profondeur + GLUT_DOUBLE| //Un seul tampon d'affichage + GLUT_RGBA); //Couleurs au format RGBA + glutInitWindowPosition(700, 100); // coordonnées de la fenêtre + glutInitWindowSize(size_screen, size_screen); //taille Fenêtre + glutCreateWindow("Cooling"); //Création de la fenêtre + // zprInit(); //Pour zoomer, translater et tourner avec la souris. NE marche pas + + glutDisplayFunc(RePaint); //On lui dit d'appeler la fonction renderFunc pour afficher + + + glutReshapeFunc(reshape); // Nécessaire pour recadrer la fonction + glutMainLoop(); //Boucle infinie du programme + exit(1); + return 0; + } + else + RePaint (); + return 0; + exit(1); +} diff --git a/Main Code 64bits/molecule.cpp b/Main Code 64bits/molecule.cpp new file mode 100644 index 0000000..f5c9ba6 --- /dev/null +++ b/Main Code 64bits/molecule.cpp @@ -0,0 +1,83 @@ +#include "molecule.h" + + + +// ------------ +// Constructors +// ------------ + +Molecule::Molecule() // Constructeur par défaut +{ +}; + +Molecule::~Molecule() +{} +; // Destructeur + +// opérateur d'affectation de l'état interne +// ATTENTION la copie de la liste est une copie seulement vers l'adresse du pointeur +// On en copie pas vraiment la liste. Cela implique que chaque molécule à la même liste! +Molecule & Molecule::operator = (const Internal_state & Intern) +{ + exc = Intern.exc; + two_Spin = Intern.two_Spin; + two_Lambda = Intern.two_Lambda; + two_Omega = Intern.two_Omega; + v = Intern.v; + two_J = Intern.two_J; + two_N = Intern.two_N; + two_M = Intern.two_M; + Sym = Intern.Sym; + deg_number = Intern.deg_number; + Energy0_cm = Intern.Energy0_cm; + Delta_FieldB = Intern.Delta_FieldB; + Linear_FieldB = Intern.Linear_FieldB; + Delta_FieldE = Intern.Delta_FieldE; + Linear_FieldE = Intern.Linear_FieldE; + one_over_lifetime = Intern.one_over_lifetime; + Energy_cm = Intern.Energy_cm; + population = Intern.population; + liste_raies = Intern.liste_raies; + return *this; +} + +//---------------------------------- +// Surdéfinition des entrées sorties +//---------------------------------- + +ostream& operator << (ostream & flux, Molecule my_molecule) +{ + my_molecule.write(flux); + return(flux); +} + +istream& operator >> (istream &flux, Molecule & my_molecule) //my_molecule est modifiée +{ + my_molecule.read(flux); + return(flux); +} + +#include "shift_molecule.h" + +// Lecture du potentiel [en Joule] de l'état interne d'une molécule (electric, magnétique) pas dipolaire +// require that mol.Energry_cm is correct +// On peut enlèver le pot au centre +// We include the Coulomb interaction with external field (not with other particle which is done in get_coulomb_potential) +double get_pot(const Molecule &mol, const Field &fieldB, const Field &fieldE) +{ + Vecteur3D pos(0.,0.,0.); + double Bcentre=fieldB.get_Field(pos).mag(); // Magnétique + double Ecentre=fieldE.get_Field(pos).mag(); // Electrique + // double E_pot_centre = HBAR*delta_field_shift_B_E(mol, Bcentre, Ecentre); // Si on veux enlever le potentiel au centre + double E_pot_centre = 0.; + double pot_electric = mol.get_charge()* fieldE.get_electric_potential(mol.get_pos()); // q V with FieldE= - Grad V + double pot_gravity = - mol.get_mass()*gravity.dot(mol.get_pos()); + double pot_internal = HBAR*(mol.Energy_cm - mol.Energy0_cm)*Conv_Ecm_delta; + return pot_electric + pot_gravity + pot_internal - E_pot_centre; +} + +// Lecture de l'énergie cinétique [en Joule] d'une molécule +double get_kin(const Molecule &mol) +{ + return 0.5*(mol.get_vel().mag2()) * mol.get_mass(); +} diff --git a/Main Code 64bits/molecule.h b/Main Code 64bits/molecule.h new file mode 100644 index 0000000..c594b92 --- /dev/null +++ b/Main Code 64bits/molecule.h @@ -0,0 +1,121 @@ +/* + Name: classe « molecule » + + Copyright: + Author: Daniel Comparat + Date: 15/10/06 11:01 + SIMPLIFIE le 12/02/2012 + + Description: + Elle dérive de la classe Atome +mol un élément de la classe +contient +1) Son état externe: la classe Atome (vecteur3D pos, vel et la masse), elle ajoute +2) Son état interne: la classe Internal_state exc (niveau électronique), v,J, MJ + +*/ + + + + +#ifndef Molecule_SEEN +#define Molecule_SEEN + +#include "Atome.h" +#include "Internal_state.h" + +#include +using namespace std; + +struct type_codage_react{ int n_mol; int n_laser; Vecteur3D quant_axis; Vecteur3D pol_vector; Vecteur3D k_eff_laser; Internal_state final_internal_state;}; +// In order to define a reaction we need to know the initial state (so the n_mol), the finale state (so final_internal_state) +// and to implement the recoil we need to have +// 1) For absorption or stimulated emission: the laser (n_laser) which will give the photon momentum. +// We also give k_eff_laser which is the laser (effectif) wave_vector. it can be zero in the case of lattice for instance (no momentum transfer) +// 2) for the spontaneous emission: the polarization vector (transition dipole vector) that will determined the emission probability of the emitted photon +// To help we also give the quantization axis where the dipole are calculated to then rotate to the lab axis if needed + +// TODO (dc#1#): Put the FULL internal_state_finale is HUGE in term of memory. ... +//Study how to put only the adress ! +// +// may be This is why the code is slow ?! + + +/*** list of electronical states ***/ +const int annihilation = -3; // Annihilized particles (P_bar or Ps for instance can annihilate) +const int photodetached = -2; +const int photoionized = -1; // Photoionized level +// So Negative values can be used for a "dead" level such as one in a continuum: +// usually 0 means ground electronical level, +// 1 is for an excited electronical level, +const int fond=0; +const int excite=1; +const int excite2=2; +const int excite3=3; + + +class Molecule : public Atome, public Internal_state +{ + +public: + // vector < Internal_state *> liste_niveaux; //La liste des raies possibles est: vecteur donnant la liste des états finaux et de la force de transition + + Molecule(); // constructeurs autres que par recopie + ~Molecule(); // destructeur + + Molecule & operator = (const Internal_state & Intern); // opérateur d'affectation d'état interne + + + + friend Molecule operator +(const Molecule , const Molecule); // surcharge de l'opérateur + + + // Affichage + + void write(ostream & flux) + { + this->Atome::write(flux); + this->Internal_state::write(flux); + } + + void write_list(ostream & flux) + { + this->Internal_state::write_liste_raie(flux); + } + + // read des données + + void read(istream & flux) + { + this->Atome::read(flux); + this->Internal_state::read(flux); + + } + + +}; + + +#include "Field.h" + +// Lecture du potentiel [en Joule] de l'état interne d'une molécule (electric, magnétique) pas dipolaire +// require that mol.Energry_cm is correct +// On peut enlèver le pot au centre +// We include the Coulomb interaction with external field (not with other particle which is done in get_coulomb_potential) +double get_pot(const Molecule &mol, const Field &fieldB, const Field &fieldE); + +// Lecture de l'énergie cinétique [en Joule] d'une molécule +double get_kin(const Molecule &mol); + + +//---------------------------------- +// Surdéfinition des entrées sorties +//---------------------------------- + +ostream& operator << (ostream & flux, Molecule my_molecule); + +istream& operator >> (istream &flux, Molecule & my_molecule); + + + + +#endif diff --git a/Main Code 64bits/one_body.h b/Main Code 64bits/one_body.h new file mode 100644 index 0000000..60fd877 --- /dev/null +++ b/Main Code 64bits/one_body.h @@ -0,0 +1,840 @@ +/* +Name: +Copyright: +Author: +Date: 12/10/06 21:38 +Description: Algorithm for the N or 1 body dynamics + + +see: N-body simulations of gravitational dynamics (http://arxiv.org/pdf/1105.1082.pdf) + +For the N-body I use nbody_sh1WD.C: an N-body integrator with a shared but variable time step +by Walter Dehnen + +Elle est effectue les calcul sur les positions, vitesses, accélération de n particules ayant une masse +qui sont des Vecteur3D (c.f. classe Vecteur3D.h) + + bod.get_vel pour avoir la vitesse, il faut aussi la pos, acc, jerk + bod.inc_vel(d_vel) et pos pour augmenter la vitesse (et la position) + bod.set_vel(d_vel) et pos, acc, jerk pour mettre la vitesse (et la position, acc, jerk) + +On utilise une fonction new_acc_pot(bod) qui calcule l'accélération via new_pot(bod) qui recalcule (et non lit ça c'est get_pot!) le potentiel +Mais si l'accélération est mise à jour ailleurs ou peut être calculé directement on utilise plutôt new_acc(bod). + +Pour l'instant si on veut la force dipolaire on utilise les potentiels (Verlet_pot) et sinon l'accélération ((Verlet_acc) + +Comme l'accélération dépent des forces, elle dépends des potentiels magnétique, électrique et laser qui peuvent démendre du temps + +ATTENTION: Elle ne met pas à jour les potentiels une fois le mouvement fait. Il faut le faire à part. + +Si la particule est trop loin (LARGE_NUMBER) on ne la fait pas évoluer +*/ + +#ifndef one_body_SEEN +#define one_body_SEEN + +using namespace std; + +#include +#include // to include sqrt(), etc. +#include // for atoi() and atof() +#include // for getopt() +#include + +#include "molecule.h" // Pour le shift en énergie delta +#include "Field.h" // Pour les champs extérieurs +#include "laser.h" +#include "params.h" + +enum N_Body_algorithmes // Hermite = 0, // NOT USED +{ + Aucun_N_corps = -1, + Hermite = 0, // Not used + Verlet_acc = 1, // Calcule l'accélération directement + Verlet_pot = 2, // Calcule l'accélération avec les potentiels + Yoshida6_acc = 3, // 6 th order symplectic algorithm based on Verlet_acc + Yoshida6_pot = 4, // 6 th order symplectic algorithm based on Verlet_pot + Runge_Kutta_Nystrom = 5, // NOT USED + Verlet_pot_gradient_high_order = 6, // Calcule l'accélération avec les potentiels mais à l'ordre supérieur + Boris_Buneman = 7 // Boris_Buneman integrator +}; + + + +template void evolve_step(const N_Body_algorithmes Algorithme_N_body, + vector &bod, const Field &fieldB, const Field &fieldE, const vector &my_laser, + const int n, double & t,const double dt, FitParams ¶ms); + +// Juste l'accélération +template void evolve_step_Aucun_N_corps(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt); + + +template void evolve_step_Verlet_via_acc(vector &bod, const Field &fieldB, const Field &fieldE, const vector &my_laser, + const int n, double & t,const double dt); + +// Accélération calculée avec new_acc_pot qui utilise les potentiel des champs. +// C'est plus lent car l'accélération est évaluée par pot(x+dx)-pot(x-dx)/2dx ... +template void evolve_step_Verlet_via_pot(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt, FitParams ¶ms); + + +// Yoshida 6 using LeapForg with acceleration +template +void evolve_step_Yoshida6_acc(vector &bod, const Field &fieldB, const Field &fieldE, const vector &my_laser, + const int n, double & t,const double dt); + +// Yoshida 6 using LeapForg with potentials +template +void evolve_step_Yoshida6_pot(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt, FitParams ¶ms); + + +// Boris–Buneman integration scheme (notation of Journal of Computational Physics 273 (2014) 255) +template void evolve_step_Boris(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt); + +// Energie potentielle de la particle i +// Définie en extern (pour nous dans la classe Molecule) cf double get_pot(const Molecule &mol, const Field &fieldB, const Field &fieldE); +template double get_pot(vector &bod, const int i, const Field &fieldB, const Field &fieldE); + + +// Pour calcul a_i= Force/masse = -Grad(E_pot)/mass et met à jour l'accélération +template Vecteur3D new_acc_pot(vector &bod, const int i, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms); +// Calcul du gradient au premier ordre +template Vecteur3D new_acc_pot_second_order(vector &bod, const int i, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms); +// Calcul du gradient à l'ordre d'après +template Vecteur3D new_acc_pot_fourth_order(vector &bod, const int i, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms); + +// Calculate the Coulombian acceleration (adapted from Walter Dehnen) +// Is added to accell +template void add_acc_N_body_Coulomb(const vector &bod, Vecteur3D *accell, const int n); + + +// Calculate the Coulombian potential for the sum_j=1^n not i qj/(r_ij)/4 pi epsilon_0 +// Is used only for statistics to check the energy conservation. So it is not fully optimized +template double get_coulomb_potential(const vector &bod, const Vecteur3D &ri, const int n); + +// add Lorentz force for charged particles +template void add_acc_Charged_particles(vector &bod, Vecteur3D *accell, const Field &fieldB, const Field &fieldE, const int n); + +// kinetic energy +template double get_kin(Body &bod); + +// temps d'évolution typique des forces (ou potentiels) ~ fraction de waist/vitesse +// A améliorer avec les champs, différents lasers ... +template double t_evol_ext(vector &bod, const Field &fieldB, const Field &fieldE, const vector &my_laser, const double Temp_estime); + + +/************************************** +JE MET ICI L'equivalent du .cpp car "On peut pas séparer un .h et .cpp pour les template". + +Si un symbole template est utilisé uniquement dans un .cpp (fichier source), il peut être implémenté dans ce .cpp +Sinon, il doit être implémenté dans un .hpp (header). + +cf http://www.commentcamarche.net/faq/11194-les-templates-en-c +***************************************/ + + + +template void evolve_step(const N_Body_algorithmes Algorithme_N_body, + vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt, FitParams ¶ms) +{ + Body *old_bod = new Body[n]; + + switch (Algorithme_N_body) + { + + case Aucun_N_corps : + evolve_step_Aucun_N_corps(bod, fieldB, fieldE, laser, n, t, dt); + break; + + + case Verlet_acc : // Accélaration calculée directement + evolve_step_Verlet_via_acc(bod, fieldB, fieldE, laser, n, t, dt); + break; + + case Verlet_pot : // Accélaration calculée avec gradient du potentiel + evolve_step_Verlet_via_pot(bod, fieldB, fieldE, laser, n, t, dt, params); + break; + + case Yoshida6_acc : // Accélaration calculée avec gradient du potentiel + evolve_step_Yoshida6_acc(bod, fieldB, fieldE, laser, n, t, dt); + break; + + case Yoshida6_pot : // Accélaration calculée avec gradient du potentiel + evolve_step_Verlet_via_pot(bod, fieldB, fieldE, laser, n, t, dt, params); + break; + + + case Verlet_pot_gradient_high_order : // Accélaration calculée avec gradient du potentiel + evolve_step_Verlet_via_pot(bod, fieldB, fieldE, laser, n, t, dt, params); + break; + + case Boris_Buneman : // Boris–Buneman integration scheme + evolve_step_Boris(bod, fieldB, fieldE, laser, n, t, dt); + break; + + default: + /* do nothing */ + break; + + } + t += dt; + delete [] old_bod; +} + + + +/*----------------------------------------------------------------------------- + * evolve_step Velocity Verlet + +old_acc = acc +@pos += @vel*dt + old_acc*0.5*dt*dt +new_acc = acc +@vel += (old_acc + new_acc)*0.5*dt + + + *----------------------------------------------------------------------------- +*/ + + +// Accélération calculée avec new_acc qui utilise directement les formules des gradients des champs. C'est plus rapide +// N'est pas utilisable toujours si on a pas les gradients des champs. +template void evolve_step_Verlet_via_acc(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt) +{ + + Vecteur3D *old_acc = new Vecteur3D[n]; + Vecteur3D *acc = new Vecteur3D[n]; + +// Might be improved if the acc is known before. because here we reclculate it! + for (int i = 0; i < n ; ++i) + old_acc[i] = new_acc(bod, i, fieldB, fieldE, laser, t); // calcul l'accélération + + add_acc_N_body_Coulomb(bod, old_acc, n); // add coulombian acceleration due to charged particles + add_acc_Charged_particles(bod, old_acc, fieldB, fieldE, n); // add Lorentz force for charged particles + + for (int i = 0; i != n ; ++i) + { + if (bod[i].get_pos().mag() > LARGE_NUMBER) + continue; // Si la particule est trop loin on la laiss là! + Vecteur3D d_pos = (dt*(bod[i].get_vel()) + (dt*dt*0.5)*old_acc[i]); + bod[i].inc_pos(d_pos); // @pos += @vel*dt + old_acc*0.5*dt*dt + } + + for (int i = 0; i != n ; ++i) + acc[i] = new_acc(bod, i, fieldB, fieldE, laser, t + dt); // new_acc = acc + + add_acc_N_body_Coulomb(bod, acc, n); // add coulombian acceleration due to charged particles + add_acc_Charged_particles(bod, acc, fieldB, fieldE, n); // add Lorentz force for charged particles + + for (int i = 0; i != n ; ++i) + { + Vecteur3D d_vel = (0.5*dt*(old_acc[i] + acc[i])); + bod[i].inc_vel(d_vel); // @vel += (old_acc + new_acc)*0.5*dt + } + + delete [] acc; + delete [] old_acc; + +} + + + + +// Accélération calculée avec new_acc_pot qui utilise les potentieldes champs. +// C'est plus lent car l'accélération est évaluée par pot(x+dx)-pot(x-dx)/2dx ... +template void evolve_step_Verlet_via_pot(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt, FitParams ¶ms) +{ + + Vecteur3D *old_acc = new Vecteur3D[n]; + Vecteur3D *acc = new Vecteur3D[n]; + + for (int i = 0; i < n ; ++i) + old_acc[i] = new_acc_pot(bod, i, fieldB, fieldE, laser, t, params); // calcul l'accélération + + add_acc_N_body_Coulomb(bod, old_acc, n); // add coulombian acceleration due to charged particles + add_acc_Charged_particles(bod, old_acc, fieldB, fieldE, n); // add Lorentz force for charged particles + + for (int i = 0; i != n ; ++i) + { + if (bod[i].get_pos().mag() > LARGE_NUMBER) + continue; // Si la particule est trop loin on la laiss là! + Vecteur3D d_pos = (dt*(bod[i].get_vel()) + (dt*dt*0.5)*old_acc[i]); + bod[i].inc_pos(d_pos); // @pos += @vel*dt + old_acc*0.5*dt*dt + } + + for (int i = 0; i != n ; ++i) + acc[i] = new_acc_pot(bod, i, fieldB, fieldE, laser, t + dt, params); // new_acc = acc + + add_acc_N_body_Coulomb(bod, acc, n); // add coulombian acceleration due to charged particles + add_acc_Charged_particles(bod, acc, fieldB, fieldE, n); // add Lorentz force for charged particles + + for (int i = 0; i != n ; ++i) + { + Vecteur3D d_vel = (0.5*dt*(old_acc[i] + acc[i])); + bod[i].inc_vel(d_vel); // @vel += (old_acc + new_acc)*0.5*dt + } + + delete [] acc; + delete [] old_acc; + +} + + + +// Pas d'accélération +template void evolve_step_Aucun_N_corps(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt) +{ + for (int i = 0; i != n ; ++i) + { + if (bod[i].get_pos().mag() > LARGE_NUMBER) + continue; // Si la particule est trop loin on la laiss là! + Vecteur3D d_pos = (dt*(bod[i].get_vel())); + bod[i].inc_pos(d_pos); // @pos += @vel*dt + } +} + + + +/*----------------------------------------------------------------------------- + * evolve_step Yoshida6 + +d = [0.784513610477560e0, 0.235573213359357e0, -1.17767998417887e0, +1.31518632068391e0] +for i in 0..2 do leapfrog(dt*d[i]) end +leapfrog(dt*d[3]) +for i in 0..2 do leapfrog(dt*d[2-i]) end + + *----------------------------------------------------------------------------- +*/ + + +// Yoshida 6 using LeapForg with acceleration +template +void evolve_step_Yoshida6_acc(vector &bod, const Field &fieldB, const Field &fieldE, const vector &my_laser, + const int n, double & t,const double dt) +{ + double d[4] = + { + 0.784513610477560e0, 0.235573213359357e0, -1.17767998417887e0, 1.31518632068391e0 + }; + for (int i = 0; i <= 3 ; ++i) // for i in 0..2 do leapfrog(dt*d[i]) + evolve_step_Verlet_via_acc(bod, fieldB, fieldE, my_laser, n, t, dt*d[i]); + for (int i = 0; i <= 2 ; ++i) + evolve_step_Verlet_via_acc(bod, fieldB, fieldE, my_laser, n, t, dt*d[2-i]); // for i in 0..2 do leapfrog(dt*d[2-i]) +} + + +// Yoshida 6 using LeapForg with potentials +template +void evolve_step_Yoshida6_pot(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt, FitParams ¶ms) +{ + double d[4] = + { + 0.784513610477560e0, 0.235573213359357e0, -1.17767998417887e0, 1.31518632068391e0 + }; + for (int i = 0; i <= 3 ; ++i) // for i in 0..2 do leapfrog(dt*d[i]) + evolve_step_Verlet_via_pot(bod, fieldB, fieldE, laser, n, t, dt*d[i], params); + for (int i = 0; i <= 2 ; ++i) + evolve_step_Verlet_via_pot(bod, fieldB, fieldE, laser, n, t, dt*d[2-i], params); // for i in 0..2 do leapfrog(dt*d[2-i]) + +} + + + + + +/*----------------------------------------------------------------------------- + +SIMULATIONS FOR ION TRAPS – METHODS AND NUMERICAL IMPLEMENTATION + +This is the book which summarise several of those ones + + +Velocity Verlet Method is energy conserving, but not applicable for this +problem, since it does not include a magnetic field. +Sometimes the Gear method is sufficient for this case. +However for uniform magnetic field Eq (57) of the book gives +v_new = v + dt q/m ( E + (v+v_new)^B/2) to be compared with the (non magnetic one Eq (53) v_new = v + dt q/m E +r_new = r + v_new dt +Sometimes the notations are with the times steps +v =v_(n-1/2) and v_new = v_(n+1/2) where r=r_n and r_new = r_(n+1) + + + +But, An energy conserving integrator for +magnetic fields has been invented by J. P. Boris in 1970. +has a weak point however; +it requires fine resolution of the Larmor angular frequency +Omega = q B/m typically dt Omega <~ 0.1 + +Theta[dt] = (qB/m)dt is the rotation angle + +Boris–Buneman integration scheme +(cf http://arxiv.org/pdf/1211.3664.pdf or http://www.particleincell.com/blog/2011/vxb-rotation/ or + Journal of ComputationalPhysics 273 (2014) 255 with space charged) +we note t= Theta[dt/2] = (qB/m)dt/2 +or +Theta[dt] = 2 Tan^{-1} (dt/2 qB/m) + +Drift: x' - x = v dt/2 + +Kick: v- = v + (qE_tot/m) (dt/2) where E_tot = E_ext + E_int (self field) +v' = v- + v-^t +v+ = v- + v' ^(2t/(1+t^2)) is the rotation (axis B) of v- with the angle Theta[dt]. Recall that Sin[theta]=2t/(1+t^2) and 1-Cos[theta] = 2t^2/(1+t^2) where t = tan [theta/2] +v_final = v+ + (qE_tot/m) (dt/2) + +Drift: x_final - x' = v_final dt/2 + + + +Spreiter and Walter: Taylor expansion algorithm works in the opposite limit (dt Omega >> 1). +it is the magnetic field generalization of the velocity-Verlet algorithm. +It is unstable when dt Omega < 1 (cf Journal of Computational Physics 228.7 (2009)). + In addition it does not exactly conserve energy, which could be a problem if used in codes where long-term +particle tracking is necessary. + +vB(r,v,dt) = v + sin[Theta] (n_B ^ v) + (1-Cos[theta])(n_B ^(n_B ^ v)) is the rotation of v around B (cf Eq (40) of PHYSICAL REVIEW E 77, 066401 (2008) +where I recall that Theta[dt] = (-qB/m)dt is the rotation angle + +n_B is the unit vector along B and ^is the cross product +The algorithm is (2a cf PHYSICAL REVIEW E 77, 066401 (2008) but only for magnetic field) +v1 = vB(r,v,dt/2) +r1 = r + v1 dt +v2 = vB(r1,v1,dt/2) + + so it is (I think): +v1 = vB(r,v,dt) +r1 = r + v1 dt +to be compare with Boris (in pure magnetic field) +r' = r + v dt +v_final = vB(r',v,dt) + + +We have the generalization is Eq (83) (85) of the book where the space charge is also taken into account +It is also well describe in "Cooling of highly charged ion Penning Trap (HITRAP)" cf Eq (3.60) Thesis of Giancarlo Maero + + +Finally a Cyclotronic integrator has been developped +(cf Journal of Computational Physics 228.7 (2009)) +but Cyclotronic integrator does not ensure energy conservation +in non-uniform magnetic field conditions, while the Boris scheme does + + + *-----------------------------------------------------------------------------*/ + + + +// Boris–Buneman integration scheme (notation of Journal of Computational Physics 273 (2014) 255) +template void evolve_step_Boris(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt) +{ + + Vecteur3D *acc = new Vecteur3D[n]; + +// Drift: x' - x = v dt/2 +// In fact I group with the other Drift to make a single one at dt (cf book) + for (int i = 0; i != n ; ++i) + { + if (bod[i].get_pos().mag() > LARGE_NUMBER) + continue; // Si la particule est trop loin on la laiss là! + Vecteur3D d_pos = bod[i].get_vel()*dt; // dt step (because of the merging with the last Drift) + bod[i].inc_pos(d_pos); // @pos += @vel*dt + old_acc*0.5*dt*dt + } + +// calcul Zeeman and Stark acceleration + for (int i = 0; i < n ; ++i) + acc[i] = new_acc(bod, i, fieldB, fieldE, laser, t); + add_acc_N_body_Coulomb(bod, acc, n); // add coulombian acceleration due to charged particles + + +// Kick: + for (int i = 0; i != n ; ++i) + { + + double q = bod[i].get_charge(); + double m = bod[i].get_mass(); + Vecteur3D r = bod[i].get_pos(); + if (r.mag() > LARGE_NUMBER) + continue; + + Vecteur3D v = bod[i].get_vel(); + Vecteur3D E = fieldE.get_Field(r) ; // E is the local field due to external field (the other fields of space charge are in acc[i]) + Vecteur3D B = fieldB.get_Field(r); + double B_norm = B.mag(); + Vecteur3D Phi = (B/B_norm)*tan(B_norm*(q/m)*(dt/2.)); // It is t. The simple formula is Vecteur3D Phi = B*(q/m)*(dt/2.). + + v = v + ((q*E/m) + acc[i])*(dt/2); // v = v + (qE_tot/m) (dt/2) + + + Vecteur3D w = v + v.cross(Phi); // w = v + v * Phi where Phi = dt/2 q B/m + Vecteur3D s = 2.*Phi/(1.+Phi.mag2()); // s = (2 Phi/(1+Phi^2)) + + v = v + w.cross(s) + ((q*E/m) + acc[i])*(dt/2.); // v = v + w * s + (qE/m) (dt/2) + + bod[i].set_vel(v); + } + +// Drift: x_final - x' = v_final dt/2 +// for (int i = 0; i != n ; ++i) +// { +// if (bod[i].get_pos().mag() > LARGE_NUMBER) continue; // Si la particule est trop loin on la laiss là! +// Vecteur3D d_pos = bod[i].get_vel()*dt/2.; +// bod[i].inc_pos(d_pos); +// } + + delete [] acc; +} + + +// Spreiter and Walter Taylor = magnetized generalization of the velocity-Verlet algorithm. +// I use notation of algorithm 2a of PHYSICAL REVIEW E 77, 066401 (2008). But because it was for B sole. I make the use of the Lorentz transform to have +// B replace by (B - v * E /v^2) so the force q v*B becomes the usual if v orthogonal to E +template void evolve_step_Spreiter_Walter(vector &bod, const Field &fieldB, const Field &fieldE, const vector &laser, + const int n, double & t,const double dt) +{ + + Vecteur3D *acc = new Vecteur3D[n]; + + + for (int i = 0; i != n ; ++i) + { + double q = bod[i].get_charge(); + double m = bod[i].get_mass(); + Vecteur3D r = bod[i].get_pos(); + if (r.mag() > LARGE_NUMBER) + continue; + + Vecteur3D v = bod[i].get_vel(); + Vecteur3D E = fieldE.get_Field(r) ; // E is the local field due to external field (the other fields of space charge are in acc[i]) + Vecteur3D B = fieldB.get_Field(r); + double Bnorm = B.mag(); + Vecteur3D n_B; // unit vector pointing in the direction of the magnetic field + if (Bnorm !=0) + n_B = B/Bnorm; // on the other case B is zero so the effect will be nul + + + double theta = (-q*B/m)*dt; // Eq (36) of Phys Rev E + + + Vecteur3D v1 = v + sin(theta)*n_B.cross(v) + (1.-cos(theta))*n_B.cross(n_B.cross(v)); // Eq (40) + + } + + delete [] acc; +} + + + + +// Pour calcul a_i= Force/masse = -Grad(E_pot)/mass; +// Calcul et met a jour l'accélération en utilisant le potentiel +template Vecteur3D new_acc_pot(vector &bod, const int i, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms) +{ + if (params.LocateParam("Choix_algorithme_N_corps")->val == Verlet_pot) + return new_acc_pot_second_order(bod, i, fieldB, fieldE, laser, t, params); + + if (params.LocateParam("Choix_algorithme_N_corps")->val == Verlet_pot_gradient_high_order) + return new_acc_pot_fourth_order(bod, i, fieldB, fieldE, laser, t, params); + + return Vecteur3D(0.,0.,0.); +} + + +// Grad calculé par (E(r+eps)-E(r-eps))/(2*eps) pour chaque axe +template Vecteur3D new_acc_pot_second_order(vector &bod, const int i, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms) +{ + Body &my_bod = bod[i]; // Body my_bod = bod[i]; is wrong. We need to take a real copy of bod[i] in order to modify its position + + Vecteur3D ai(0.,0.,0.); // Accélération de la particule i (pour masse = 1, voir à la fin) + + double epsilon = params.LocateParam("choix_epsilon")->val; // paramètre petit pour le calcul du gradient. Erreur en epsilon^2 + + Vecteur3D epsx(epsilon,0.,0.); + + my_bod.inc_pos(epsx); // position + epsx + double Eplus = new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(-2.*epsx); // position - epsx + double Eminus= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(epsx); // remet la particule à sa place + double aix=-((Eplus-Eminus)/(2.*epsilon)); + ai += Vecteur3D(aix,0.,0.); // Force selon x + + + Vecteur3D epsy(0.,epsilon,0.); + my_bod.inc_pos(epsy); // position + epsy + Eplus = new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(-2.*epsy); // position - epsy + Eminus= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(epsy); // remet la particule à sa place + ai += Vecteur3D(0.,-((Eplus-Eminus)/(2.*epsilon)),0.); // Force selon y + + + Vecteur3D epsz(0.,0.,epsilon); + my_bod.inc_pos(epsz); // position + epsz + Eplus = new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(-2.*epsz); // position - epsz + Eminus= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(epsz); // remet la particule à sa place + ai += Vecteur3D(0.,0.,-((Eplus-Eminus)/(2.*epsilon))); // Force selon z + + Vecteur3D acc; + acc = gravity + ai/my_bod.get_mass(); + + my_bod.set_acc(acc); + return acc; // ACCELERATION +} + +// Calcul du gradient par +// (1/12 E(r-2 eps)-2/3 E(r-eps) + 2/3 E(r+eps ) - 1/12 E(r-2 eps))/(eps) pour chaque axe +// cf http://en.wikipedia.org/wiki/Finite_difference_coefficients +// http://en.wikipedia.org/wiki/Five-point_stencil +template Vecteur3D new_acc_pot_fourth_order(vector &bod, const int i, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms) +{ + Body &my_bod = bod[i]; + + Vecteur3D ai(0.,0.,0.); // Accélération de la particule i (pour masse = 1, voir à la fin) + + double epsilon = params.LocateParam("choix_epsilon")->val; // paramètre petit pour le calcul du gradient. Erreur en epsilon^2 + + double E2,E1,Em1,Em2; + + Vecteur3D eps(epsilon,0.,0.); + + my_bod.inc_pos(-2.*eps); // position - 2 eps + Em2 = new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(eps); // position - eps + Em1= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(2.*eps); // position + eps + E1= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(eps); // position + 2*eps + E2= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(-2.*eps); // position + double ac=((1./12.)*Em2 - (2./3.)*Em1 + (2./3.)*E1 - (1./12.)*E2)/(epsilon); + ai += Vecteur3D(-ac,0.,0.); // Force selon x (- gradient) + + + eps = Vecteur3D(0.,epsilon,0.); + + my_bod.inc_pos(-2.*eps); // position - 2 eps + Em2 = new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(eps); // position - eps + Em1= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(2.*eps); // position + eps + E1= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(eps); // position + 2*eps + E2= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(-2.*eps); // position + ac=((1./12.)*Em2 - (2./3.)*Em1 + (2./3.)*E1 - (1./12.)*E2)/(epsilon); + ai += Vecteur3D(0.,-ac,0.); // Force selon y + + + eps = Vecteur3D(0.,0.,epsilon); + + my_bod.inc_pos(-2.*eps); // position - 2 eps + Em2 = new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(eps); // position - eps + Em1= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(2.*eps); // position + eps + E1= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(eps); // position + 2*eps + E2= new_pot(bod, i, fieldB, fieldE, laser, t, params); + my_bod.inc_pos(-2.*eps); // position + ac=((1./12.)*Em2 - (2./3.)*Em1 + (2./3.)*E1 - (1./12.)*E2)/(epsilon); + ai += Vecteur3D(0.,0.,-ac); // Force selon y + + + + Vecteur3D acc; + acc = gravity + ai/my_bod.get_mass(); + + my_bod.set_acc(acc); + return acc; // ACCELERATION +} + + +/*----------------------------------------------------------------------------- + * get_acc_jerk_coll -- calculates accelerations and jerks, and as side + * effect also calculates the time scale coll_time for + * significant changes in local configurations to occur. + * + * force on i due to j/m_i = a_ji = q_i q_j r_ji/(4 pi epsilon_0 ||r_ji||^3) where r_ji = r_i - r_j (vector from j to i) + * + * Modifications by Walter (but adapted to Coulombian case by Daniel Comparat) to improve performance: + * + * - using of vector + * - (re-) using of register variables. + * - avoiding divisions + * - computing forces rather than accelerations: + * the loop to compute accelerations looks like this (with obvious notation): + * + * for(i=0; i!=n; ++i) + * a[i] = 0. // reset accelerations to 0 + * for(i=0; i!=n; ++i) { + * qi = q[i]; // get charge and pos of ith + * ri = r[i]; // body into register + * ai = 0.; // to hold force due to j>i + * for(j=i+1; j!=n; ++j) { // loop pairs j>i + * rji = ri- r[j] ; // distance vector + * rji *= qi*q[j] / |rji|^3 // mutual force + * ai += rji; // add: force_i due to j>i + * a[j]-= rji; // add: force_j due to i void add_acc_N_body_Coulomb(const vector &bod, Vecteur3D *accell, const int n) +{ + + Vecteur3D *acc = new Vecteur3D[n]; + + for (int i = 0; i < n ; i++) + acc[i] = Vecteur3D(0.,0.,0.); + + for (int i = 0; i != n ; ++i) + { + const double qi = bod[i].get_charge(); // qi + if (qi == 0.) + continue; + + const Vecteur3D ri = bod[i].get_pos(); // ri + register Vecteur3D ai = Vecteur3D(0.,0.,0.); // ai due to j>i + for (int j = i+1; j != n ; ++j) + { + // pre-compute some auxiliary quantites + Vecteur3D rji= -bod[j].get_pos(); + rji += ri; // rji = distance vector + register double + r2 = rji.mag2(), // rji^2 + pr2 = 1./r2; // 1 / rji^2 + + // add the {j (i)} contribution to the {i (j)} values of + // force + pr2 *= bod[j].get_charge()*qi*sqrt(pr2); // mi*mj / |rji|^3 (for Newton, here qi qj/ 4pi epsilon_0 r^3) + rji *= pr2; // mutual force = mi*mj*da + ai += rji; // force at i due to j>i + acc[j] -= rji; // force at j due to ii and divide by mass to get accelerations + register double tmp = kCoulomb/bod[i].get_mass(); // kCoulomb=1/(4 pi epsilon_0) + acc[i] += ai; + acc[i] *= tmp; + } + + for (int i = 0; i < n ; i++) + accell[i] += acc[i]; + + delete [] acc; + +} + + +// Calculate the Coulombian field for the sum_j=1^n not i +template Vecteur3D get_coulomb_field(const vector &bod, const int i, const Vecteur3D &ri) +{ + Vecteur3D Ei=Vecteur3D(0.,0.,0.); + + for (int j = 0; j != bod.size() ; ++j) + { + // pre-compute some auxiliary quantites + Vecteur3D rji= -bod[j].get_pos(); // -rj + rji += ri; // rji = ri-rj = distance vector + double r2 = rji.mag2(); // rji^2 + if (r2 < VERY_SMALL_NUMBER) + continue; // this mean that rji=0 and so i = j + + double pr2 = 1./r2; // 1 / rji^2 + + pr2 *= bod[j].get_charge()*sqrt(pr2); // qj/ r^3 + rji *= pr2; + Ei += rji; // qj vec(rji)/rji^3 + } + + return kCoulomb*Ei; // kCoulomb=1/(4 pi epsilon_0) + +} + + + + +// Calculate the Coulombian potential for the sum_j=1^n not i qj/(r_ij)/4 pi epsilon_0 +// Is used only for statistics to check the energy conservation. So it is not fully optimized +template double get_coulomb_potential(const vector &bod, const Vecteur3D &ri, const int n) +{ + + double pot_i = 0.; + + for (int j = 0; j != n ; ++j) + { + double rji2 = (ri - bod[j].get_pos()).mag2(); // r_ij^2 + if (rji2 < VERY_SMALL_NUMBER) + continue; // this mean that rji=0 and so i = j + pot_i += kCoulomb*bod[j].get_charge()/sqrt(rji2); // kCoulomb=1/(4 pi epsilon_0) + } + return pot_i; + +} + + +// add Lorentz force for charged particles +template void add_acc_Charged_particles(vector &bod, Vecteur3D *accell, const Field &fieldB, const Field &fieldE, const int n) +{ + for (int i = 0; i < n ; i++) + { + double q = bod[i].get_charge(); + double m = bod[i].get_mass(); + Vecteur3D r = bod[i].get_pos(); + Vecteur3D v = bod[i].get_vel(); + Vecteur3D E = fieldE.get_Field(r); + Vecteur3D B = fieldB.get_Field(r); + Vecteur3D crossedvalue = v.cross(B); + Vecteur3D force = q*(E + crossedvalue)/m; + accell[i] += q*(E + v.cross(B))/m; // Lorentz force + } + +} + + + +// kinetic energy +template double get_kin(Body &bod) +{ + double ekin = 0.; + const double m = bod.get_mass(); // mi + + const Vecteur3D v = (bod.get_vel()); // vi + ekin += m * v*v; + + ekin *= 0.5; + + return ekin; +} + +// temps d'évolution typique des forces (ou potentiels) ~ 0.1 waist/vitesse. Le 0.1 est empirique et dépend des paramètres comme la largeur de la transition +// A améliorer avec les champs, différents lasers (pas le seul premier) et Temp_estime = Temp ?... +template double t_evol_ext(vector &bod, const Field &fieldB, const Field &fieldE, const vector &my_laser, const double Temp_estime) +{ + double t_evol; + double waist = my_laser[0].get_waist().mag(); // Waist (Attention juste du premier laser, en supposant qu'il représente bien les autres waits) + double vitesse_therm = sqrt(kB*Temp_estime/bod[0].get_mass()); // vitesse thermique en m/s 1/2 m vx^2 = 1/2 kB T + t_evol = min(0.1*waist/vitesse_therm,0.001); // au max 1 ms + return t_evol; +} + + + +#endif + + diff --git a/Main Code 64bits/params.cpp b/Main Code 64bits/params.cpp new file mode 100644 index 0000000..cdc3e4b --- /dev/null +++ b/Main Code 64bits/params.cpp @@ -0,0 +1,311 @@ +#include +#include + +#include // for strcmp + +#include "params.h" + + +// Sortie du paramètre (val, minv , ...) +void Param::dump(ostream &stream, bool nice_formated_output) const +{ + stream << setprecision(12) << Name() << ' ' << val << ' ' << minv << ' ' << maxv << ' ' << nbstep << ' ' << boolalpha << is_scanned << ' ' << boolalpha << is_time_dependent << ' ' << tau << ' ' << val_t0 ; +} + + + +//pour atteindre un param Retourne le pointeur Param* vers le param qui à le nom ParamName +const Param* FitParams::LocateParam(const string &ParamName) const +{ + ParamCIterator i = begin(); + for ( ; i != end(); ++i) + if ((*i)->Name() == ParamName) break; + if (i == end()) + { + cerr << " Param " << ParamName << " does not exist " << endl; + return NULL; + } + return (*i); +} + +//Elimine le param qui à le nom ParamName. Retourne true si trouvé et false sinon +bool FitParams::DeleteParamIfExists(const string &ParamName) +{ + ParamIterator i = begin(); + for ( ; i != end(); ++i) + if ((*i)->Name() == ParamName) + { + erase(i); + return true; + } + return false; +} + + +//pour atteindre un param Retourne le pointeur Param* vers le param qui à le nom ParamName +Param* FitParams::LocateParam(const string &ParamName) +{ + ParamIterator i = begin(); + for ( ; i != end(); ++i) + if ((*i)->Name() == ParamName) break; + if (i == end()) return NULL; + return (*i); +} + +//fait un vecteur const de class Param +const Param * FitParams::LocateOrAddParam(const string &ParamName) +{ + const Param* i = LocateParam(ParamName); + if (i != NULL) return i; +// no there : add one + push_back(new Param(ParamName)); + return LocateParam(ParamName); +// ParamCIterator last = end(); +// return (--last); // i.e. the one just inserted (since end() is beyond last) +} + +//fait un vecteur de class Param +Param * FitParams::LocateOrAddNonConstParam(const string &ParamName) +{ + Param* i = LocateParam(ParamName); + if (i != NULL) return i; +// no there : add one + push_back(new Param(ParamName)); + return LocateParam(ParamName); +// ParamCIterator last = end(); +// return (--last); // i.e. the one just inserted (since end() is beyond last) +} + +// return the number of variable (not the fixed ones) parameters +size_t FitParams::VariableParamCount() const +{ + size_t npars = 0; +// count and locate actually variable parameters + for (ParamCIterator i=begin(); i != end(); ++i) + if ((*i)->is_scanned) npars++; + return npars; +} + + +//Sort dans "stream" le message et les paramètres (cf dump) +void FitParams::dump(ostream &stream, const string &Message, bool nice_formated_output) const +{ + stream << "BEGIN_OF_FITPARAMS " << name << endl; + if (Message != "") stream << Message << std::endl; + + stream << "Name" << ' ' << "val" << ' ' << "minv" << ' ' << "maxv" << ' ' << "nbstep" << ' ' << "is_scanned" << ' ' << "is_time_dependent" << ' ' << "tau" << ' ' << "val_t0" << endl; + + for (ParamCIterator i=begin(); i != end(); ++i) + { + (*(*i)).dump(stream,nice_formated_output); + stream << endl ; + } + + stream << "END_OF_FITPARAMS " << name << endl; +} + +//Sort dans "stream" les paramètres: nom val +void FitParams::dump_model(ostream &stream, const string &Message) const +{ + if (Message != "") stream << Message << std::endl; + for(size_t i=0; i< this->size(); ++i) + { + stream << setprecision(12) << (*this)[i]->name << " " <<(*this)[i]->val << endl ; + } +} + + + + +#include + +#include "datacards.h" +//permet de recuperer les différents Param dans un vector de Param +// La ligne contient +// Le nom, Valeur_in, Valeur_fin, Nb_steps, is_scanned ("true" or "false"), is_time_dependent("true" or "false"), tau; +void FitParams::read(const std::string &FileName) +{ + DataCards data_list(FileName.c_str()); // Lit le fichier et crée les datacards. + double Tau_Modif = data_list.DParam("Tau_Modif"); // Valuer par défaut de la variation temporelle + + ifstream S(FileName.c_str()); + + string line; + while (getline(S, line)) + { + if(line == "BEGIN_OF_FITPARAMS") break; + } + + while (getline(S, line)) + { + if (line == "END_OF_FITPARAMS") break; + + string name, boolean; // nom de la variable et nom avec SCAN_ + if (line.compare(0,6,"@SCAN_") == 0) // C'est un paramètre a scanner + { + size_t p = 6; // longueur de "@SCAN_" + size_t q = line.find_first_of(" \t"); // Prend la fin du nom (séparé des autres par TAB) + name = line.substr(p,q-p); // on enlève @SCAN_ pour prendre le nom + } + + Param *p=LocateOrAddNonConstParam(name); // AJOUTE UN PARAMETRE DU NOM Name + char name_scanned [100]; + char bool_is_scann [100]= {'f','a','l','s','e'}; + char bool_is_time_dependent [100]= {'f','a','l','s','e'}; + p->tau = Tau_Modif; //Met par défaut la variation temporelle de Tau_Modif. Sera modifier ci dessous si une autre valeur est donnée + +// Lit le fichier. Si il n'y a pas toute les données il n'affecte pas les valeurs sui restent à leur valeur par défaut + std::sscanf (line.c_str(),"%s %lf %lf %d %s %s %lf %lf", name_scanned, &(p->minv), &(p->maxv), &(p->nbstep), bool_is_scann, bool_is_time_dependent, &(p->tau), &(p->val_t0)); + boolean = bool_is_scann; + if (boolean == "true") p->is_scanned = true; + else p->is_scanned = false; // is_scanned(false) par défaut + boolean = bool_is_time_dependent; + if (boolean == "true") p->is_time_dependent = true; + else p->is_time_dependent = false; // is_time_dependent(false) par défaut + } + + S.close(); +} + +//Lit les paramètres dans le "stream" +//void FitParams::read(istream &S) +//{ +// +//} + + +void FitParams::operator = (const FitParams &other) +{ + + +// if (name == "NoName" ) name = other.name; +// don't know why the name was not copied. +// A real copy constructor should copy the name as well: + name = other.name; + +// first clear the parameters in this instance that are not in the other + FitParams::iterator i=begin(); + while(i != end()) + { + if ( ! other.LocateParam((*i)->name)) + { + delete *i; // free memory (delete parameters) + i = erase(i); + } + else + { + ++i; + } + } + + + for (FitParams::const_iterator i=other.begin(); i != other.end(); ++i) + { + Param *p = LocateOrAddNonConstParam((*i)->name); // get a pointer to the parameter of this instance + *p = *(*i); // copy the content of parameters + } + +} + +FitParams::FitParams(const FitParams &other) : + vector() +{ + (*this) = other; +} + +#include + +vector FitParamNames(const string &FileName) +{ + vector names; + FILE* f = fopen(FileName.c_str(), "r"); + + char line[4096]; + while (fgets(line,4096,f)) + { + char name[100]; + if (sscanf(line,"BEGIN_OF_FITPARAMS %s",name) == 1) + names.push_back(name); + } + return names; +} + +// Initialise les paramètres selon la valeur non scannée de la dataCard (cf datacards.h) ou à la valeur min si scannée +void FitParams::init_value(const std::string &FileName) +{ + DataCards data_list(FileName.c_str()); // Lit le fichier et crée les datacards. + for (DataCards::CardList::iterator i = data_list.cards.begin(); i != data_list.cards.end(); i++) + Param *p=LocateOrAddNonConstParam((*i).kw ); // AJOUTE (si n'existe pas) UN PARAMETRE DU NOM du paramètre dans la dataCard + + for (ParamIterator i=(*this).begin(); i != (*this).end(); ++i) // boucle sur les paramètres + { + Param &p = **i; + + if( p.is_scanned == false && data_list.HasKey(p.name)) // Si paramètre ne sera pas à scanner + { + p.val = data_list.DParam(p.name); // Si paramètre constant on prend sa valeur dans la datacard(si elle existe) + p.val_t0 = p.val; + } + else + { + p.val = p.minv; // Si paramètre à scanner on l'initialise à sa valeur de départ (min) + p.val_t0 = p.val; + } + + } + +} + + + + +// Modification des paramètres dans l'ordre +// Nb_steps = 1 signifie que l'on va prendre 2 valeurs min et max. nb_step=2 on prend 3 valeurs: min, moitié et max . +// On retourne la condition de fin: false s'il faut encore continuer à modifier et true si on a fini les boucles. +// C'est à dire à priori on ne modifie qu'un paramètre à la fois dans l'ordre d'apparition dans la liste des scans +bool FitParams::Scan_Param() +{ + for (ParamIterator i=(*this).begin(); i != (*this).end(); ++i) // boucle sur les paramètres + { + Param &p = **i; + // cout << p << endl << endl; + if( p.is_scanned == false ) // Pas de boucle pour ce paramètre + continue; + + if(p.val_t0 >= p.maxv) // On a fini la ième boucle on réinitailise ce paramètre et on passe à la boucle suivante + { + p.val_t0 = p.minv; + p.val = p.val_t0; + } + else // On n'atteind pas encore la fin de la boucle + { + p.val_t0 += (p.maxv - p.minv)/p.nbstep; // On augmente le paramètre + p.val = p.val_t0; + return false; // et on arrete donc les boucles + } + } + return true; +} + + +// Modification des paramètres aléatoirement +bool FitParams::Scan_Param_aleatoire(const gsl_rng * r) +{ + for (ParamIterator i=(*this).begin(); i != (*this).end(); ++i) // boucle sur les paramètres + { + Param &p = **i; + + if( p.is_scanned == false ) // Pas de boucle pour ce paramètre + continue; + else + { + p.val_t0 = gsl_ran_flat (r, p.minv, p.maxv); // tirage au hasard entre les valeur min et max possibles + p.val = p.val_t0; + } + cout << p.name << " " << p.val_t0 << endl; + } + return false; +} + + + diff --git a/Main Code 64bits/params.h b/Main Code 64bits/params.h new file mode 100644 index 0000000..b510cfe --- /dev/null +++ b/Main Code 64bits/params.h @@ -0,0 +1,167 @@ +/** Classe Paramètre (Param) et Liste de Paramètre (FitParams) + +Un paramètre est: +un nom +un booléan is_scanned disant si il est fixé ou non. Par défaut false +un booléan is_time_dependent disant si il est varie dans le temps ou pas. Par défaut false +Une liste de: + val, minv, maxv, nbstep, tau, val_t0; + // val_t0 = minv + steps * (maxv - minv )/nbstep + // tau = taux de variation temporelle --> val = val_t0 exp^(-t/tau) + + +Exemple d'utilisation de FitParam + + + FitParams ¶ms; // this is a vector + Param *pDayMax; + pDayMax = params.LocateOrAddNonConstParam("DayMax"); + + +// fixer un parametre de nom paramname + param_a_fixer->is_scanned = false; + +// mettre un parametre de nom paramname a une certaine valeur value + Param* param_to_set = params.LocateOrAddParam(paramname); + param_to_set->val = value; //peut rajouter pour vérifier si il est fixé: if(!param_to_set->is_scanned) + + +// pour initialiser tout d'un coup avec un tableau tab de la bonne taille : + for(size_t i=0; ival=tab[i]; + + + +// boucle sur les parametres de params : + for (ParamIterator i=params.begin(); i != params.end(); ++i) + { + Param &p = **i; + if (p.is_scanned) continue; + // faire la boucle sur la valeur de param ici + for (int n = 0 ; n < p.nstep ; n++) + // etc. + + } + +****************************/ + +#ifndef PARAM__H +#define PARAM__H + +#include +#include +#include +#include + +#include // for random generator +#include // for flat random generator + +using namespace std; + +//! Named parameters (i.e. what estimation theory call parameters). +class Param +{ +public : + + double val, minv, maxv, val_t0, tau; + int nbstep; + bool is_scanned, is_time_dependent; + std::string name; + Param() : val(0.), minv(0.), maxv (0.), val_t0(0.), tau(1e100), nbstep(1), is_scanned(false), is_time_dependent(false), name("UNKNOWN") {}; + Param(const string &Name) : val(0.), minv(0.), maxv (0.), val_t0(0.), tau(1e100), nbstep(1), is_scanned(false), is_time_dependent(false), name(Name) {}; + +// Donne le nom. + std::string Name() const + { + return name; + } + +// Sortie du paramètre (val, minv , ...) + void dump(ostream &stream = cout, bool nice_formated_output=false) const; + + friend ostream& operator << (ostream &stream, const Param &p) + { + p.dump(stream); + return stream; + } +}; + + +//! the ensemble of all parameters of the fit +// It is vector of pointers, in order to keep always the proper allocation. + +class FitParams : public vector +{ + string name; + +public : + + FitParams(const string &Name) : name(Name) {}; + FitParams() : name("NoName") {}; + void SetName(const string &Name) + { + name=Name; + } + + FitParams(const FitParams &); + +//pour atteindre un param Retourne le pointeur Param* vers le param qui à le nom ParamName + const Param* LocateParam(const string &ParamName) const; + Param* LocateParam(const string &ParamName); + +//fait un vecteur de class Param + const Param* LocateOrAddParam(const string &ParamName); + Param* LocateOrAddNonConstParam(const string &ParamName); + +//Elimine le param qui à le nom ParamName. Retourne true si trouvé et false sinon + bool DeleteParamIfExists(const string &ParamName); + +// return the number of variable, scanned, parameters (not the fixed ones) + size_t VariableParamCount() const; + + + //Sort dans "stream" le message et les paramètres (cf dump):val, val_t0 + void dump(ostream &stream = cout, const string &Message = "",bool nice_formated_output=false) const; + + //Sort dans "stream" les paramètres: nom val + void dump_model(ostream &stream = cout, const string &Message = "") const; + + + friend ostream& operator << (ostream &stream, const FitParams &p) + { + p.dump(stream); + return stream; + } + + /*! if FitParam has a name, read the block with the same name else reads the first block and assigns name */ +// L'ordre dans le fichier doit être name_scanned, minvalue, maxvalue, nombrestep, bool_is_scann, bool_is_time_dependent, tau_var, erro + void read(const std::string &FileName); +// void read(istream &S); + +// Initialise les paramètres selon la valeur non scannée de la dataCard (cf datacards.h) ou à la valeur min si scannée + void init_value(const std::string &FileName); + +// Modification des paramètres +// Nb_steps = 1 signifie que l'on va prendre 2 valeurs min et max. nb_step=2 on prend 3 valeurs: min, moitié et max . +// On retourne la condition de fin: false s'il faut encore continuer à modifier et true si on a fini les boucles. +// C'est à dire à priori on ne modifie qu'un paramètre à la fois dans l'ordre d'apparition dans la liste des scans + bool Scan_Param(); + + +// Modification des paramètres aléatoirement + bool Scan_Param_aleatoire(const gsl_rng * r); + + ~FitParams() + { + for (FitParams::iterator i=begin(); i != end(); ++i) delete *i; + } + + void operator = (const FitParams &); +}; + +typedef FitParams::iterator ParamIterator; +typedef FitParams::const_iterator ParamCIterator; + + +vector FitParamNames(const string &FileName); + +#endif /* PARAM__H */ diff --git a/Main Code 64bits/scaling_velocities.cpp b/Main Code 64bits/scaling_velocities.cpp new file mode 100644 index 0000000..11ee354 --- /dev/null +++ b/Main Code 64bits/scaling_velocities.cpp @@ -0,0 +1,134 @@ +#include "scaling_velocities.h" +#include "Atome.h" +#include "Internal_state.h" +#include "Vecteur3D.h" +#include "Laser.h" // Classe Laser +#include "Molecule.h" +#include "one_body.h" +#include "Stat_Molecule.h" + +// fonction qui applique la constante lambda(t) aux vitesses(t). +//INPUTS: -coupling_efficiency is in percentage. +//OUTPUT: -file_scal: the aimed temperature and the rescaled one are outputs. +void scaling_velocities( const double t, vector &Mol, const int nb_mol,const vector &Level, const Field &fieldB,const Field &fieldE, FitParams ¶ms,double coupling_efficiency, ofstream & file_scal) +{ + + + Stat stat_Mol; //for having the T temperature of the cloud (Ti= stat.Temp_1D_100) + vector liste_Adresses_Mol; //List of Molecule of first type + for (int i=0; i!= nb_mol; i++) + { + liste_Adresses_Mol.push_back(Mol[i]); + } + + stat_molecule_form_list(Mol, liste_Adresses_Mol, stat_Mol, Level, fieldB, fieldE, nb_mol, params); + +//Parameters of the scaling: + //temperature that we want to reach : + double Temp_ini_x = params.LocateParam(string("Temp_ini_x[0]"))->val; + double Temp_ini_y = params.LocateParam(string("Temp_ini_y[0]"))->val; + double Temp_ini_z = params.LocateParam(string("Temp_ini_z[0]"))->val; + Vecteur3D Temp_0(Temp_ini_x,Temp_ini_y,Temp_ini_z); // (Tx0,Ty0,Tz0) + + + Vecteur3D Temp_instant; //temperature instantanée du nuage, à temps t + + Temp_instant= stat_Mol.Temp_1D_50; + +// coefficient LAMBDA for rescaling + Vecteur3D ratio_T; + Vecteur3D factor1; + double coeff=coupling_efficiency; + + ratio_T = Temp_0/Temp_instant; + ratio_T= ratio_T-1.; + factor1= coeff*ratio_T; + factor1= factor1+1.; + factor1= abso(factor1); + //BERENDSEN constant: + Vecteur3D Lambda=racine(factor1); + + + vector liste_Adresses_Mol_dans_niveau; //List of Molecule of first type + for (int i=0; i!= nb_mol; i++) + { + Vecteur3D tot; + tot= Hadamard(Mol[i].get_vel(),Lambda); + Mol[i].set_vel(tot); //on multiplie les vitesses selon x,y et z par Lambda_x,y,z(t) + liste_Adresses_Mol_dans_niveau.push_back(Mol[i]); + } + + stat_molecule_form_list(Mol, liste_Adresses_Mol_dans_niveau, stat_Mol, Level, fieldB, fieldE, nb_mol, params); + + Temp_instant = stat_Mol.Temp_1D_50; // on recalcule T + + file_scal << t << " " << Temp_0<< " " << Temp_instant << " " ; + file_scal << endl; + + liste_Adresses_Mol.clear(); // erase the vector: + + +} +//DEUX FONCTIONS POUR PERMETTRE DE RESCALER A UN TEMPS t+dt: +// v'(t+dt)=v(t+dt)*Lambda(t) +//Fonction qui calcule lambda à t (il faut appliquer le facteur de rescalng Lambda aux vitesses à t+dt_scal) +Vecteur3D calcul_lambda( const double t, vector &Mol, const int nb_mol,const vector &Level, const Field &fieldB,const Field &fieldE, FitParams ¶ms,double coupling_efficiency, ofstream & file_scal) +{ + + Stat stat_Mol; //for having the T temperature of the cloud (Ti= stat.Temp_1D_100) + vector liste_Adresses_Mol; //List of Molecule of first type + for (int i=0; i!= nb_mol; i++) + { + liste_Adresses_Mol.push_back(Mol[i]); + + } + stat_molecule_form_list(Mol, liste_Adresses_Mol, stat_Mol, Level, fieldB, fieldE, nb_mol, params); + +//Parameters of the scaling: + //temperature that we want to reach : + double Temp_ini_x = params.LocateParam(string("Temp_ini_x[0]"))->val; + double Temp_ini_y = params.LocateParam(string("Temp_ini_y[0]"))->val; + double Temp_ini_z = params.LocateParam(string("Temp_ini_z[0]"))->val; + Vecteur3D Temp_0(Temp_ini_x,Temp_ini_y,Temp_ini_z); // (Tx0,Ty0,Tz0) + + + Vecteur3D Temp_instant; //temperature instantanée du nuage + Temp_instant= stat_Mol.Temp_1D_50; +cout << " Temp_1D_50 avant " << Temp_instant << endl; + // coefficient LAMBDA for rescaling + Vecteur3D ratio_T; + Vecteur3D factor1; + double coeff=coupling_efficiency; + + ratio_T = Temp_0/Temp_instant; + ratio_T= ratio_T-1.; + factor1= coeff*ratio_T; + factor1= factor1+1.; + factor1= abso(factor1); + //BERENDSEN constant: + Vecteur3D Lambda=racine(factor1); + + + return Lambda; +} +//fonction qui applique Le coefficient Lambda aux vitesses, à un temps t. (il faut l'appliquer à t+dt_scal). +void rescaling_velocities_after_dt ( const double t, vector &Mol, const int nb_mol,const vector &Level, const Field &fieldB,const Field &fieldE, FitParams ¶ms,double coupling_efficiency, ofstream & file_scal, Vecteur3D Lambda) +{ + Stat stat_Mol; //for having the T temperature of the cloud (Ti= stat.Temp_1D_100) + vector liste_Adresses_Mol_dans_niveau; //List of Molecule of first type + for (int i=0; i!= nb_mol; i++) + { + Vecteur3D tot; + tot= Hadamard(Mol[i].get_vel(),Lambda); + Mol[i].set_vel(tot); + liste_Adresses_Mol_dans_niveau.push_back(Mol[i]); + } + + stat_molecule_form_list(Mol, liste_Adresses_Mol_dans_niveau, stat_Mol, Level, fieldB, fieldE, nb_mol, params); + +Vecteur3D Temp_instant = stat_Mol.Temp_1D_50; // on recalcule T + cout << " Temp_1D_50 apres " << Temp_instant << endl; + file_scal << t << " " << Temp_instant << " " ; + file_scal << endl; + +} diff --git a/Main Code 64bits/scaling_velocities.h b/Main Code 64bits/scaling_velocities.h new file mode 100644 index 0000000..545afde --- /dev/null +++ b/Main Code 64bits/scaling_velocities.h @@ -0,0 +1,35 @@ +/* +Scaling velocities: to make mean temperature of the clouds converge to the initial value that is entered in liste_param.h +*/ + + +//#ifndef scaling_velocities_SEEN +//#define scaling_velocities_SEEN + + + + + +#include "Atome.h" +#include "Internal_state.h" +#include "Vecteur3D.h" +#include "Laser.h" // Classe Laser +#include "Molecule.h" +#include "one_body.h" +#include "Stat_Molecule.h" + + +#include "algorithmes.h" // Pour qsort +#include "params.h" + + +#include "Field.h" + +// fonction rescale velocities - applique Lambda aux vitesses, à un même temps t. +void scaling_velocities( const double t, vector &Mol, const int nb_mol,const vector &Level, const Field &fieldB,const Field &fieldE, FitParams ¶ms,double coupling_efficiency, ofstream & file_scal); +// fonction qui calcule le coefficient lambda de Berendsen, à un tmeps t. +// Briefly v(t+dt) = v(t) * sqrt[1+coef(T0/T(t)-1)] +// So T(t+dt) ~ T(t)+coef(T0-T(t)) +Vecteur3D calcul_lambda( const double t, vector &Mol, const int nb_mol,const vector &Level, const Field &fieldB,const Field &fieldE, FitParams ¶ms,double coupling_efficiency, ofstream & file_scal); +//fonction qui applique Le coefficient Lambda aux vitesses, à un temps t. (il faut l'appliquer à t+dt). +void rescaling_velocities_after_dt ( const double t, vector &Mol, const int nb_mol,const vector &Level, const Field &fieldB,const Field &fieldE, FitParams ¶ms,double coupling_efficiency, ofstream & file_scal, Vecteur3D Lambda); diff --git a/Main Code 64bits/shift_molecule.cpp b/Main Code 64bits/shift_molecule.cpp new file mode 100644 index 0000000..2e0216e --- /dev/null +++ b/Main Code 64bits/shift_molecule.cpp @@ -0,0 +1,167 @@ +// CALCUL DU SHIFT EN ENERGIE DE LA MOLECULE +// Zeeman- Stark, dipolaire ensuite + +#include "shift_molecule.h" +#include "one_body.h" +#include "algorithmes.h" +#include "Transition_rate_calcul.h" + + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + + + +// Calcul (sans mise à jour des énergies) du potentiel de l'état interne de la molécule juste avec les champs +// Il n'y a pas la gravité elle est rajouté directement à la main dans l'accélération +double new_pot(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms) +{ + // Vecteur3D pos=my_mol.get_pos(); + // double delta =delta_field_shift_B_E(my_mol, fieldB.get_Field(pos).mag(), fieldE.get_Field(pos).mag()); // Mettre si on ne veux pas le potentiel dipolaire + double delta = delta_shift(Mol, n_mol, fieldB, fieldE, laser, t, params); + // my_mol.Energy_cm = my_mol.Energy0_cm + delta/Conv_Ecm_delta; + return HBAR*delta; +} + + +// Mise à jour du potentiel de l'état interne de la molécule +// Ne prend pas en compte le potentiel dipolaire pour éviter des accumulation de detuning +void set_pot_mol(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms) +{ + Molecule my_mol = Mol[n_mol]; + double pot; + Vecteur3D pos=my_mol.get_pos(); + double B=fieldB.get_Field(pos).mag(); // Magnétique + double E=fieldE.get_Field(pos).mag(); // Electrique + pot = HBAR * delta_field_shift_B_E(Mol, n_mol, B, E); // Recalcul le shift (dipolaire, magn, électrique) de cette molécule + my_mol.Energy_cm = my_mol.Energy0_cm + (pot/HBAR)/Conv_Ecm_delta; + return; +} + +// Mise à jour du potentiel de l'état interne de toutes les molécules +// Ne prend pas en compte le potentiel dipolaire pour éviter des accumulation de detuning +void set_pot_all_mol(vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms) +{ + for (int nb = 0; nb < nb_mol; nb ++) + set_pot_mol(Mol, nb, fieldB, fieldE, laser, t, params); + + return; +} + + + +// Mise à jour (et retourne) de l'accélération de la molécule +Vecteur3D new_acc(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t) +{ + Molecule my_mol = Mol[n_mol]; + + Vecteur3D grad_pot_B,grad_pot_E; + Vecteur3D pos=my_mol.get_pos(); + double B=fieldB.get_Field(pos).mag(); // Magnétique + double E=fieldE.get_Field(pos).mag(); // Electrique + Vecteur3D grad_field_B2=fieldB.get_grad_field_F2(pos); // gradient de ||B||^2 (Magnétique) + Vecteur3D grad_field_E2=fieldE.get_grad_field_F2(pos); // Electrique + + grad_pot_E = my_mol.Grad_Energy_Shift_E(E, grad_field_E2); + grad_pot_B = my_mol.Grad_Energy_Shift_B(B, grad_field_B2); + + Vecteur3D acc; + + acc = gravity - grad_pot_E/my_mol.get_mass() - grad_pot_B/my_mol.get_mass() ; + + my_mol.set_acc(acc); + + return acc; +} + + +// Mise à jour de l'accélération de toutes les molécules +void set_acc_all_mol(vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms) +{ + for (int nb = 0; nb < nb_mol; nb ++) + new_acc(Mol, nb, fieldB, fieldE, laser, t ); + + return; +} + + + +// Shift of particl i +// Due tio fields: zeeman, Stark, dipolar +double delta_shift(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms) +{ + Molecule my_mol = Mol[n_mol]; + + // double delta= delta_dipolaire_shift(my_mol, my_laser, params); // Dipolaire + double delta=0.; // Pas de dipolaire + + Vecteur3D pos=my_mol.get_pos(); + double B=fieldB.get_Field(pos).mag(); // Magnétique + double E=fieldE.get_Field(pos).mag(); // Electrique + delta +=delta_field_shift_B_E(Mol, n_mol, B, E); + delta += delta_dipolaire(Mol, n_mol, fieldB, fieldE, laser, t, params); + return delta; +} + + +// Calcul du shift en champ E ou B in s^-1 +double delta_field_shift_B_E(vector &Mol, const int n_mol, const double Bfield, const double Efield) +{ +// cout << "B " << Bfield << endl; +// cout << " my_mol.Energy_Shift_B_cm " << my_mol.Energy_Shift_B_cm(Bfield) << endl; + Molecule my_mol = Mol[n_mol]; + double delta = (my_mol.Energy_Shift_B_cm(Bfield) + my_mol.Energy_Shift_E_cm(Efield))*Conv_Ecm_delta ;// cm^(-1) -> s^-1 + return delta; +} + + +/*** Calcul du shift dipolaire +// Gamma (force de raie Coeff Einstein de Cette raie précisement) et GammaTot = Gamma + tout autres élergissement (laser, collision, desexcitations vers d'autres niveaux ...) +// on prend par définition hbar delta_dip = delta Gamma'/Gamma_Tot si l'état est bas en énergie et - cela si l'inverse +// où Gamma'=taux d'absorpion = taux d'emission stimulée = Gamma_Tot OmegaRabi^2/(Gamma_tot^2 + 4 delta^2) +// De plus pour les lasers façonnés cela peut poser problème. + +// Evidemment si il y a 2 lasers à 3 niveaux déjà cela pose problème en général si s>>1. Il faut habiller proprement les niveaux. +En s'inspirant de l'article "an atom faucet" nous cherchons une formule ne dépassant pas l'effet à haute intensité et correcte à basse. +Ainsi le décalage delta_j ln(1+s_j) crée par le laser j devient +[(Sum_j delta_j s_j) ln (1+sum_j s_j)]/sum_j s_j qui est correct à basse intensité (s_j <<1) et aussi si on fait I= I/2+I/2 +EN fait nous n'utilisons pas cette formule encore +***/ + +/** + Même si il n'y a pas de lumière à la raie correspondante on calcul, comme si il y en avait, le détuning +Cela semble correct pour des spectres avec peu de trous, mais si on a des peignes il faut prendre I_reel et non I_tot avant façonnage +**/ + + +// Potentiel dipolaire(/Hbar) de l'état j par Σ i>j delta_ij gamma_ij/Gamma_ij - Σ k &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms) +{ + + + double delta_pot_dipolaire =0.; + vector rate_local; + vector reaction_list_local; + + vector Level; // Require to call the function +// TODO (dc#5#): To be modified if we want to have the correct dipolar force in diagonalized case + + // rates_molecule(Level, reaction_list_local, rate_local, Mol, n_mol, fieldB, fieldE, laser, t, delta_pot_dipolaire, params, false); + + return delta_pot_dipolaire; +} + + + + + + diff --git a/Main Code 64bits/shift_molecule.h b/Main Code 64bits/shift_molecule.h new file mode 100644 index 0000000..29a0dad --- /dev/null +++ b/Main Code 64bits/shift_molecule.h @@ -0,0 +1,54 @@ +// CALCUL DU SHIFT EN ENERGIE DE LA MOLECULE +// Zeeman pour l'instant mais Stark, dipolaire ensuite, ils peuvent dépendre du temps + + +#include "Molecule.h" +#include "Laser.h" +#include "Field.h" +#include "Initialisation_programme.h" // Pour les champs +#include "params.h" + +#include +using namespace std; + +#ifndef Shift_molecule_SEEN +#define Shift_molecule_SEEN + +// Calcul (sans mise à jour des énergies) du potentiel de l'état interne de la molécule (Zeeman, Stark, dipolaire) sans gravité +double new_pot(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms); + +// Mise à jour du potentiel de l'état interne de la molécule +// Ne prend pas en compte le potentiel dipolaire pour éviter des accumulation de detuning +void set_pot_mol(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms); + +// Mise à jour du potentiel de l'état interne de toutes les molécules +// Ne prend pas en compte le potentiel dipolaire pour éviter des accumulation de detuning +void set_pot_all_mol(vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms); + + + +// Mise à jour (et retourne) de l'accélération de la molécule +// Acc = -grad E_pot/mass +Vecteur3D new_acc(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t); + +// Mise à jour de l'accélération de toutes les molécules +void set_acc_all_mol(vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms); + + + +// Shift de la particule lié aux champ: zeeman, Stark ou dipolaire +double delta_shift(vector &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms); + + +// Calcul du shift en champ E ou B in s^-1 +double delta_field_shift_B_E(vector &Mol, const int n_mol, const double Bfield, const double Efield); + + +// Potentiel dipolaire de l'état j par Σ i>j delta_ij gamma_ij/Gamma_ij - Σ k &Mol, const int n_mol, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, FitParams ¶ms); + +// For more complex case we want to diagonalize the Energy levels and hte transition Frequncies in B, E fields +double diagonalization_new_Levels_Lines(Internal_state const & Internal_state_in, Internal_state const & Internal_state_out, Vecteur3D const pol_locale); + + +#endif diff --git a/Main Code 64bits/sortie_donnees.cpp b/Main Code 64bits/sortie_donnees.cpp new file mode 100644 index 0000000..d703773 --- /dev/null +++ b/Main Code 64bits/sortie_donnees.cpp @@ -0,0 +1,660 @@ +/* + Fichier de sortie des données moléculaires: transition, probablilitées ... +*/ + +#include "sortie_donnees.h" + + +//Sauve l'état du générateur de nombre aléatoire pour ne jamais reprendre le même +void save_random_generator(gsl_rng * r, const char *nom_file) +{ + FILE *fp; + fp=fopen(nom_file, "wb"); // Fichier contenant les données du générateur de nombre aléatoire + int ran_gen_result = gsl_rng_fwrite (fp, r); // This function writes the random number state of the random number generator r + if (ran_gen_result == GSL_EFAILED) + cout << " Problem writing to the file: Data/random_gen.txt" << endl; + fclose(fp); +} + + +/* Création du fichier de sortie des données totales */ +void sortie_fichier(ofstream & /* file2 */, Molecule /* Mol[] */) +{ + + /* A mettre si on veut une numérotation automatique (ainsi que la partie finale) + + + ifstream file_in("Data/file_num.txt"); // Ouvre le fichier contenant le futur numéro de fichier + int num; + file_in >> num ; + file_in.close(); + + char snum[256]; + sprintf(snum,"%d",num); + string ssnum = snum ; + string nom_fichier = "Data/param_Ryd_" + ssnum + ".txt" ; + + ofstream file_out(nom_fichier.c_str()); // créer le fichier de donné de sortie param_Ryd_N° .txt contenant i, exc[i], x[i], y[i], z[i], pot[i], pot_ji (plus proche voisin), theta_ji, d_ji + + */ + + + /* A mettre si on veut une numérotation automatique (ainsi que la partie commentée initiale ) + file_out.close(); + ofstream file_num_out("Data/file_num.txt"); // créer le fichier contenant le futur numéro de fichier + file_num_out << ++num; + file_num_out.close(); + */ +} + + + +void Sortie_donnee_etat_int_simple(ofstream & file_out, const vector &Mol, const vector &my_laser, const double t, FitParams ¶ms) +{ + file_out<< setprecision(8); + for(int i=0; i<(int) Mol.size(); i++) + { + file_out << " " << t << " " << i << " " << Mol[i].exc << " " << Mol[i].two_J/2. << " " << Mol[i].two_N/2. << " " << Mol[i].two_M/2. << " " << Mol[i].Energy0_cm << endl ; + } + // cout << endl << " time t = " << t << endl ; + file_out << endl; + + return; +} + + + + + +void Sortie_test_debug(ofstream & file_out, vector &Mol, const vector &Level, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms, DataCards &data, const int number_photons) +{ + +// int number_matrix_lines = 2480; +// fieldB.Calculate_Derivative_Matrix(number_matrix_lines, "Data/Na/MagneticField2D_derivative.dat"); + + double step_r = 0.001; + double step_z = 0.001; + double nb_steps = 100; + + // for (double x= -nb_steps*step_r; x < nb_steps*step_r; x+=step_r) + //for (double y= -nb_steps*step_r; y < nb_steps*step_r; y+=step_r) + for (double x= 0.003; x < 0.005; x+=step_r) + + for (double z= -nb_steps*step_z; z < nb_steps*step_z; z+=step_z) + { + double y=0.; + file_out << sqrt(x*x+y*y) << " " << x << " " << y << " " << z << " " << fieldB.get_Field(Vecteur3D(x,y,z)) << " " << fieldB.get_grad_field_F2(Vecteur3D(x,y,z)) << endl; + } + file_out << endl; + + return; +} + + + + + +void Sortie_donnee(ofstream & file_out, vector &Mol, vector &Level, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms, DataCards &data, const int number_photons) +{ + //set_pot_all_mol(Mol, fieldB, fieldE, laser, t, nb_mol, params); //Met à jour de tous les potentiels (gravité, PAS dipolaire, magnétique, electrique, ...) avec la nouvelle position pour uen sortie +// ATTENTIION THIS DOES NOT WORK FOR THE POTENTIALS + + +// SOrtie des paramètres scannés + if( ((int) params.LocateParam("is_param_scanned_out")->val) == ((int) true) ) + { + for (ParamIterator i=params.begin(); i != params.end(); ++i) // boucle sur les paramètres + { + Param &p = **i; + if (p.is_scanned == true) + { + // file_out << p.name ; + // file_out << p.val_t0 << " " ; + } + } + } + + file_out<< setprecision(8); + + const int i = (int) params.LocateParam("num_niveau_etudie")->val; // numéro du niveau étudié pour faire des stats. -1 pour toutes les molécules + + Stat stat_Mol; + stat_molecule_un_niveau(Mol, stat_Mol, Level, fieldB, fieldE, i, Mol.size(), params); + + + for (int i = 0; i < nb_mol; i++) + { + set_pot_mol(Mol, i, fieldB, fieldE, laser, t, params); //Met à jour de tous les potentiels (gravité, PAS dipolaire, magnétique, electrique, ...) avec la nouvelle position pour une sortie + } + +// double Temp_ini_z = params.LocateParam("Temp_ini_z[0]")->val; +// const double vitesse_therm_z = sqrt(kB*Temp_ini_z/Mol[0].get_mass()); // vitesse thermique en m/s 1/2 m vx^2 = 1/2 kB T + + + +// file_out << t << " "; +// file_out << number_photons << " "; +// file_out << stat_Mol.Temp_3D_50 << " "; +// file_out << stat_Mol.population << " "; +// file_out << stat_Mol.Temp_1D_50.z() << " "; + + +// Attention relative à la température E_pot = 3/2 k T, E_cin =3/2 kT; E tot=3 kT + +// file_out << (stat_Mol.E_pot/kB)/mK/1.5/nb_mol << " "; + // file_out << (stat_Mol.E_cin/kB)/mK/1.5/nb_mol << " "; + // file_out << (stat_Mol.E_pot+stat_Mol.E_cin)/kB/mK/1.5/nb_mol << " "; + +// cout << (stat_Mol.E_pot/kB)/mK/1.5/nb_mol << " "; +// cout << (stat_Mol.E_cin/kB)/mK/1.5/nb_mol << " "; +// cout << (stat_Mol.E_pot+stat_Mol.E_cin)/kB/mK/1.5/nb_mol << " "; +// +// cout << endl; + + for (int i = 0; i < nb_mol; i++) + { +// double z_init = 3.*(i-nb_mol/2.)*(params.LocateParam("size_z[0]")->val)/nb_mol; +// double vz_init = 3.*(i-nb_mol/2.)*vitesse_therm_z/nb_mol; +// file_out << z_init << " "; +// file_out << Mol[i].get_pos().z() << " "; +// file_out << vz_init << " "; +// file_out << Mol[i].get_vel().z() << " "; +// file_out << t << " "; +// file_out << Mol[i].get_pos() << " "; +// file_out << Mol[i].get_vel() << " "; +// file_out << Mol[i].deg_number << " "; +// file_out << endl; + + + /***** CALCUL of parameters for the dipoles (in Debye)or diagonalization *******/ + + + MatrixXd d[3] ; + SelfAdjointEigenSolver es; // eigenstates and eigenvalues + Vecteur3D v; + v = Mol[i].get_vel(); + + Vecteur3D Bfield; + Bfield= fieldB.get_Field(Mol[i].get_pos()); + double B = Bfield.mag(); + double v_perp= (v.cross(Bfield)).mag()/B; + Diagonalization_Energy_dipole(Level, B, v_perp, es, d); + for (int j=0; j< Level.size(); j++) // we scan over the levels to calculate the parameter + { + double tripletness = 0.; //This is the parameter we want to calculate (here the triplet character) + + for (int j0=0; j0< Level.size(); j0++) // | j> = sum_|j>_O 0_ |j>_0 so we scan over |j>_0 hat is the order in the Level file + // 0_ is given by es.eigenvectors()(j0,j) . This is the coefficient of the |j> level (ordered in Energy) on the |j>_0 Level (the order in the Level file). We round it to 100% + { + // file_out << B << " " << v_perp << " " << i << " " << j << " " << j0 << " " << Level[j0].two_M << " " << abs(round(100.*es.eigenvectors()(j0,j)))/100 << endl; + if (Level[j0].two_Omega == 2) // If the state is triplet (2S+1=3 so S=1) we look on the decomposition, |0_|^2 , and sum them + { + tripletness += pow((es.eigenvectors()(j0,j)),2); // sum_|triple, j>_O |0_|^2 + } + } + // file_out << endl; + // PARAMETER THAT GIVE THE TRIPLETNESS OF THE STATE // + file_out << B << " " << v_perp << " " << j << " " << Level[j].Energy_cm << " " << tripletness << endl; + } + } + + + + /****** The new dipole are given by d[polar] = evec^dag.d0[polar].evec that is + d[n_polar+1] = (es.eigenvectors().adjoint())*d0[n_polar+1]*(es.eigenvectors()); + With d0[q+1]_ij = 0__0 + d[q+1]_ij = = sum_|j>_O _0 0_ + ********/ + + + + + /** Stat for specific states v **/ + +// vector liste_Adresses_Mol_dans_niveau; //List of Molecule of first type +// int nb_Mol_in_this_state = 0; +// for (int i=0; i!= nb_mol; i++) +// if (Mol[i].v == 0) // Molecules not in v=1,2,3 of X state +// { +// liste_Adresses_Mol_dans_niveau.push_back(Mol[i]); +// nb_Mol_in_this_state++; +// } +// stat_molecule_form_list(Mol, liste_Adresses_Mol_dans_niveau, stat_Mol, Level, fieldB, fieldE, nb_mol, params); +// file_out << nb_Mol_in_this_state << " "; +// file_out << stat_Mol.Temp_1D_50.z() << " "; +// file_out << stat_Mol.population << " "; +// file_out << stat_Mol.E_pot/kB/mK/1.5/nb_mol << " "; +// file_out << stat_Mol.E_cin/kB/mK/1.5/nb_mol << " "; +// file_out << (stat_Mol.E_pot+stat_Mol.E_cin)/kB/mK/1.5/nb_mol << " "; +// liste_Adresses_Mol_dans_niveau.clear(); // erase the vector: +// +// cout << " t " << t << " photons = " << (double) number_photons ; +// cout << " Epot " << stat_Mol.E_pot/kB/mK/1.5/nb_mol << " "; +// cout << " Ekin " << stat_Mol.E_cin/kB/mK/1.5/nb_mol << " "; +// cout << " E " << (stat_Mol.E_pot+stat_Mol.E_cin)/kB/mK/1.5/nb_mol << " "; +// cout << endl; + + /** Stat for specific states of "best" molecules in the sens of position **/ + + /**** + + vector liste_Adresses_Mol; //List of Molecule of this type + // double size_limite = params.LocateParam("size_x[0]")->val; + double size_limite = 0.02; + int nb_Mol_in_this_state = 0; + double niveau_moyen = 0.; + for (int i=0; i!= nb_mol; i++) + if (Mol[i].get_pos().mag() < size_limite) // Molecules within initial size (in x) + { + liste_Adresses_Mol.push_back(Mol[i]); + nb_Mol_in_this_state++; + niveau_moyen += Mol[i].exc; + } + niveau_moyen = niveau_moyen/nb_Mol_in_this_state; + stat_molecule_form_list(Mol, liste_Adresses_Mol, stat_Mol, Level, fieldB, fieldE, nb_mol, params); + file_out << t << " "; + file_out << nb_Mol_in_this_state << " "; + file_out << niveau_moyen << " "; + // file_out << stat_Mol.sigma_pos.mag() << " "; + // file_out << (stat_Mol.E_pot+stat_Mol.E_cin)/kB/mK/1.5/nb_mol << " "; + file_out << stat_Mol.E_cin/kB/mK/1.5/nb_mol << " "; + // cout << " N " << nb_Mol_in_this_state << " T " << stat_Mol.E_cin/kB/mK/1.5/nb_mol << endl; + liste_Adresses_Mol.clear(); // erase the vector: + + ***/ + + + // file_out << endl; + return; +} + + +void Sortie_donnee_electrons(ofstream & file_out, vector &Mol, const vector &Level, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int number_mol, FitParams ¶ms, DataCards &data, const int number_photons) +{ + Vecteur3D r,v; + r = Mol[number_mol].get_pos(); + v = Mol[number_mol].get_vel(); + Vecteur3D E = fieldE.get_Field(r); + double V = fieldE.get_electric_potential(r); + double Vcoulomb = get_coulomb_potential(Mol, r, Mol.size()); + + file_out<< setprecision(8); + file_out << t << " "; + file_out << r << " "; + file_out << E.mag() << " "; + file_out << get_coulomb_field(Mol, number_mol, r).mag() << " "; + file_out << V << " "; + file_out << Vcoulomb << " "; + + file_out << endl; + return; +} + + +// Toutes à la suites en temps +void Sortie_donnee_pop_vJ(ofstream & file_out, const vector &Mol, const int nb_Mol, const double t, const int NX, const int N_two_JX, FitParams ¶ms) +{ + if( ((int) params.LocateParam("is_param_scanned_out")->val) == ((int) true) ) + { + for (ParamIterator i=params.begin(); i != params.end(); ++i) // boucle sur les paramètres + { + Param &p = **i; + if (p.is_scanned == true) + { + // file_out << p.name ; + file_out << " " << p.val_t0 << " " ; + } + } + } + + + int **pX=new int*[NX]; + for (int vX=0; vX &Mol, const int nb_Mol, const double t, const int NX, FitParams ¶ms, int number_photons) +{ + // SOrtie des paramètres scannés + if( ((int) params.LocateParam("is_param_scanned_out")->val) == ((int) true) ) + { + for (ParamIterator i=params.begin(); i != params.end(); ++i) // boucle sur les paramètres + { + Param &p = **i; + if (p.is_scanned == true) + { + // file_out << p.name ; + file_out << " " << p.val_t0 << " " ; + } + } + } + + int *pX=new int[NX]; + + for (int vX = 0; vX < NX; vX++) + pX[vX] = 0; + + for (int i = 0; i < nb_Mol; i++) // Calcul des populations dans vX + if (Mol[i].exc == 0) + pX[Mol[i].v]++; + + cout << " time t = " << t << endl << endl ; + file_out << t << " "; + file_out << (double) number_photons/nb_Mol << " "; + + + for (int vX = 0; vX < NX; vX++) + { + // cout << " pop[vX="<< vX << "] = " << pX[vX] << endl; + file_out << pX[vX] << " "; + } + + file_out << endl ; + + delete[] pX; + + return; +} + + +void Sortie_rate(ofstream & file_rate, const vector &rate, vector &Level, const vector &reaction_list, const vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const int N_Mol, const double t, FitParams ¶ms) +{ + file_rate<< setprecision(12); +// file_rate << " time t = " << t << endl; + + int nb_levels=Level.size(); // Level.size() + + double rate_level_i_vers_level_2[nb_levels] = {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}; + double rate_level_i_vers_level_3[nb_levels] = {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}; + double rate_level_i_total[nb_levels] = {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}; + double Ecm_i[nb_levels] = {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.}; + + int nb_rate = rate.size(); + double B, current_rate ; + Vecteur3D r,v,k_laser,Bfield; + Internal_state Internal_state_in,Internal_state_out; + + for (int i = 0; i < nb_rate; i++) + { + // file_rate << " " << i; + // file_rate << " " << rate[i]; + current_rate = rate[i]; + int n_mol= reaction_list[i].n_mol; + int n_laser = reaction_list[i].n_laser; + //reaction is {n_mol; n_laser; quant_axis; pol_vector; k_eff_laser; final_internal_state;}. + // For stimlated emission it is { n_mol, n_las, k, k, k, Internal_state_out} + // For spontaneous emission { num_mol, -1, axe_quant, Vecteur3D(d[0](i,j),d[1](i,j),d[2](i,j)), Vecteur(k,0,0) , Level[j]} + + // file_rate << " " << n_mol ; + // file_rate << " " << n_laser; + + r = Mol[n_mol].get_pos(); + v= Mol[n_mol].get_vel(); + Bfield= fieldB.get_Field(r); + B = Bfield.mag(); + k_laser = reaction_list[i].k_eff_laser; +// file_rate << " " << r ; +// file_rate << " " << v.mag(); ; +// file_rate << " " << B ; +// file_rate << " " << k_laser.mag()/(2*pi*100.) ; // k = 2*pi*100.*Energy_transition_cm; +// double E = fieldE.get_Field(r).mag(); + Internal_state_in = Mol[n_mol] ; // état interne de la molecule +// double Energy_in = Internal_state_in.Energy_cm; +// double Energy_in = Internal_state_in.Energy0_cm + (Internal_state_in.Energy_Shift_B_cm(B) + Internal_state_in.Energy_Shift_E_cm(E)); +// file_rate << " " << Internal_state_in.deg_number ; + + Internal_state_out = reaction_list[i].final_internal_state ; // état interne de la molecule après la réaction +// double Energy_out = Internal_state_out.Energy_cm; +// +// +// double Energy_out = Internal_state_out.Energy0_cm + (Internal_state_out.Energy_Shift_B_cm(B) + Internal_state_out.Energy_Shift_E_cm(E)); +// double Energy_transition_laser_cm = cm/laser[n_laser].get_lambda(); // Energie de la transition laser en cm^-1 + + +// file_rate << " " << Bfield.z(); +// file_rate << " " << Energy_out- Energy_in - Energy_transition_laser_cm; +// file_rate << " " << Energy_in ; + +// file_rate << " " << Internal_state_in.deg_number; +// file_rate << " " << Internal_state_out.deg_number; +// file_rate << " " << Internal_state_in.Energy_cm ; + + + int i_in = Internal_state_in.deg_number; + int i_out = Internal_state_out.deg_number; + Ecm_i[i_in] = Internal_state_in.Energy_cm; + + if (i_out == 2) rate_level_i_vers_level_2[i_in] += current_rate; + if (i_out == 3) rate_level_i_vers_level_3[i_in] += current_rate; + rate_level_i_total[i_in] += current_rate; + + + /***** CALCUL of parameters for the dipoles (in Debye)or diagonalization, + because the Internal States are not the correct one we need to diagonalized in order to find + the proper one + + + for all 21 levels j Energy_j Energy_J-Energy_out TRIPLET_CHARACTER + + *******/ + + /**** + if ( (params.LocateParam("is_Levels_Lines_Diagonalized")->val) ) + { + int level_in = Internal_state_in.deg_number; + int level_out = Internal_state_out.deg_number; + + file_rate << " " << level_in ; // is the number for the level of the molecule + file_rate << " " << level_out ; // is the number for the level of the molecule + + file_rate << endl; + MatrixXd d[3] ; + SelfAdjointEigenSolver es; // eigenstates and eigenvalues + + double v_perp= (v.cross(Bfield)).mag()/B; + Diagonalization_Energy_dipole(Level, B, v_perp, es, d); + + + // for (int i=0; i = sum_|j>_O 0_ |j>_0 so we scan over |j>_0 hat is the order in the Level file + // 0_ is given by es.eigenvectors()(j0,j) . This is the coefficient of the |j> level (ordered in Energy) on the |j>_0 Level (the on in the Level file) + { + if (Level[j0].two_Omega == 2) // If the state is triplet (2S+1=3 so S=1) we look on the decomposition, |0_|^2 , and sum them + { + param += pow((es.eigenvectors()(j0,j)),2); // sum_|triple, j>_O |0_|^2 + } + } + // file_rate << " " << j << " " << es.eigenvalues()(j)<< " " << es.eigenvalues()(j) - es.eigenvalues()(level_out) << " " << abs(round(10.*param))/10. << endl; + // file_rate << " " << es.eigenvalues()(j) << " " << abs(round(100.*param))/100. ; + } + } + ****/ + +// file_rate << " " << (reaction_list[i].final_internal_state).two_M ; +// file_rate << " " << Mol[reaction_list[i].n_mol].two_M << endl; + +// file_rate << endl ; + } + + + + + + MatrixXd d[3] ; + SelfAdjointEigenSolver es; // eigenstates and eigenvalues + Diagonalization_Energy_dipole(Level, B, v.mag(), es, d); + for (int i = 0; i &laser, FitParams ¶ms, int num_laser) +{ + Laser my_laser = laser[num_laser]; + double Energy_transition_laser_cm = cm/my_laser.get_lambda(); // Energie de la transition laser en cm^-1 + + file_out<< setprecision(8); + double intensity0=intensity_Convolution_linewidth(1., 0., 0., my_laser.get_Gamma_Laser(), my_laser.get_type_laser(),num_laser, 0., 0., params); + + for (int E_cm = 0; E_cm < 20000; E_cm++) + { + double I_shape = my_laser.transmission_spectrum(E_cm); // Intensité laser façonnée + double delta =(E_cm - 0.01/my_laser.get_lambda())*Conv_Ecm_delta ;// detuning de la transition en s^-1 + double I_laser = intensity_Convolution_linewidth(1., delta, 0., my_laser.get_Gamma_Laser(), my_laser.get_type_laser(),num_laser,Energy_transition_laser_cm, E_cm, params)/intensity0; // + file_out << E_cm << " " << I_shape << " " << I_laser << endl; + } + + return; +} + +// Debug. Gives state, potential, ... +void Sortie_debug(ofstream & file_rate, const vector &rate, const vector &reaction_list, const vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const int n_reac, const double t, FitParams ¶ms) +{ + // t rate nlas z B delta E_fin E_in 2J_fin 2J_in 2Mfin 2M_in + + file_rate<< setprecision(12); + // file_rate << " time t = " ; + file_rate << t << " "; + + int i= n_reac; + +// file_rate << " rate[" << i << "] = "; + file_rate << rate[i] << " "; + int n_mol= reaction_list[i].n_mol; + int n_laser = reaction_list[i].n_laser; +// file_rate << " nMol = " ; + // file_rate<< n_mol << " "; +// file_rate << " nlas = "; + file_rate << n_laser << " "; + + Vecteur3D r; + r = Mol[n_mol].get_pos(); + // file_rate << " pos = " ; + file_rate << r.z() << " "; + + double B = fieldB.get_Field(r).mag(); + double E = fieldE.get_Field(r).mag(); + Internal_state Internal_state_in = Mol[n_mol] ; // état interne de la molecule + double Energy_in = Internal_state_in.Energy0_cm + (Internal_state_in.Energy_Shift_B_cm(B) + Internal_state_in.Energy_Shift_E_cm(E)); + Internal_state Internal_state_out = reaction_list[i].final_internal_state ; // état interne de la molecule après la réaction + double Energy_out = Internal_state_out.Energy0_cm + (Internal_state_out.Energy_Shift_B_cm(B) + Internal_state_out.Energy_Shift_E_cm(E)); + double Energy_transition_laser_cm = cm/laser[n_laser].get_lambda(); // Energie de la transition laser en cm^-1 + + +// file_rate << " B " ; + file_rate << B << " "; +// file_rate << " detuning_cm " ; + file_rate << abs(Energy_out- Energy_in) - Energy_transition_laser_cm << " "; +// file_rate << " Efin0 " ; +// file_rate << Internal_state_out.Energy0_cm<< " "; + // file_rate << "E_in0 "; + // file_rate << Internal_state_in.Energy0_cm << " "; + // file_rate << " Efin " ; + file_rate << Energy_out << " "; + // file_rate << "E_in "; + file_rate << Energy_in << " " ; + // file_rate << " 2J_fin "; + file_rate << (reaction_list[i].final_internal_state).two_J << " "; + // file_rate << " 2J_in "; + file_rate << Mol[reaction_list[i].n_mol].two_J << " "; + file_rate << Mol[reaction_list[i].n_mol].two_M << " " ; + + file_rate << endl ; + +} + + +// collisional cross section for charge exchange Ps Pbar. + +double Cross_section_Ps(double v, const int n) +{ + double s1= 1.32e-16; + double s2= 1.12e-15; + double v_electron = ALPHA * C/(2. * n); + double kv = v/v_electron; + double sigma = n*n*n*n*(s1/(kv * kv) + s2)/(1.+pow(kv/1.8,20)); // Cf PRA 94, 022714 (2016) fitted + + double B = 4.5*tesla; // MAGNETIC FIELD (PUT HERE BY HAND !!!!!) + + double E_max_field_ionization = (-QE/(4.*pi*EPSILON0 *(2.*A0)*(2.*A0)))/(16.*n*n*n*n) ; // Maximum field for field iniastion. 1/16n^4 can be replaced by 1/9 n^4 in pure electric field + + if ( v*B < E_max_field_ionization) + { + return sigma ; + } + else + { + return 0. ; // because the particles is field ionized + } +} + + + diff --git a/Main Code 64bits/sortie_donnees.h b/Main Code 64bits/sortie_donnees.h new file mode 100644 index 0000000..3e56ed9 --- /dev/null +++ b/Main Code 64bits/sortie_donnees.h @@ -0,0 +1,65 @@ + + +#ifndef Sortie_Donnee_SEEN +#define Sortie_Donnee_SEEN + +#include +using namespace std; + + +#include // for random generator +#include // for gaussian random generator + +#include +#include +#include // to read the data and put them in files + +#include // for setprecision +#include + +#include "Molecule.h" // Classe molecule +#include "Laser.h" // Classe Laser +#include "Field.h" // Classe Laser + +#include "Stat_Molecule.h" // statistiques sur un ensemble de molecules +#include "Transition_rate_calcul.h" // pour le spectra façonné + +#include "params.h" // Pour les paramètres +#include "datacards.h" // Pour les paramètres +#include "diagonalization.h" // Pour les paramètres + + +//Sauve l'état du générateur de nombre aléatoire pour ne jamais reprendre le même +void save_random_generator(gsl_rng * r, const char *nom_file); + +/* Création du fichier de sortie des données totales param_Ryd_N° .txt*/ +void sortie_fichier(ofstream & file2, vector &Mol); + + +void Sortie_test_debug(ofstream & file_out, vector &Mol, const vector &Level, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms, DataCards &data, const int number_photons); + +void Sortie_donnee_etat_int_simple(ofstream & file_out , const vector &Mol, const vector &my_laser, const double t, FitParams ¶ms); + +void Sortie_donnee(ofstream & file_out, vector &Mol, vector &Levels, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms, DataCards &data, const int number_photons); + +void Sortie_donnee_electrons(ofstream & file_out, vector &Mol, const vector &Levels, const Field &fieldB, const Field &fieldE, const vector &laser, const double t, const int nb_mol, FitParams ¶ms, DataCards &data, const int number_photons); + + +// Toutes à la suites en temps +void Sortie_donnee_pop_vJ(ofstream & file_out, const vector &Mol, const int nb_Mol, const double t, const int NX, const int N_two_JX, FitParams ¶ms); + +// Sortie des populations dans l'état vX à la suite les unes des autres en temps +void Sortie_donnee_pop_v(ofstream & file_out, const vector &Mol, const int nb_Mol, const double t, const int NX, FitParams ¶ms, int number_photons); + +void Sortie_rate(ofstream & file_rate, const vector &rate, vector &Level, const vector &reaction_list, const vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const int N_Mol, const double t, FitParams ¶ms); + +// Sortie du spectre laser +void Sortie_laser_spectrum(ofstream & file_out, const vector &laser, FitParams ¶ms, int num_laser=0); + +// Debug. Gives state, potential, ... +void Sortie_debug(ofstream & file_rate, const vector &rate, const vector &reaction_list, const vector &Mol, const Field &fieldB, const Field &fieldE, const vector &laser, const int n_reac, const double t, FitParams ¶ms); + +// collsisional cross section for charge exchange Ps Pbar. Cf PRA 94, 022714 (2016) fitted +double Cross_section_Ps(double v, const int n); + +#endif diff --git a/Modif_code.txt b/Modif_code.txt new file mode 100644 index 0000000..12a14ee --- /dev/null +++ b/Modif_code.txt @@ -0,0 +1,88 @@ +2020/08/07 +Full 64bit compilation using msys2 mingw64 and package manager. All installation of gsl, Eigen and freeflut is simpler. +The code is modify to acoomodate for this. + +2020/08/05 +For 64bits compilation. Modify some stream and char comparaison (that are not supported aymore). + +2020/05/23 +Modification of the definition of the dipole and laser parameters. Clarification of all notation in a new user Guide + +2020/05/11 +Some C++ part of the code are compilor dependant (Ask Pauline Yzombard) + +2020/05/11 +Test Ps diagonalization and put correct new levels, lines and matrix files + + +2019/06/26 +Imporved spontaneous emission in diagonalizaiton (using the proper photon energy k_spon) + + +2019/06/04 + + Body &my_bod = bod[i]; in one_body (if not the position are not really apply to bod!) + + + + + 2019/01/04 + +test diagonalizaiton and polarization seems OK. Small modification and todo added + + +2018/11/11 +ADD linear polarization adn new angle (psi) in the Laser definition. +Thus more general laser deal or emission angle with (almost because still real numbers) arbitrary polarization is possible. +So in the case of Diagonalization fo the hamiltonian the spontaneous emission is correct even for non pure circular emission + + + +2018/09/17 +In compiler -Wl,--allow-multiple-definition is required (for glut.h that is probably called multiple times ?) +The Eigen (better than GSL) library still create bugs ! + + +2018/08/16 +Adding possibility of diagonalization of the Energy of the states (so adding so matrix in Internal_State) +Big modification of the User Guide +SMALL_NUMBER_RATE_EXCITATION ~ 1 is added to control the rates that shall not be considered + +2018/04/28 +Add Hydrogen +Add anti-Helmholtz coils +ERREUR 3/2en 3 on brhosurrho= ERROR IN GRADIENT (when z goes to zeor the gradient (accceleartion) change signe) + +2018/04/24 +Add option Procedure_init_y (4) : perfect ordered gaussian in velocity (random in position) + + +2018/04/03 +Add sigmaSB in Siconstantes +Add cross section + +2017/08/28 +Pseudo_BBR calcul of intensity = energy density/c + +2017/08/21 +Modify the factor 3 in E_tot=3 kB T for the Affichage_Mol + + +2017/07/08 +Modify Draw Molecules for color and size (taille) to allow for Manifold >3 (100 max) + + +2017/06/30 +Add a pseudo BBR laser. +The Power is like the integrated power (Stefan-Boltzmann's law sigma T^4 per surface: 1W/m^2 at 65K) emmited by a real BBR of a circular surface of diameter waist +The central energy has no meaning in this case even if the Wien's displacement law states that the max frequency scales with temperature (Emax_cm-1 ~2 T). +So for simplicity + +2017/06/26 +Possibility to initialise the thermal position in a harmonic trap for charged particles + +2017/06/14 +Verif Pgopher S Spol and A and (minor) correction in UserGuide + +2016/07/23 +Put the correct recoil (probability distrbution for the spontaneous emission depending on the polarization of the transition) diff --git a/User Guide Laser Cooling.pdf b/User Guide Laser Cooling.pdf new file mode 100644 index 0000000..cb5cbc0 Binary files /dev/null and b/User Guide Laser Cooling.pdf differ diff --git a/User Guide/Figures.pptx b/User Guide/Figures.pptx new file mode 100644 index 0000000..9a0ecd4 Binary files /dev/null and b/User Guide/Figures.pptx differ diff --git a/User Guide/User Guide Laser Cooling.pdf b/User Guide/User Guide Laser Cooling.pdf new file mode 100644 index 0000000..6283f81 Binary files /dev/null and b/User Guide/User Guide Laser Cooling.pdf differ diff --git a/User Guide/User Guide Laser Cooling.tex b/User Guide/User Guide Laser Cooling.tex new file mode 100644 index 0000000..ea675eb --- /dev/null +++ b/User Guide/User Guide Laser Cooling.tex @@ -0,0 +1,1366 @@ +% Template article for preprint document class `elsart' +% SP 2001/01/05 +% and 2 sets of keywords - 21.05.03 - file called phys-english.tex +% Modified CG (ESME) for Model 4, single column, 2 titles, abstract/rÈsumÈ, +% English Version for Physique (CRAS series 4, now COMREN) - a Note in English +% Revamped, CG, 18.08.04, adding header, dates, +% and name of presenter + +\documentclass[amsmath,amssymb]{revtex4} + +\usepackage[toc,page]{appendix} + +\usepackage{xcolor} + + +%\def\journal@prl{prl}% +%$@$ifx{$@$journal\journal@prl}{% + + +\def\cpl{Chem. Phys. Lett.} +\def\aj{{AJ}} +\def\araa{{ARA\&A}} +\def\apj{{ApJ}} +\def\apjl{{ApJ}} +\def\apjs{{ApJS}} +\def\ao{{Appl.~Opt.}} +\def\apss{{Ap\&SS}} +\def\aap{{A\&A}} +\def\aapr{{A\&A~Rev.}} +\def\aaps{{A\&AS}} +\def\azh{{AZh}} +\def\baas{{BAAS}} +\def\jrasc{{JRASC}} +\def\memras{{MmRAS}} +\def\mnras{{MNRAS}} +\def\pra{{Phys.~Rev.~A}} +\def\prb{{Phys.~Rev.~B}} +\def\prc{{Phys.~Rev.~C}} +\def\prd{{Phys.~Rev.~D}} +\def\pre{{Phys.~Rev.~E}} +\def\prl{{Phys.~Rev.~Lett.}} +\def\pasp{{PASP}} +\def\pasj{{PASJ}} +\def\qjras{{QJRAS}} +\def\skytel{{S\&T}} +\def\solphys{{Sol.~Phys.}} +\def\sovast{{Soviet~Ast.}} +\def\ssr{{Space~Sci.~Rev.}} +\def\zap{{ZAp}} +\def\nat{{Nature}} +\def\iaucirc{{IAU~Circ.}} +\def\aplett{{Astrophys.~Lett.}} +\def\apspr{{Astrophys.~Space~Phys.~Res.}} +\def\bain{{Bull.~Astron.~Inst.~Netherlands}} +\def\fcp{{Fund.~Cosmic~Phys.}} +\def\gca{{Geochim.~Cosmochim.~Acta}} +\def\grl{{Geophys.~Res.~Lett.}} +\def\jcp{{J.~Chem.~Phys.}} +\def\jgr{{J.~Geophys.~Res.}} +\def\jqsrt{{J.~Quant.~Spec.~Radiat.~Transf.}} +\def\memsai{{Mem.~Soc.~Astron.~Italiana}} +\def\nphysa{{Nucl.~Phys.~A}} +\def\physrep{{Phys.~Rep.}} +\def\physscr{{Phys.~Scr}} +\def\planss{{Planet.~Space~Sci.}} +\def\procspie{{Proc.~SPIE}} +\def\icarus{{Icarus}} +\let\astap=\aap +\let\apjlett=\apjl +\let\apjsupp=\apjs +\let\applopt=\ao + + +\usepackage{isomath} +% Scientific organisations like IUPAP\_, IUPAC\_, NIST\_, BIPM\_, and others recommend typesetting math according to the International Standard ISO 31`Quantities and units` [ISO-31] + +\usepackage{upgreek} % to have roman greek letter + + + + +\usepackage{graphicx}% Include figure files +\usepackage{mathtools}% For \MoveEqLeft +\usepackage{dcolumn}% Align table columns on decimal point +\usepackage{bm}% bold math +\usepackage{rotating} +\usepackage{color} +\usepackage{amssymb} +\usepackage[latin1]{inputenc} +%\nofiles +%\usepackage{epstopdf} +\DeclareGraphicsRule{.tif}{png}{.png}{`convert \#1 `basename \#1 .tif`.png} + + +\begin{document} + +\title{USER GUIDE For the simulation of Laser cooling of particles} +\author{Daniel Comparat} +\affiliation{Laboratoire Aim\'e Cotton, CNRS, Univ Paris-Sud, B\^at. 505, 91405 Orsay, France} + +\date{\today} + + + + +\begin{abstract} +This document gives an introduction to the use of the C++ Laser Cooling code described in PHYSICAL REVIEW A 89, 043410 (2014) + and available on git: https://github.com/dcompara/Laser-interaction-in-fields. +The program solves the rate equations to study laser excitation, forces (scattering + dipolar + magnetic + electric + coulombian interactions). +It has been developed under Code::Blocks and Windows. +The inputs are 2 external files describing the levels (with information about their energy + linear or quadratic Stark, Zeeman effect) and the + transitions lines (dipole transitions, photodetachement or photoionization cross sections) +Then a file named Liste\_Param.h contains parameters to run the simulation such as sample size, temperature, magnetic fields and for the laser beams (waist size and position, polarisation, power, linewidth, wavelength, ...). +When running, the program calculates at time t all absorption and emission rates. Then a Kinetic Monte Carlo algorithm gives the exact time t+dt for an event (absorption or emission) compare this time to a typical external motion time then it evolves in motion and event. +The output is writen in a file containing relevant information such as population in given levels and statistics about velocities (temperature), potential energy ... +Output is also performed through 3D snapshots. +% An update of the modifications done in the code can be find in Modif\_code\_rate\_eq.txt. +\textbf{Any modifications, bugs, improvement, ... should be refereed to +Daniel.Comparat$@$u-psud.fr} +\end{abstract} + + +\maketitle + + + + + +\section{Introduction} +The program solves the rate equations, for spontaneous, absorption and stimulated-emission. It studies laser excitation and motion under external forces (scattering + dipolar + magnetic + electric + gravity) and take into account N-body coulombian interactions and Lorentz forces if charged particles. The momentum recoil is also implemented. +The algorithm and detail of some calculations can be found on the appendix of \cite{comparat2014molecular}, thus I will not recall it here. + But to run the code you do not need to read it! + +% The programm can be download at: https://www.dropbox.com/sh/8iivh04gvf0vk6p/AAA0dtvHDgeZQSjZ7oJJ7zlWa + +In brief it requires: Windows (Linux might be possible but I did not write this guide for it) and Code::Blocks. + +Then the program requires: + + + +\begin{enumerate} + \item input files + + +\begin{itemize} + \item levels: containing their energy + linear or quadratic Stark, Zeeman effects. + \item lines: containing the dipole transitions or some cross sections such as for photodetachement or photodissociation. + + +\end{itemize} + +\item File with parameters (named Liste\_Param.h): contains parameters needed to run the code (sample size, temperature, magnetic fields, laser parameters, ...) + + The file Liste\_Param.h contains a lot of lines with comments, \textbf{so read them carefully!}. As a single example, if you do not change the initialization of the random number generator in this file, the simulation will always be the same when you run a new simulation (which is good for debug!). + +Liste\_Param.h is not an header file and it will not be compiled when compiling the project files. The .h is here simply because it is opened by the text editor. + + + + \item Laser Shaping + + If needed (for optical pumping of molecules for instance) + each laser can be spectrally shaped using files such as Laser\_Spectrum[1].dat for the second laser. + + \item Output: + + A 3D visual output help to see in "real" time the evolution of the sample. But informations at given time intervals are writen in a file (donnee\_Mol.dat). + + + You will probably have to modify the file Sortie\_donnee.cpp depending on what output you want. + + + +\end{enumerate} + + + + +To run the code it is not required to understand it. But briefly, at time t: the program calculates all absorption and emission rates for all particles (so the most important part of the code is the function rates\_molecule). Then Kinetic Monte Carlo algorithm gives exact time t+dt for event (absorption or emission) compare this time to the time for the external motion. Finally it evolves all particles in motion to realize the event. A more detailed explanation is given at the end of this guide in section \ref{section_algorithm}? + + +An update on the modifications done in the code can be find in Modif\_code\_rate\_eq.txt but you have the last version so in principle you do not have to read it. + + +In the following section you will have more informations about each files. + +\section{Code::blocks Installation} + + + + + + +\begin{figure} + \centering + \includegraphics[width=1\linewidth]{linker} + \caption{Example of possible installation (in the case of the simple gsl 1-13). To put either in the Settings/Compiler directory, either in the Project/Build options one.} + \label{fig:linker} +\end{figure} + + +If you are not at all familiar with CodeBlock I suggest that you follow a small tutorial such as http://www.codeblocks.org/user-manual. + + + +You may have to adapt the following names for your own installation. +\textbf{But, you first need to install Code::Blocks (also called Codeblocks) the free C++ IDE, + as well as some scientific and 3D-visual libraries (GLUT, GSL, Eigen, ...). It will always be the same idea for all packages: put the headers (.h) in an \textbackslash{}include, the .lib (or .a) in a \textbackslash{}lib and the .dll files of the packages in a \textbackslash{}bin directory + that the code and the compiler will find. For this we have to configure the project $\rightarrow$ build options as in Fig. \ref{fig:linker}.} + + + + +\subsection{64bits} + + I modify the code to run on 64bits, for the 32bits version see section \ref{32bits}. +The steps are: + + +\begin{enumerate} + \item Install last stable version of codeblocks: a mingw-setup.exe binary file from www.codeblocks.org/ (we need MinGW: a contraction of "Minimalist GNU for Windows"). + It will install the codeblocks in a directory such as C:\textbackslash{}Program Files\textbackslash{}CodeBlocks (see note \footnote{For the 32bits the mingw-32bit-setup.exe it will be installed in C:\textbackslash{}Program Files (x86)\textbackslash{}CodeBlocks where the (x86) is here to say that it is a 32bits file but on a 64bits computer. All other "normal" cases will be on C:\textbackslash{}Program Files (that is 32bits on 32system or 64bits files or 64 computer)}). + + + If you want the +newest codeblocks version you can download the last version from the Nightly built: http://forums.codeblocks.org/index.php/board,20.0.html +: download three .7z files, unzip them (you need 7Zip) in CodeBlocks directory by replacing all the old files with them. + + + + + + \item 64bit installer (MSYS2 MinGW) + + Even if codeblocks is now in 64bits we need MSYS (a contraction of "Minimal SYStem") to create some pakages. So get an installer of MSYS2 MinGW w64-bit and run it. Then using the package manager (pacman) do: + \begin{itemize} + \item pacman -Syu + \item pacman -Syu base-devel (then make the selection that avoids pacman: typically 1-39,41-58 that avoids pacman at number 40 in this example) + \item pacman -Syu mingw-w64-x86\_64-toolchain (then choose all) + \end{itemize} + + + \item C++ 64bits compiler + + Codeblocks provide a gcc mingw64 bit compiler but, +because when building packages by msys2 the .h, .lib and .dll will be directly put on msys2 \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin directories it is simpler to use the msys2 compiler because it will automatically find these files. + +To change compiler go to codeblocks Settings/compiler/ and select the default compiler and copy, give a name, for example MSYS2 MINGW64. + Go to Settings/compiler/GlobalCompilerSettings/ToolchainExecutables" to set the path of MinGW64 installed at the beginning: C:/msys64/mingw64. If needed (probably not) change +file names in the "program files" tab of executable toolchain (you will find the names in the bin folder of mingw64). + +Then in Project / Build options... you have to select the right compiler (the MSYS2 MINGW6 should be at the very bottom of the list) + + +\item Add extra packages: freeglut, gsl= GNU Scientific Library and Eigen Library + + + +In the +MSYS2 MINGW 64bit window launch + +pacman -S mingw-w64-x86\_64-freeglut + +pacman -S mingw-w64-x86\_64-gsl + +pacman -S mingw-w64-x86\_64-eigen3 + +This automatically copy the 64bit files from \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin directories of freeglut, gsl and Eigen in the correspondings \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin of the C:/msys64/mingw64 directory. + +For Eigen they choose to call the path Eigen3/Eigen which is strange because this will change if the version change. So I have chosen to give the location in the project + +\end{enumerate} + + +\subsection{Just run the code} + +\subsubsection{Codeblocks configuration} +The main think you have to do to make the code compiling is to make sure that codeblocks find the files you want (the Eigen, gsl or glut ones), the headers (the .h), the library (the .a or .lib files) and the way for windows to handle (the .dll files). +An example of what should be done is given in Fig. \ref{fig:linker}. + + +In the linker option you need to add the needed libraries related to the function you use in the code so +opengl32, +glu32, +gsl, +freeglut. + +For instance for freeglut this +mean that the compiler has to look for a library file such as libfreeglut.a or freeglut.lib + +and for the corresponding .dll + +If you have some problems, may be you need to add your compiler \textbackslash{}bin path (for instance C:\textbackslash{}msys64\textbackslash{}MinGW64\textbackslash{}bin) + to the Path of the System Environment Variables (look at "How to add to the Path on Windows 10") + + +\subsubsection{speed consideration} +Finally, if wanted, you can increase the speed by looking to project $\rightarrow$ Build option $\rightarrow$ Compilator and choose your processor (mine is Intel Core i7). However I almost never find any speed increase (on the contraty so be careful). + +For a speed up, you can also use Ctrl+Alt+del and Process $\rightarrow$ to change priority of the program from Normal to high in Windows. + + +\subsection{Comment on 32 bits codeblocks version.} +\label{32bits} + +All this should work if you use a 64 bit computer. For a 32 bit computer you should use the 32bit GSL version (for 32 bits see note \footnote{For 32 bits the simplest way is to install Gsl-1.13-1.exe. then you would need to modify from the Search directories in the Project Build Options + the location of the .h files + C:\textbackslash{}Program Files (x86)\textbackslash{}GSL-1.13\textbackslash{}include. You need also to modify the location of the global variable}) (see + https://sourceforge.net/p/mingw-w64/wiki2/GeneralUsageInstructions/ to understant +the complex notations files or directories[you can have a 32 (or 64) bit computer, and use old 32 bit library but at the end produce an executable that work on a 64bit computer] +so names -- such as i686-w64-mingw32, x86\_86-w64-mingw32, gcc-mingw-w64-i686 -- provide this information + i386 or i686 or x32 mean a 32-bit and x64 (or sometimes x86\_64 or) mean a 64-bit. + + + + +\section{Short overview} + +\subsection{Overview of the Program} + +You do not need to know the code in detail, but an overview of its C++ structure is given in the Figures \ref{fig:Class} and \ref{fig:Program_evolution}. + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{classes} + \caption{Schematic of the structure and some basics functions used by the code. The blocks are the different files (.cpp or .h) present with their names in bold and an quick explanation of what they do.} + \label{fig:Class} +\end{figure} + + +Figure \ref{fig:Class} gives the list of the basic structure or classes used such as lasers or fields. Molecules are just seen as Levels, Lines and their positions and velocities. + +Figure \ref{fig:Program_evolution} is the core of the code with the main evolution summarized in the Main\_laser\_cooling.cpp program, that is usually the only code that you may have to modify (with the output one: sortie\_donnee). +As you see the code as still some French in it such as: + +\begin{itemize} + \item donnee = data + \item affichage = plot + \item sortie = output + \item champ = field + \end{itemize} + + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{evolution} + \caption{Schematics of how the code evolve its time. The blocks are the different files (.cpp or .h) present with their names in bold and an quick explanation of what they do.} + \label{fig:Program_evolution} +\end{figure} + + + + + +\subsection{graphics} + + +Once run. You will see two screens appearing as shown in figure +\ref{fig:picture}. + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{picture} + \caption{Snapshot (screen capture) of the code.} + \label{fig:picture} +\end{figure} + + + +If you do not want the graphics you have to change the option in Liste\_Param file. +Some parameters like the screen size are directly part of the code but other ones like size of view of the sample are part of Liste\_Param. + + +For now the graphics do not indicate the lasers locations but show the particles behavior at every time steps, set by the parameter +$@${}dt\_out of Liste\_Param + +The graphics (uses OPEN\_GL library for 3D plotting) represent the particles with the following choices: +\begin{itemize} + \item Red arrow along x, green along y and blue along z (gravity is along -Oz) to see the origin and orientation of the view. Global screen rotations are possible in Liste\_Param, the usual one puts gravity down, but if no rotation is performed we would have x toward the right, y up and z toward the screen. + \item Molecules are represented like diatomic molecules (a line connecting 2 balls) +and depend of their ro-vibronic level and mass. + The length is proportional to the vibrational quantum number $v$, the angle in $x y$ is proportional to the rotational quantum number $J$ and the angle in $x z$ is proportional to its projection (along the local field axis) $M$. + Then the ball size and the color reflects the molecule and its state: Ground state are green, excited state are yellow, dead (photodetachment, ionization, annihilation) are blue (and antiprotons are olive). + +\end{itemize} + + + +Then some statistical data are given like the temperature, positions and velocities of the laser cooled molecules. +As well as the temperature of the second species (if they exist). +Finally the total energy of all molecules is given (it should be conserved in absence of laser cooling). + + +\subsection{Output: Export data in files} + +In addition to the graphics output we have several others possible outputs. + +Mainly Sortie\_donnee\_pop\_vJ gives the population in each $v,j$ levels or simply Sortie\_donnee\_pop\_v gives the population in each $v$ levels. But the standard one is +Sortie\_donnee that gives useful data such as positions, velocities or temperatures. + +The current example Sortie\_donnee (call in main\_Laser\_cooling.cpp in "(t $>$= t\_dia)" section) +gives for each diagnositic time: the parameters that you scan, the time, the position (x,z) and v\_z. + +{\bf You Should probably modify those outputs for your own purpose.} +Use the comment lines to inspire you for your own choice. + + +Finally you can stop the code to run by pressing CTRL+C after if you want to stop before the end or to avoid producing too big files. + +\section{Input files} + + +The code requires source input files +(their locations and names are defined in Liste\_Param). The files are the following: + +\begin{enumerate} +\item Liste\_Param.h (it has to have this exact name) + +Contains all relevant parameters such as number, temperatures, locations of the particles, lasers parameters and some output properties and algorithm choices. +The location of the files are also given in $@${}nom\_file\_Levels, +$@${}nom\_file\_Lines or $@${}nom\_file\_Laser\_Spectrum + + + + \item "Levels". + + Contains informations about the levels of the chosen particle (BaF, Cs$_2$, NH, Cs, CO, Ps, ...). The basic informations are the energy levels and their linear and quadratic Zeeman (and eventually Stark) shifts. + + \item "Lines" . + + Give the dipole transition strength between two levels. + + \item "Laser Spectrum[i]" + + It is optional (if not present no laser attenuation is taken into account and the laser is "normal"). But it can be used to create spectral shaping of a laser. + + + +\end{enumerate} + + +ALL FILES SHOULD NOT contain a return line neither an extra character, like a space, at the end! + + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{laser_axis_polarization} + \caption{Definition of the differents frame: laser axis (for the polarization basis), field axis (that is the quantization because we assume adiabatic following of the states) and lab fixed frame. To go from the lab fix frame to the laser axis one a first rotation is by an angle $\phi$ about the $z$-axis then a second rotation is by an angle $\theta$ about the new $y$-axis + } + \label{fig:laseraxispolarization} +\end{figure} + + + +The structure of the files have been chosen because it is the one given by the Pgopher program: PGOPHER, a Program for Simulating Rotational Structure, C. M. Western, University of Bristol, http://pgopher.chm.bris.ac.uk. See Journal of Quantitative Spectroscopy \& Radiative Transfer 186 (2017) 221, where Pgopher is described. + +A more detail description of all files is now given. + +\subsection{Liste\_Param} + +Liste\_Param.h contains: +\begin{itemize} + \item Particles parameters: numbers, type, temperatures, initial positions and velocities + \item Graphics: size and angle of the field of view, time for each output. + \item Fields. Usually given in 3D up to the second order. We can put Helmholtz coils for the magnetic field. For now we can have a trapping magnetic or electric field but not both. With the exception of a Penning trap where the electric field acts on the charge but is supposed to not produce internal energy shifts. + \item Laser beams: waist sizes and positions, polarisations, powers, linewidths, wavelengths, spectral shapes (Lorentzian, Gaussian, comb lines) and possible coherence (intensity interference to create optical lattice) between them.... The polarization could be purely circular (left=$\sigma^+$ or right=$\sigma^-$) or linear and are defined using the laser propagation axis and a rotation angle cf Fig. \ref{fig:laseraxispolarization}. Linear polarizations are thus possible but (to be checked..) then no interference effects are taken into account. Other 'fictuous' laser types can be invented in order to take into account other rates (such as collisional, field ionization, ...) + \item Algorithm parameters: evolution time and steps. Among them we have +the Kinetic Monte Carlo, the First Reaction Method or the less accurate but faster Random Selection Method or even the Fast Rough Method for the internal state. Verlet or Boris-Buneman for the external motion but with different types: either using the analytical acceleration (and no dipolar force) either using gradient of the potential (the epsilon "size step" has to be manually optimized). A N-body algorithm is also implemented. + +\end{itemize} + + +In principle all parameters are in SI units. If not, the name suggests the value such as Gamma\_L\_MHz or Energy\_cm because all energies are in cm$^{-1}$. + + +All parameters have their name staring with $@$ symbol followed by their value (so no symbol $@$ should be use in this file except for this purpose). + + +A loop on the parameters values can be done if the parameters names are written with a +$@${}SCAN\_ prefix and a "true" value between +BEGIN\_OF\_FITPARAMS +and +END\_OF\_FITPARAMS +at the end of Liste\_Param.h file. + + + + +If needed, a new parameter can be added in the file, and then used, in some files of the program using the sentence + params.LocateParam("Nom\_Parametre")-$>$val +that takes its value. + + + + +\subsection{Levels} + + +The name of the file can be chosen as wanted but then put in the Liste\_Param.h file. + +The columns of the file are the following: + + \bigskip + + \textbf{ Manifold 2M Sym \# population } v 2J 2N 2$\Omega$ \textbf{ E$_{\rm cm}$ $\Delta$ C} + \bigskip + +Columns are separated by tabulation. Points (not coma) are used for decimal separations. + + + \textbf{ manifold, 2M, \#, Sym are the only data used to label a Level}. Thus v, 2J, 2N or 2$\Omega$ are extra data and are here only for a better understanding of the file. They can also be used for an output of the data. + +The detail of the columns are(in bold the data that should absolutely be correct): + +\begin{itemize} +\item \textbf{Manifold}: usually 0 means ground electronical level, 1 is for an excited electronical level, 2 for another one ... Negative values can be used for a "dead" level such as one in a continuum (photo-ionization -1, photodetachement -2, or annihilation -3). + + \item \textbf{2M}: where M is the projection of the total angular momentum. We note 2M and not M to be able to use integer in the code for M=1/2 for instance. + In the code the particle will be assumed to always follow (adiabatically) the local quantification axis given by the local field. + +{\it If you want to simulate states without sub-structure like pure ro-vibrational transition in zero field you coudld impose $M$=0 for all states and use $\pi$ laser polarization.} + +\item \textbf{Sym}: Originally it was the parity of the state but this not the case but it should be +1 or -1 to design bound states and 0 for an continuumm state (that is above the continuum threshold such as for photodetachment or photoionization). + +\item \textbf{\#}: "number" of the state. It lifts the degeneracy between levels having the same 3 parameters: manifold, 2M and \#. Usually it is ordered (0,1,2, ...) by energy but for the vibrational levels you could add 10000v to keep trace of it. + +\item \textbf{population}: This is proportional to the initial population in the levels (that will be taken randomly at the beginning of the run). The sum should not have to be 1. + + +\item v: vibrational level. As said previously this is not used by the code except may be for some output data. + +\item 2J: J = total angular momentum (F if nuclear spin present) + +\item 2N: N = rotational angular momentum, including L (L=electron orbital angular momentum). + +\item 2$\Omega$ : $\Omega$ = Projection of J along the molecular axis. + + +\item \textbf{E$_{\rm cm}$}: energy of the level in cm$^{-1}$. For a continuum state, we put the energy of the threshold, like that we can test if the laser transition reach the continuum or not (but we assume a cross section independent of the energy). + +\item \textbf{$\Delta$ and C} give the energy shift of the level under an electric or magnetic field $F$. + +The formula is $E_{\rm cm}(F)= {E_0}_{\rm cm} + {\rm sign}(C) [-\Delta/2+\sqrt{(\Delta/2)^2+(C F)^2}]$. +Thus if $\Delta = 0$ we have a linear variation $E(F)= E_0 + C F$. +Thus, for the magnetic field case, units are cm$^{-1}$/Tesla for $C$. A magnetic moment of 1 $\mu_{\rm Bohr}$ correspond to a value for $C$ of 0.4668645 cm$^{-1}$/Tesla. + + +\end{itemize} + +If needed, an option exists (is\_File\_FC in Liste\_Param) in order to automatically produce new Levels and Lines files from a file containing only $v_X=0 \rightarrow v_A =0$ transition by reading extra Franck-Condon and vibrational and rotational constant files. + + + +\subsection{Lines} + +The lines file can content more lines than used by the Level file. In this case the program only read the useful ones. + + The columns (separated by tabulation) of the file are the following: + + + + \bigskip + + \textbf{UpperManifold 2M' Sym' \#' LowerManifold 2M'' Sym'' \#''} $\Delta_E$ Intensity E$_{\rm upper}$ E$_{\rm lower}$ \textbf{Strength} + +\bigskip + + \textbf{The first 4 columns design the upper level $|1\rangle$ and the second 4 the lower level $|0\rangle$. +So they have to be the same as in the Level file!} + + The last 5 columns give informations about the transitions between these levels. +But \textbf{only the last column (Strength) is used by the code}. However, usually they are composed on: + +\begin{itemize} + + +\item $\Delta_E$: energy difference between the 2 states $|1\rangle$ and $|0\rangle$. + +\item Intensity: Einstein coefficient = spontaneous emission rate of the transition (this is not the total decay rate of the state $|1\rangle$, because it can decay to several levels). + +\item E$_{\rm upper}$: energy in cm$^{-1}$ of the upper state $|1\rangle$. + +\item E$_{\rm lower}$: energy in cm$^{-1}$ of the lower state $|0\rangle$. + +\item \textbf{Strength}: $S_{\rm pol}=d_{\rm axe}^2/3$, where $d_{\rm axe}$ is the dipole (in Debye) of the transition along the polarization axis that authorize the transition between the sum-Zeeman levels). This notation was used due to historical reasons linked to Pgopher. + +So A=Intensity = $\Gamma = 3 S_{\rm pol} C_{{\rm Debye},s} E_{\rm cm}^3$ +with $C_{{\rm Debye},s} = (8\times 10^6 \pi^2 c^3 {\rm Debye}^2 )/(3. \varepsilon_0 c^3 \hbar) = 3.13618932 \times 10^{-7}$ is the conversion from the dipole (in Debye) to the Einstein's coefficient A (s$^{-1}$) for an energy in cm$^{-1}$. + + + +\end{itemize} + + + +For an continuum transition (so with Sym' = 0), the idea to treat it, is to put a "fake" level: the energy should be just at the ionisation threshold (thus the program can test if the laser wavelength is enough to ionize). But, in this case the $S_{\rm pol}$ column is not $d^2/3$ but $\sigma/$cm$^2$ which is the ionization cross section in cm$^2$. + + + + +\subsection{LASER\_SPECTRUM} + +This file is used only if you want to shape spectrally a laser. If you do not create such a file a default one (containing only one line: 0 1) is created which does not affect the laser intensity. + + +The code reads a file one file per laser (number). +Laser\_spectrum[i] for laser number i+1 +that contains 2 columns: E$_{\rm cm}$ (Energy in cm$^{-1}$) and Attenuation (intensity attenuation coefficient). + + +When a transition should occur at the energy $E_{\rm cm}$. +The program look in this file for the line $i$ such as $E_{\rm cm}[i] \leq E_{\rm cm} < E_{\rm cm}[i+1]$ and then it takes the corresponding value +Attenuation$[i]$. This will be the multiplicative factor for the laser intensity for this transition energy. +So in summary the energy in the file is the energy just below yours and the intensity would thus just be multiplied by the amplitude factor. + + + + +\section{Troubleshooting} + + +Figures \ref{fig:Program_evolution} is the core of the code with the main evolution summarized in the Main\_laser\_cooling.cpp program, that is usually the only part of the code that you have to modify (with the output one: sortie\_donnee). + + +If the program does not run for the first time it is usually a problem of links and library in Code::Blocks. + +But if it usually runs but then bug after some modifications it is 90\% due to an error in the input files: levels or lines! + + +For debugging use the debugger in the Debug file. But you can also use Sortie\_rate which gives all rates, or Sortie\_donnee\_etat\_int\_simple that gives the list of levels, and that are commented on Main\_Laser\_Cooling. You have also Sortie\_laser\_spectrum to check the laser spectrum you make or Sortie\_transition to check the transition per + +\textcolor{red}{The best way to debug is to use a simple two level system and to look for the rates to understand if they are as expected. 95\% of the time the problems comes from the Levels or Lines files} + + +\subsection{CodeBlocks problems} + +If you have not strictly followed the rules you might have the following problems!! + + +If Code::Blocks is installed in the C: directories but you have put your project in D: +this does not work. +Thus, you have to put in +"Settings" $\rightarrow$ "Compiler and Debugger" $\rightarrow$ "Toolchain executeables" $\rightarrow$ "Program files" +some link. +For instance modify "mingw32-g++.exe" in "C:\textbackslash{}MinGW\textbackslash{}bin\textbackslash{}mingw32-gcc.exe" +in the "linker for dynamics libs:"... + +More generally the problems are almost always coming from a bad links. + You can specify them for your global environment or just for your project. + +For global environment : +\begin{itemize} + \item Menu Settings/Compiler and debugger +\item In the Global compiler settings, select the Search directories +\item Add the required paths for compiler and linker. +\end{itemize} + + +For your project : +\begin{itemize} + \item Right click on the project then select Build options +\item Select the Search directories +\item Add the required paths for compiler and linker. +\item Add your specific libraries in the linker tab. +\item Pay attention to project settings and target settings. +\end{itemize} + + + +ALWAYS verify that your modifications of directories affect all the project and not only Debug or Release + +Do not forget to recompile the full code after any modification!! + + +\subsection{Common tests} + + +\begin{itemize} + \item It is always good to go back to a situation where the results are known such as: 1 particle at the center, zero temperature, no lasers, no trapping, single laser at resonance, ... +\item Checking energy conservation is always of good practice! +\item Check for the proper time step (dt\_dyn\_epsilon\_param that is the one for the external motion; eventually choix\_epsilon that is the spatial step to calculate the gradient of the potential in some algorithms). + \item Do not forget to recompile the overall project. + \item The most common mistake comes from errors in the Levels or Lines files + \item A too big number of molecules or Levels or Lines may lead to memory overflow. So check also the use of the memory, for instance by using the Windows resource monitor. + \item You can use the code::blocks debugger or simply write some test lines in the code. A very common test is to uncomment the two lines (just before "if (t >= t\_dia)" in main\_laser\_cooling.cpp) with Sortie\_rate and Sortie\_donnee; this will produce at each time step output of all calculated rates and output data. + +\end{itemize} + + + + + +\section{Algorithm used in the code to calculate the evolution and the rates} +\label{section_algorithm} + +\subsection{Diagonalization} +\label{diagonalization} + +We add the possibility cf parameter is\_Levels\_Lines\_Diagonalized +to diagonalize the hamiltonian in order to calculate the energy and the transitions. This was done for positronium (but this is more general) where we had to use the fact that the levels are mixed in $E$ and $B$ fields and that the velocity create a dynamical Stark effect. + +However we do the diagonalization only for the reactions not for the external motion of the particles! So the particles stays in the same levels during their motion (no level crossing during motion) as shown in Figure \ref{fig:diagonalization}. The light shift is not included also. + +\begin{figure} + \centering + \includegraphics[width=0.6\linewidth]{diagonalization.png} + \caption{Schematics of the Energy level due to recoil momentum. The diagonalization thus works only if the energy levels before and after spontaneous emission have the same order in energy. No other dynamical evolution is taken into account, we assume constant velocity during motion (in the excited states).} + \label{fig:diagonalization} +\end{figure} + + +The matrices (Zeeman, Stark, dipoles\footnote{From a dipole Matrix between all levels the dipole matrices could be calculated using Create\_dipole\_Lines\_from\_Matrices. And thus they are correct for the emission-absorption polarization.}) should be put by hand in diagonalization.cpp and should follow the same ordering than the Levels and Lines (and should be ascending in energies). + + + +The most important is that in the degeneracy number \# of the state should be the number of the state staring from 0 (so Level[\#] is the Level itself) [recall that in C++ the index of the first element of the table is 0]. +% The Lines file should contains all transitions (even the nul ones) between i\_low and j\_up. +The levels are thus always refers as Level[i] that is the (i+1)$^{th}$ in energy level ordering (which is not necessary the order you put originally in your level file, EXCEPT for ground state, cf FIG.{fig:diagonalization}). But, for the "sortie" or analysis Level[i] keeps its characteristics (such as M values) given in the input Level file: only Energy\_cm is updated. + + +% Because the magnetic $m$ quantum number, that defines the quantification of the light, is not anymore a good quantum number, the angular emission pattern for the spontaneous emission is done isotropically. + + \subsection{Overview external versus internal dynamics} + +We do not discuss here the Kinetic Monte Carlo (KMC) neither the N-Body solver used to solve rate equations, this is discussed in PRA 89, 043410 (2014). +But we explain the way how code calculates the evolutions for $N$ particles, in order for interested people to modify it. +The main part is the main.cpp file in the + \textit{ while(velocity\_scaling == false)} +loop (before is a tentative to reach thermal equilibrium is a trap using the Berendsen thermostat Algorithm) and especially the +\textit{ calcul\_rates\_molecules} +function. + +The code calculate a time for an internal state evolution dt\_KMC (typically one over the maximal rate) and compare it to the time for the external state evolution dt\_dyn (that is now fixed and given is a parameter in the liste\_Param, even if a commented line to calculate it can by tried). +Then the internal evolution \textit{do\_reaction} and the external \textit{evolve\_step} evolution +depends on the Choix\_algorithme\_Monte\_Carlo and Choix\_algorithme\_N\_corps parameters chosen in in Liste\_Param. + For instance the Choix\_algorithme\_N\_corps is commented in the Liste\_Param. This can be of importance if Coulomb interactions are present or not, or if the dipolar force is included (not well calculated for spectrally shaped laser for instance) or if we calculate it directly using gradient of the fields analytical formula (if implemented) + or through the potential derivative (this is the most general way fo doing it). + + \subsection{Calcul (internal) rates molecules} + +The \textit{ calcul\_rates\_molecules} +function is the most important one. + +In order to not spent too much time on updating all the rates of all molecules we only recalculate the rate of the molecule (number\_mol) that has evolved internally. All others rates will be updated only after (t\_mise\_a\_jour) the dynamical (external state evolution dt\_dyn) time, so when they have moved enough to be in another environment (laser or fields intensity for instance) where the excitation-deexcitation rates have evolved. + +It is possible to force some rates (like by using Pompage\_optique\_force paramter) but genearly we let the system calculate first the spontaneous emission rate and then the key function is the \textit{ \textbf{rates\_molecule}} function. +It is quite complex but commented, here I simply mention that the local parameters such as local intensity, polarization, dipole moment $d$ etc... are calculate and the rate is calculated in \textit{ \textbf{rates\_single\_molecule\_laser\_level}} that is usually the only function that has to be modified if you want to add a new laser type (such as Black Body one). +The stimulated and absorption rate for an $i\leftrightarrow j$ transition for a laser of polarization vector $\bm \epsilon$ is given by $$\gamma= \frac{\pi ({\bm d}.{\bm \epsilon})^2 I_\upomega \otimes L(\omega+\bm k.\bm v-\omega_{ij}) }{\hbar^2 \epsilon_ 0 c}$$ (cf Formula (B.7) of the PRA 2014 article with the correct $\hbar^2$ factor!). So with a local intensity resulting of the convolution of the laser spectrum $I_\upomega$ with the +transition Lorentzian $L(\delta) = \frac{\Gamma_{ij}}{2\pi}\frac{1}{\left( \frac{\Gamma_{ij}}{2}\right)^2 + \delta^2}$. + +For instance for a laser with a Lorentzian spectrum of FWHM $\Gamma_L$ we have, for the Doppler induced detuning $\delta = \omega+\bm k.\bm v-\omega_{ij}$, the rate: +$\gamma= +I \frac{\pi ({\bm d}.{\bm \epsilon})^2 }{\hbar^2 \epsilon_ 0 c} + \frac{\Gamma_{ij}+\Gamma_L}{2\pi}\frac{1}{\left( \frac{\Gamma_{ij}+\Gamma_L}{2}\right)^2 + \delta^2}$ where $I= \varepsilon_0 E^2 c /2$ is the total laser irradiance (intensity). + + + + \subsection{Calcul (external) motion} + +The \textit{ evolve\_step} is the function that evolves the external degree of freedom depending on the chosen algorithm (Verlet, Boris, ..) and most important on the way we calculated the force. We can use directly the acceleration or the derivative of the potential (depending on the choix\_epsilon parameter typically 10nm). +The fastest is clearly the use of the acceleration calculate in the + the key function is the \textit{ \textbf{new\_acc}} function. But this require that the gradient of the fields are analytically calculated. This is not the case for the dipolar potential neither if there is $N$ body interaction where in this case algorithm use the gradient of the potential to calculate the force through the \textit{ \textbf{new\_pot}} function. The dipolar potential requires to calculate all dipolar transitions (so it calls the rates\_molecule function) and this might be very slow! + + + \subsection{Comments} + +The code has evolved and because it is time consuming ot keep all the time the internal Energy of the molecule correct (especially if dipolar potential is used) we do not use anymore the +set\_pot\_all\_mol function and and we therefore do not +the Internal\_state.Energy\_cm is not correct. It should not be used but (see rates\_molecule) recalculated when needed. + +In order to avoid gigantic storage we have single Levels and Lines files and ALL particles point to this and only the Zeeman , Stark and dipolar shift are added to this. For more complex situation where the internal state quantum numbers are modified for instance we need to use the Levels\_Lines\_Diagonalized + + \subsection{Levels Lines Diagonalized } +This is controled using the is\_Levels\_Lines\_Diagonalized parameter + + \section{Performance test} + + N=100 Hydrogen atoms during 50 microsecond and plot every microsecond. 64.571s with graphics versus 57.502 without and 55.826 without any output + \footnote{ Depending on what the computer is doing meanwhile those times can fluctuate within few percent}. + + + \subsection{Nb of molecules} + + \begin{tabular}{|c|c|} + \hline +Time & Nb atoms \\ +\hline +\hline +0.632 & 1 \\ +\hline + 6.984 & 10 \\ + \hline + 26.362 & 50 \\ + 57.502 & 100 \\ + \hline + \end{tabular} + + So the code is very linear in $N$ which is good news ! This is because the particle are not charged if not probably (to be tested) the variation will be in $N^2$. + + \subsection{Kinetic Monte Carlo algorithm} + +It is be interested to compare them (cf + https://en.wikipedia.org/wiki/Kinetic\_Monte\_Carlo) + because the default one + Kinetic\_Monte\_Carlo + is not the fastest in principle but First\_Reaction\_Method + is also perfect as well as Random\_Selection\_Method if the rate are time independent. + + + + + \begin{tabular}{|c|c|} + \hline + Time & Algorithm \\ + \hline + \hline + 58.604 & Kinetic Monte Carlo (0) \\ + \hline + 132.343 & Random Selection Method (1) \\ + \hline + 73.606 & First Reaction Method (2) \\ + \hline + 6.118 & Fast Rough Method (3) \\ + \hline + 0.537 & No laser included \\ + \hline + \end{tabular} + + So Fast Rough Method (to be tested in more detail) may be a good way to start. + +Random Selection Method has probably a problem in the code to be this slow! + + + + \subsection{Motion algorithm} + + for dt\_dyn\_epsilon\_param = $10^{-7}$ the time (for 100 atoms) is 57.502s whereas for $10^{-8}$ the time is 72.933s. Always choix epsilon is 1e-8. + + For 1e-7 we made test of the algorithm. Obviously the accuracy of higher order are better so dt\_dyn\_epsilon\_param can be reduced if using such algorithm but this gives an idea. + + \begin{tabular}{|c|c|} + \hline + Time & Algorithm \\ + \hline + \hline + \\ + 44.639 & Aucun N corps (-1) \\ + \hline + 49.647 & Verlet acc (sans force dipolaire) (1) \\ + \hline + 252.635 &Verlet pot (avec potentiel dipolaire) (2) \\ + \hline + 86.587 & Yoshida6 acc (3) \\ + \hline + 113.549 & Yoshida6 pot (4) \\ + \hline + 474.885 & Verlet pot gradient high order (6) + \\ + \hline + 49.341 & Boris Buneman (with Magnetic field for charged particles) \\ + \hline + \end{tabular} + + + + + \section{Futur} + Despite the fact that the code could largely be improved to use more C++ spirit (like maps between reaction and rates, ...), a long list of possible improvements exists among them are: + + \begin{itemize} + + \item Use of adaptive time steps (like t\_evol\_ext) for the algorithms (under consideration). + + \item Possibilities to use more general laser beam (Laguerre Gauss, others polarizations). Put the phase given by the polarizations to take into account linear polarisation in the interference lattice case. + + \item Optimize the link between the renew of the rates, the KMC steps and the external evolution steps. For instance if the acceleration is known we do not need to recalculate each time in the evolution algorithms ... + + \item Parallelization of the code. Using OpenMP for multiprocessor seems quite easy: If needed, download the last MinGW 64bits version. + Copy-paste and erase the old one in Codeblock directory. Then in Global Compiler setting (or simply in your project) use in Other option -fopenmp. + Linker settings: Adds the MinGW/bin libgomp-1.dll. Then test using simple program + with \# include + + \# pragma omp parallel + + + \item Combine electric and magnetic field of arbitrary orientations. This is partially done using the diagonalization cf section \ref{diagonalization} + + \item Treat chemical reactions during collisions. + + \item Treat coherent dark states by choosing the proper basis. + + \item Use an ionization or photodetachment cross-section which is dependent on the energy. + + \item For strongly focused lasers, we can put the local wave-vector $\bf k$, not the global one as it is now. + + \item Draw lasers using the hyperbolic function (nor the elliptic one). + + \item Improve the statistical initial distribution. Until now we calculate the trapping field using a linear approximation for the potential energy. + + \item Improve the calculation of the dipolar shift. Until now the dipolar potential is not included in the shift for the transition. This avoids accumulation, but in some cases, it may be good to have it. + + \item Improve performance using GNU Gprof (Code Profiler Pluggin in Code::Blocks) + + + \end{itemize} + + + + \newpage + + \appendix + \section{Use of Pgopher} + + As mentioned before you can use Pgopher (pgopher.chm.bris.ac.uk/) to create your input files. It is in fact recommended because they have been written from it. + + Be sure to have a good simulation. For instance for a single pair of equivalent nuclei (such as in I$_2$) the statistical weights should be SymWt=1, AsymWt = 0, rather than both 1. + Be sure to have enough J but not too much to avoid too big files... + + So read carefully Pgopher manual. + + Then in the Pgopher data use the following options. Hopefully with obvious notations: + + \begin{itemize} + \item + MIXTURE: + Precision 12 + + QuantumNumberFormat 2J. But be careful that all values such as tensor rank, max J are thus doubled, so it is sometimes difficult to follow them. So it is better to do this only at the end, it is just use to produce the "Levels" and "Lines" files. + + BField 1e-10. In order to separate M levels and have all transitions! + + \item SIMULATION: + IntensityUnits: EinsteinA (to have the rate for spontaneous emission) + + + \item SPECIES: + ShowJ, ShowOmega, ShowN, .. all TRUE + + + + \item TO PRODUCE THE "LINES" FILE: Use the following option + File Export Line List .txt (tab separation). Intensity Threshold 1e-8. No "Fit File Format" + + + \item TO HAVE THE ENERGY LEVELS IN FIELDS: + + View, Levels List (To have the energy at each points). Verify to have All symmetry, Omega M values ... + Then use "Track State" and click on "Summary". This gives levels + fit linear + quadratic of the field dependence. So be careful to plot with the proper B field T values (0-1T or 0-1mT for instance) + Save the file in LEVEL. + + + + \item THEN GO TO ORIGIN (http://www.originlab.com/) or to any other data acquisition software (in the Directory Data: Pgopher\_Level\_List.opj) and follow the following procedure. + + Your case can be slightly different if you have more molecules or several vibrational levels or .. so adapt it! + + + \begin{itemize} + + + \item To produce the "LEVELS" file: + + Remove the \% from the LEVEL file + + Use Import Wizard in Origin with 11 headers, 1 subheader (should be recognized). + The name of the columns should be (if not modify by coping this line, or use the example in): + + Molecule Manifold 2M Sym \# g Population Label State 2J 2N 2Omega Fn parity*M Energy Linear Dipole Err Quadratic Err 2\_Level Delta C Dipole2 Err + + + Sometimes Pgopher does not create the first column Molecule neither the last columns of E\_2\_Level ... + + + Then we have to calculate the C and $\Delta$ (that is Delta) coefficients when they are not given, that is if Level Delta C Dipole2 Err columns are missing. + If the effect is not linear but quadratic or more complex then create the 2\_level fit by: + Add one column for numbers, + Sort by 2\_Level. + For those who do not have a 2\_Level then create one (for instance take the Linear and the same energy because C=Linéaire, Delta=0). The intermediate case between linear and quadratic is more complex and an appropriate formula should be derived. + Sort again (a priori the file is sort in M, Sym and \#). It is also possible to sort in Energy + + Duplicate the workbook and keep only the following columns (v is State): + + Manifold 2M Sym \# population v 2J 2N 2Omega Energy Delta C + + + Remark: One possibility to remove "v=" that appears when exporting from Pgopher in "State" and to keep only the vibrational level value is: after the exportation remove "v=" (and change "," in "." if needed) and import again. + + Then use only values not the text, so: + In Manifold use 0 for the X state (lower) et 1, 2, ... for higher Manifold and + +/-1 for Sym. + + If wanted you can sort the workbook in Energy and modify the population column to put the desired one. + Export the Workbook without headers (no Label) and in a file with .dat extension + + Check that the decimal are with "." not "," + Remove the space at the end of the file. + + + + + + \item TO PRODUCE THE "LINES" file: + + Remove the first and last 2 lines of the file LINES.txt + Import it in Origin (using options: delimator, Tab/space). + Change the name of the lines: (copy paste the one below) + + Molecule Upper Manifold 2M' Sym' \#' Lower Manifold 2M" Sym" \#" Position Intensity Eupper Elower Strength A Width Branch LabelUpperManifold state 2J' 2N' 2Omega' Fn' 2M' Sym Upper Manifold state 2J'' 2N'' Omega'' Fn'' 2M'' + + + Duplicate the workbook and keep only the columns: + + UpperManifold 2M' Sym' \#' LowerManifold 2M" Sym" \#" Position Intensity Eupper Elower Strength + + then do the same as for Levels: X=0, Sym =+/-1 ... + + Finally divide by 3 the Strength column and export in .dat file + + \end{itemize} + + \end{itemize} + + + \section{Detail of laser interaction} + +The code is based on \cite{comparat2014molecular}; on \cite{chaneliere2018phase} (supplementary material) for quantization, recoil and Doppler effects; and on +\cite{manual_Steck,varshalovich1988quantum} for vector and angular momenta. +We recall here some important points. The notations differ sometimes from \cite{comparat2014molecular} but are more general and should be preferred, because we use less assumptions here (especially about the reality of some vectors). + + + \subsection{Spherical and helicity vectors } + + We use the notation of \cite{varshalovich1988quantum} such as the (covariant) spherical vectors + $ {\bf e}_0 = {\bf e}_z, {\bf e}_{\pm 1} = \mp \frac{{\bf e}_x \pm + i {\bf e}_y} { \sqrt{2}}$. + Using ${\bf{e}}^q = ({\bf{e}}_q)^* = (-1)^q {\bf{e}}_{-q}$ (that leads to the normalization ${\bf{e}}^p {\bf{e}}_q = \delta_{pq} $) we find for any (complex) vector + $$\bm A = \sum_q A^{q} {\bf{e}}_q = \sum_q (-1)^q A_{-q} {\bf{e}}_q $$ + where + $A_q = \bm A. + {\bf{e}}_q$ so for instance $A_0 = A_z, A_{\pm 1} = \mp (A_x \pm + i A_y)$. + % If $\bm A$ is a \textit{real} vector we have $\bm A = (\bm A)^*$ and $ A^q = A_q^*$ so $\bm A = \sum_q A_q^* {\bf{e}}_q $. + We will often have the case where the $A_q$ or $A^q$ are reals (example of the dipoles or of pure laser polarization) but in general we should keep in mind that the vectors are complex. + + + + \subsection{Lasers using complex notations} + + + + + The electromagnetic field, due to the lasers $\rm L$, can be written + $${\bm E}(\bm r,t) = {\bm E'}(\hat{\bm r},t)+ {\bm E'}^\dag(\hat{\bm r},t) = \frac{1}{2}\sum_{\rm L} \left[ {\bm E}_{\rm L} e^{i( {\bm k}_{\rm L}. {\bm r} - \Phi_{\rm L} + (t))} + {\bm E}_{\rm L}^\ast e^{-i( {\bm k}_{\rm L}. {\bm r} - \Phi_{\rm L} + (t))} \right] $$ + + the irradiance, called improperly intensity, is + $ + I_{\rm L}= \varepsilon_0 |E_{\rm L}|^2 c/2 $. + + + + The Doppler effect, and the laser linewidth, are taken into account by writing $\Phi_{\rm L} (t) = (\omega_{\rm L} - {\bm k}_{\rm L}. {\bm v}) t + \Phi^{\rm L} (t)$. Where $\Phi^{\rm L} (t) $ is a fluctuating phase. + + + As shown in Fig. \ref{fig:laseraxispolarization}, + we use the (covariant polar basis) frame linked with the laser propagation: + $({\bf{e}}'_{\rm x} = {\bf{e}}_{\theta} , {\bf{e}}'_{\rm y} = {\bf{e}}_{\phi}, {\bf{e}}'_{\rm z} = {\bf{e}}'_{\rm r} = \bm{k}/\| \bm{k} \|)$ . + The laser polarization is conveniently described in the (covariant) helicity basis + $ {\bf e}'_0 = {\bf e}'_z, {\bf e}'_{\pm 1} = \mp \frac{{\bf e}'_x \pm + i {\bf e}'_y} { \sqrt{2}}$. + For each laser $\rm L$ + the polarization vector, defined by + $ {\bm E}_{\rm L}(\bm r,t) = E_{\rm L}(\bm r,t) {\bm \epsilon}_{\rm L} $, is $ {\bm \epsilon}_{\rm L} = + \sum_{p= -1,0,+1} \epsilon'^p + {\bf e'}_{p} $. + + + In the code we deal (for simplicity and for calculus speed) only with reals. So for instance + \textbf{the polarisation is coded using only 3 real parameters Pol\_circulaire\_right\_sm ($a_{-}$), Pol\_circulaire\_left\_sp ($a_{+}$) and polar\_angle\_degree ($\Psi$) (in degree in Liste\_Param). These 3 parameters + define + \begin{equation} + {\bm \epsilon}_{\rm L} = {\rm Pol\_circulaire\_right\_sm} \ e^{i \Psi} {\bf e'}_{-1} + {\rm Pol\_circulaire\_left\_sp} \ e^{-i \Psi} + {\bf e'}_{+1} = a_{-} \ e^{i \Psi} {\bf e'}_{-1} + a_{+} \ e^{-i \Psi} + {\bf e'}_{+1} + \end{equation}} + % ${\bf{e}}'_{\rm L,pol} = \{ Pol\_circulaire\_right\_sm = \epsilon'^{-1} e^{-i \Psi}, \epsilon'^0 , Pol\_circulaire\_left\_sp = \epsilon'^{+1} e^{i \Psi} \}$ + + This does not authorize arbitrary polarizations but only pure circular (right with $\epsilon'^{-1} =1$, or left with $\epsilon'^{+1}=1$) or + a pure linear polarization. For example, (cf. Fig. + \ref{fig:laseraxispolarization}) linear polarization turned by an angle $\Psi$ from $ {\bf e'}_{x} $ +is ${\bm \epsilon}_{\rm L} = {\bf e}'_x \cos\Psi + {\bf e}'_y \sin \Psi = + \frac{1}{\sqrt{2}} e^{i \Psi} {\bf e'}_{-1} - \frac{1}{\sqrt{2}} e^{-i \Psi} + {\bf e'}_{+1} $, that is $a_{-} = \frac{1}{\sqrt{2}}, a_{+}= - \frac{1}{\sqrt{2}}$. + % and is thus ${\bf{e}}'_{\rm L,pol} = \{ \frac{1}{\sqrt{2}} e^{i \Psi}, 0 , - \frac{1}{\sqrt{2}} e^{-i \Psi} \}$ which is not real. + + + + \subsection{Transition dipole moment} + + + + The transition dipole moment + ($\bm d = e \bm r$ in the simple case of H, Ps or alkali atoms, and we will use often this simplification for the notation) + between 2 levels is defined (for now in the lab fixed frame but this will be precised in section \ref{pol_vector}) as + $ \bm d_{ij} = \langle i | \bm d | j \rangle = \sum_q (-1)^q d_{ij;q} {\bf{e}}_q = \sum_q d_{ij;q} {\bf{e}}^q $ so $ d_{ij;q} = \bm d_{ij}.{\bf{e}}_q$. The notation $d_{ij}^{(q)} = d_{ij;q}$ is often used but has to be avoided because of possible confusion with the (contravariant) notation $d_{ij}^{q}$. + The correct component that forms an irreductible tensor (rank 1) $\hat d_{1q} = \hat d_{q}$ are $ d_{ij;-1},d_{ij;0},d_{ij;+1} $. + In the code this vector is called + the "polarization" dipole vector $\bm d_{ij} $ and is recorded as $ \{ d_{ij;-1},d_{ij;0},d_{ij;+1} \} $ (obviously in C++ the array number will be respectively dipole[0], dipole[1], dipole[2]). + With the proper (Condon-Shortley's type) convention \cite{varshalovich1988quantum}, these dipoles are reals. + + % We also the polarization dipole vector by ${\bf{e}}_{\rm pol,ij} = \bm d_{ij}/|d_{ij}| = \{ d_{\rm pol,ij}^{-1}, d_{\rm pol,ij}^0 , d_{\rm pol,ij}^{+1} \} $ + + + + + + \subsection{Absorption, stimulated or spontaneous emission} + + For a transition between two states $|j\rangle$ to $|i\rangle$, it is important to known if we deal with absorption (rising level energy) or stimulated or spontaneous emission (lowering level energy) to know which term in the rotating wave approximation shall be used. + + \textbf{ In the following, we assume $E_j> E_i$}. + + \subsubsection{Ordered energy levels and rotating wave approximation} + + +The rotating wave approximation leads (for level $j$ above level $i$: $E_j>E_i$) leads to: + + \begin{equation*} + \hat H = \frac{\bm \hat {\bm p}^j}{2 m} + + V_i(\hat {\bm r},t) |i\rangle\langle i| + V_j(\hat {\bm r},t) |j\rangle \langle j| + - \langle j | q \hat {\bm r}| i \rangle .\bm E' (\hat {\bm r} ,t) |j\rangle \langle i| - \langle i | q \hat {\bm r}| j \rangle . \bm E'^\dag (\hat {\bm r} ,t) |i\rangle \langle j| \label{hamiltonianRWA} + \end{equation*} + + where we have added some potential traps $V_i$ and $V_j$ to be more general. + % where the coupling term is $\displaystyle \hat V = - \bm d .\bm E' (\hat r ,t) = - \frac{\bm d}{j}\sum_{\rm L} {\bm E}_{\rm L}(t) e^{i( {\bm k}_{\rm L}. {\hat{\bm r}} - \omega_{\rm L} t - \Phi_{\rm L}(t) )} = \sum_{\rm L} \hat V_{\rm L} $. + + The recoil effect will be present only after the interaction by a $\hbar \bm k$ term added to the momentum. This is clarified, cf Eq. (9) and (20) of \cite{chaneliere2018phase}, by using the (single plane wave, in a volume $L^3$) + quantized field: + $\displaystyle \hat{\bm{E}} (\bm{r},t) = \sum_{\bm{k},\sigma} i \sqrt{\frac{ \hbar \omega_k}{2 \epsilon_0 L^3} } \left( \hat a_{\bm{k} \sigma} e^{- i \omega_k t} \bm{\epsilon}_{\bm{k}\sigma} {\rm e}^{i \bm{k}.\bm{r} } - \hat a_{\bm{k} \sigma}^\dag e^{ i \omega_k t} \bm{\epsilon}_{\bm{k}\sigma}^\ast {\rm e}^{-i \bm{k}.\bm{r} } \right)$, where $ {\bm \epsilon}_{\bm k \pm 1} = {\bf e}'_{\pm 1}$. We thus have: + \begin{equation*} + \hat H = \frac{\hat{\bm p}^2}{2 m} + + V_i(\hat{\bm r},t) |i\rangle\langle i| + V_j(\hat{\bm r},t) |j\rangle \langle j| \label{eq_base_at} + - \bm d_{ji}. \hat{\bm E'} (\hat{\bm r} ,t) |j\rangle \langle i| + \bm d_{ij} .{\hat{\bm E'}}^\dag (\hat{\bm r} ,t) |i\rangle \langle j| + + \sum_{\bm{k} \sigma} \hbar \omega_k \left( \hat a^\dag_{\bm{k} \sigma} \hat a_{\bm{k} \sigma} + 1/2 \right) + \end{equation*} + where $\bm d_{ji} = \langle j | q \hat {\bm r}| i \rangle = \bm d_{ij}^* $ is the transition dipole element. The quantization clarifies the recoil effect because of + $ + e^{ \pm i \bm k.\hat{\bm r}} | \bm p\rangle = |\bm p \pm \hbar \bm k\rangle$. + + + + Descriptions of the rate equations and forces can be find in the appendix of Ref. \cite{comparat2014molecular,chaneliere2018phase} and are not recalled here. + + + + + + + + \subsubsection{Absorption, Stimulated or spontaneous emission} + + + + Absorption is thus a transition $i \rightarrow j$ ($E_j> E_i$). For absorption + the only relevant term is due to $-\bm d.\bm E'$ through the Rabi frequency\footnote{ For more generality we do not (yet) assume real dipoles and so the notation is different (better here even if careful has to be taken in the $i,j$ order because $\Omega_{ji} =\Omega_{i \rightarrow j} $ ) than in \cite{comparat2014molecular}.} +\begin{equation} +\hbar \Omega_{ji} = E_{\rm L} \langle j, \bm p + \hbar \bm k | \hat{\bm d} . \bm \epsilon_L + e^{ i \bm k.\hat{\bm r}} | i, \bm p\rangle = E_{\rm L} \bm d_{ji} . \bm \epsilon_L = E_{\rm L} + \sum_q d_{ji;q} {\bf{e}}^q . \sum_{p} \epsilon'^p {\bf e'}_{p} + \label{Rabi_frequancy} + \end{equation} + + + + + + The stimulated emission $j \rightarrow i$ with the same laser is govern by the $-\bm d.{\bm E'}^\dag$ term and thus arises with the Rabi frequency +$\hbar \Omega_{ij} = E_{\rm L} \langle i, \bm p - \hbar \bm k | \hat{\bm d} . {\bm \epsilon_L}^\dag + e^{ - i \bm k.\hat{\bm r}} | j, \bm p\rangle = E_{\rm L} \bm d_{ij} . {\bm \epsilon_L }^\dag =\hbar \Omega_{ji}^*$ + + We recover the well known fact that the dipole transition rates are the same (conjugated Rabi frequencies) for spontaneous and for stimulated emission. + + + The simplest (ideal) case is when + \begin{itemize} + \item The quantization axis and laser axis (for the polarization) are equal ${\bf{e}}_q={\bf{e'}}_q$. In this case, the absorption is driven by $\hbar \Omega_{ji} = E_{\rm L} \sum_q d_{ji;q} \epsilon'^q $ + \item The laser is of pure polarization $ \epsilon'^q =1$ for a given $q$ and $0$ for others. So $\hbar \Omega_{ji} = E_{\rm L} d_{ji;q} $ + \item states are pure (that is with well defined magnetic quantum numbers $m_i,m_j$ projection on the quantization axis ${\bf{e}}_0$). So $\hbar \Omega_{ji} = E_{\rm L} d_{ji;q} = E_{\rm L} \langle j | d_{1q} | i \rangle $ will verifies $m_j = q+ m_i $. We recover the fact that + $ q=-1$ for a $\sigma-$, $ q=0$ for a $ \pi$ and + $ q= +1$ for a $\sigma+$ light. + \end{itemize} + + +We now have to treat the most general case where none of these 3 assumption is correct. + \subsection{Rotation matrices} + + We have to deal with three frames: + \begin{itemize} + \item The fixed lab frame $(\bf{e}_{\rm x}, \bf{e}_{\rm y}, \bf{e}_{\rm z} )$ + \item The local (different for each particle position $\bm r$) field $\bm F(\bm r)$ frame, $(\bf{e}_{\rm X}, \bf{e}_{\rm Y}, \bf{e}_{\rm Z})$. It defines the quantization axis. It will also be noted + $(\bf{E}_{\rm X}, \bf{E}_{\rm Y}, \bf{E}_{\rm Z} = \bm{F}/\| \bm{F} \|)$ in order to define ${\bf{E}}_{\pm 1}$ without any confusion with ${\bf{e}}_{\pm 1}$. + \item The laser frame $(\bf{e}'_{\rm x}, \bf{e}'_{\rm y}, \bf{e}'_{\rm z} = \bm{k}/\| \bm{k} \|)$. + \end{itemize} + These frames are defined by their $z,z',Z$ axis, and the angle of rotation around this axis is defined such that (cf Fig. + \ref{fig:laseraxispolarization}), taken the example of the laser $z'$ frame, the frame is the polar frame of which $Oz'$ is the direction and $Ox'$ is the meridian. + + + All this explain that in the code a reaction is coded using the type\_codage\_react reaction=$\{n\_mol; n\_laser; \bm F; \bm \epsilon_L; \bm k; final\_internal\_state\}$ for the particule number $n\_mol$, under the laser number $n\_laser$ (-1 for spontaneous emission). + + \subsubsection{Euler angles} + + To go from one $(\bf{e}_{\rm x}, \bf{e}_{\rm y}, \bf{e}_{\rm z} )$ frame to a new one $(\bf{e}'_{\rm x}, \bf{e}'_{\rm y}, \bf{e}'_{\rm z} )$ it is convenient to use the Euler angles. + Different conventions exists: Mathematica and \cite{varshalovich1988quantum} (1.4 schema A) are in the so called z y z (noted also Z Y Z) convention, whereas Wikipedia is in z x z convention. For completeness, we thus recall here the + Euler rotations angles $(\alpha,\beta,\gamma)$ convention. + For instance in the + z y z convention: + \begin{itemize} + \item the first rotation is by an angle $\alpha$ about the $z$-axis. + \item the second rotation is by an angle $\beta$ about the new $y$-axis + \item the third rotation is by an angle $\gamma$ about the new $z$-axis (now $z'$). + \end{itemize} + + Clearly (Fig. + \ref{fig:laseraxispolarization}) our convention to use + the spherical basis leads simply to + $(\alpha,\beta,\gamma) = (\phi,\theta,0)$ in the + z y z convention, but to $(\alpha,\beta,\gamma) = (\phi+\pi/2,\theta,-\pi/2)$ in the z x z convention. + + The z x z convention is the one used (for historical reason) in the code (cf Euler\_angles function). + The z x z convention is useful to find the polar angle $\phi,\theta$ knowing only the vector ${\bf{e}}'_{\rm z} = x_e {\bf{e}}_{\rm x} + y_e {\bf{e}}_{\rm y} + z_e {\bf{e}}_{\rm z} $ that defines the new frame by: + $\alpha = \phi+\pi/2 = {\rm atan2}(x_e, - y_e)$ and $\beta = \theta = \arccos(z_e)$. + + The main function in the code is thus rotation\_axis\_lab that calculates, using simple notation such as $s_1 = \sin (\alpha)$ or $c_3 = \cos (\gamma)$ , the new coordinates + $$ \begin{pmatrix} x \\ y \\ z + \end{pmatrix} + =\begin{pmatrix}c_{1}c_{3}-c_{2}s_{1}s_{3}&-c_{1}s_{3}-c_{2}c_{3}s_{1}&s_{1}s_{2}\\c_{3}s_{1}+c_{1}c_{2}s_{3}&c_{1}c_{2}c_{3}-s_{1}s_{3}&-c_{1}s_{2}\\s_{2}s_{3}&c_{3}s_{2}&c_{2}\end{pmatrix}. \begin{pmatrix} x' \\ y' \\ z' + \end{pmatrix}$$ + The reverse rotation\_lab\_axis is used to find the laser intensity (cf intensity\_lab\_axis function) at the particle location $\bm r = x {\bf{e}}_{\rm x} + y {\bf{e}}_{\rm y} + z {\bf{e}}_{\rm z} $. + \subsubsection{Polarization vectors} + \label{pol_vector} + + % We can write the laser polarization vector in the two frames as \cite{varshalovich1988quantum} Eq. 1-(49): $ {\bm \epsilon} = \sum_{p'= -1,0,+1} {\epsilon'}^\ast_{p'} {\bf e'}_{p'} = \sum_{p= -1,0,+1} \epsilon_p^\ast {\bf e}_{p} $, with $ \epsilon_{p} = \sum_{p' =0,\pm 1 } (-1)^{p'} \epsilon'_{p'} D_{p p'}^{\ast (1)} (0,\theta,\varphi)$. + + To evaluate Eq. \ref{Rabi_frequancy} we + write the laser polarization vector in the three frames + $ {\bm \epsilon}_{\rm L} = + \sum_p \epsilon'^p + {\bf e'}_{p} = \sum_p \mathcal{E}^p + {\bf E}_{p} = \sum_p \epsilon^p + {\bf e}_{p} + $. + Using $ {\bm \epsilon}^. = \begin{pmatrix} \epsilon^{-1} \\ \epsilon^{0} \\ \epsilon^{+1} + \end{pmatrix}, {\bm e}_. = \begin{pmatrix} {\bf e}_{-1} \, {\bf e}_{0} \, {\bf e}_{+1} + \end{pmatrix}, + {{\bm \epsilon}'}^. = \begin{pmatrix} {\epsilon'}^{-1} \\ {\epsilon'}^{0} \\ {\epsilon'}^{+1} + \end{pmatrix} = \begin{pmatrix}a_{-} \ e^{i \Psi} \\ 0 \\ a_{+} \ e^{-i \Psi} + \end{pmatrix} , {\bm e}'_. = \begin{pmatrix} {\bf e'}_{-1} \, {\bf e'}_{0} \, {\bf e'}_{+1} + \end{pmatrix}, + {\mathcal{\bm E}}^. = \begin{pmatrix} \mathcal{E}^{-1} \\ \mathcal{E}^{0} \\ \mathcal{E}^{+1} + \end{pmatrix}, {\bm E}_. = \begin{pmatrix} {\bf E}_{-1} \, {\bf E}_{0} \, {\bf E}_{+1} + \end{pmatrix}$ we have + $ {\bm \epsilon}_{\rm L} = {\bf e'}_. {\bm \epsilon'}^. = {\bf E}_. \mathcal{\bm E}^. = {\bf e}_. {\bm \epsilon}^. $ + + + + We will note $\phi_{\bm k},\theta_{\bm k}$ the polar angles of ${\bm k}$ (to go from the lab fix frame to the laser frame) and $\phi_{\bm F},\theta_{\bm F}$ the polar angles of ${\bm F}$ (so to go from the lab frame to the field frame). Eq. (1.1 53) of Ref. + \cite{varshalovich1988quantum} gives + $ \sum_p {\bf e}_{p} {\rm D}_{p p'}^{1} (\phi_{\bm k},\theta_{\bm k},0) = {\bf e'}_{p'} $ +that is +$ {\bf e}_. {\rm {\bm D}} (\phi_{\bm k},\theta_{\bm k},0) = {\bf e'}_. \mbox{ and similarly } {\bf e}_. {\rm {\bm D}} (\phi_{\bm F},\theta_{\bm F},0) = {\bf E}_. $ + where + $({\rm {\bm D}})_{ij} = {\rm D}_{i j}^{1} $ is the + WignerD function. + Several conventions exists: Mathematica + WignerD$[\{j,m_1,m_2\},\alpha, \beta, \gamma]= {\rm D}_{m_1,m_2}^j (-\alpha, -\beta, -\gamma)$ of \cite{varshalovich1988quantum}. We use the \cite{varshalovich1988quantum} concention, that is also the one chosen by Wikipedia with: + $ {\rm {\bm D}} (\phi,\theta,0) = + \begin{pmatrix} + \frac{1}{2} e^{i \phi} (1+\cos \theta) &\frac{e^{i \phi} \sin \theta}{\sqrt{2}} & e^{i \phi} \sin^2(\theta/2) \\ + -\frac{\sin \theta}{\sqrt{2}} & \cos \theta & \frac{\sin \theta}{\sqrt{2}} \\ + e^{-i \phi} \sin^2(\theta/2) & -\frac{e^{-i \phi} \sin \theta}{\sqrt{2}} & \frac{1}{2} e^{-i \phi} (1+\cos \theta) \end{pmatrix} + $ with the order $i,j = -1,0,1$ in the lines and columns. + + Because the states $|i\rangle$ are defined with the quantization axis frame ${\bf{E}}_.$ we note + $ \bm d_{ij} = \langle i | \bm d | j \rangle = \sum_q D_{ij;q} {\bf{E}}^q $ with $ D_{ij;q} = \bm d_{ij}.{\bf{E}}_q$. So in matrix notation, with +$ {\bm D_{ij}}_. = \begin{pmatrix}D_{ij;-1} \, D_{ij;0} \, D_{ij;+1} \end{pmatrix} = \begin{pmatrix}D_{-1} \, D_{0} \, D_{+1} \end{pmatrix} $ + and $ {\bm E}^. = \begin{pmatrix} {\bf E}^{-1} \\ {\bf E}^{0} \\ {\bf E}^{+1} + \end{pmatrix}$, we have + $\bm d_{ij} = {\bm D_{ij}}_. {\bf E}^. $ + + We can thus now write Eq. \ref{Rabi_frequancy} as + \begin{equation} + \hbar \Omega_{ji} / E_{\rm L} = \bm d_{ji} . \bm \epsilon_L = [ {\bm D_{ij}}_. {\bf E}^. ].[ {\bf e'}_. {\bm \epsilon'}^. ] + % = [{\bm D_{ij}}_. {\bf E}^. ].[ {\bf E}_. {\rm {\bm D}}^{-1} (\phi_{\bm F},\theta_{\bm F},0) {\rm{ \bm D}} (\phi_{\bm k},\theta_{\bm k},0) {\bm \epsilon'}^. ] + = {\bm D_{ij}}_. {\rm {\bm D}}^{-1} (\phi_{\bm F},\theta_{\bm F},0) + {\rm{ \bm D}} (\phi_{\bm k},\theta_{\bm k},0) \begin{pmatrix}a_{-} \ e^{i \Psi} \\ 0 \\ a_{+} \ e^{-i \Psi} + \end{pmatrix} + \end{equation} + + This formula is used in the code in the effectif\_dipole\_local function and the final result is + \begin{eqnarray*} + & & \hbar \Omega_{ji} / E_{\rm L} = \frac{1}{4} e^{-i + (\psi +{\phi_{\bm F}}+{\phi_{\bm k}})} \times \\ + & & \Big[ \cos ({\theta_{\bm k}}) \left(-{a_+}+{a_-} + e^{2 i \psi }\right) \left(\left(e^{2 i {\phi_{\bm F}}}+e^{2 i + {\phi_{\bm k}}}\right) \left(\sqrt{2} {D_0} \sin ({\theta_{\bm F}})+({D_-}-{D_+}) \cos ({\theta_{\bm F}})\right)-({D_-}+{D_+}) \left(e^{2 i {\phi_{\bm F}}}-e^{2 i + {\phi_{\bm k}}}\right)\right) \\ + & & -2 \sin ({\theta_{\bm k}}) e^{i + ({\phi_{\bm F}}+{\phi_{\bm k}})} \left(-{a_+}+{a_-} e^{2 i \psi }\right) \left(\sqrt{2} {D_0} \cos ({\theta_{\bm F}})+({D_+}-{D_-}) \sin ({\theta_{\bm F}})\right) \\ + & & +\left({a_+}+{a_-} e^{2 i \psi + }\right) \left(({D_-}+{D_+}) \left(e^{2 i {\phi_{\bm F}}}+e^{2 i + {\phi_{\bm k}}}\right)-\left(e^{2 i {\phi_{\bm F}}}-e^{2 i {\phi_{\bm k}}}\right) \left(\sqrt{2} {D_0} \sin ({\theta_{\bm F}})+({D_-}-{D_+}) \cos ({\theta_{\bm F}})\right)\right) \Big] + \end{eqnarray*} + + \subsection{Angular distribution of spontaneous emission: recoil} + + + The spontaneous emission rate between a level $| i \rangle $ and $|j\rangle$ is given by + $\Gamma =\|\rm d_{ij}\|^2 C_{{\rm Debye},s} E_{\rm cm}^3$ (function Gamma\_Level\_from\_diagonalized\_dipole in the code). In order to properly take into account the recoil momentum we need to know the angular distribution of the emitted photon. + For this we have to go back to the calculation of the spontaneous emission rate that originates form the quantized field + so from (Fermi golden rule) + $\sum_{\bm k,\pm 1} | \langle i | \bm d | j \rangle. {\bm \epsilon}_{\bm k \pm 1}|^2 = \sum_{\bm k} \left[ \sum_p | \bm d_{ji} . {{\bm e'}_{\bm k}}_p |^2 - | \bm d_{ji} . {{\bm e'}_{\bm k}}_0 |^2 \right] $. So by defining the + "polarization" vector of the emitted light as ${\bf{e}}_{\rm pol} = \bm d_{ji} /\|\bm d_{ji} \|$ we find that the probability distribution, for + the direction $\bm r = \bm k/k$ of the emitted photon, is + given by + $ \frac{3}{8\pi} [1-|\bm r.{\bf{e}}_{\rm pol}|^2]$, with the proper normalization (to $1$). + We recover Eq. (1.45) (see also Eq. (7.427)) of Ref. \cite{manual_Steck}. In the code (get\_unit\_vector\_spontaneous\_emission function) the photon is taken randomly (with the Von Neumann's acceptance-rejection sampling method) using this distribution. % That is in the quantization axis (field) frame $d_{ji} {\bf{e}}_{\rm pol} = \sum_q D_{ij;q} {\bf{E}}^q $. + + \subsection{Diagonalization of the states} + + + In most of the cases the eigenstates themselves are not changing during the evolution, only the energy changes. However, + as explained in section \ref{diagonalization} + we have the possibility + to diagonalize the hamiltonian, for instance, to calculate Zeeman and Stark effect for the magnetic $\bm B$ and electric $\bm E$ fields more exactly. For this purpose, + we give the bare states $|i\rangle_0$, their energies ${E_i}_0$, and the dipole transition moments + (in the Diagonalization\_Energy\_dipole function) as three matrix $\{ \bm d0_{-1},\bm d0_{0},\bm d0_{+1} \} $ in the quantization frame (so always assuming adiabatic following) with $ + (\bm d0_{q})_{ij} = + d0_{ij;q} = {}_0\langle i | \hat {\bm d} | j \rangle_0 . {\bf{E}}_q $. + + + Then, for each local perturbation $\hat V(\bm B(\bm r), \bm E(\bm r) )$ + (the perturbation $\hat V$ matrix is given in the Diagonalization\_Energy function), + we diagonalized $ \hat H = \hat H_0+\hat V$ to get the new eigenvectors + $| i\rangle = \sum_{i_0} {}_0\langle i_0 | i\rangle |i_0\rangle_0 = \sum_{i_0} {\rm \bm evec}_{i_0 i } |i_0\rangle_0 $ with the eigenvectors matrix ${\rm \bm evec}_{i_0 i } = + {}_0\langle i_0 | i\rangle$. We can then calculate the new dipoles + $ \langle i | \hat d_q | j \rangle = ({\rm \bm evec}^\dag.{\bm d0}_q.{\rm \bm evec})_{ij} $ that is coded with the dipole vector $ \{ d_{ij;-1},d_{ij;0},d_{ij;+1} \} $. + + +\bibliographystyle{unsrt} +\bibliography{bibli_user_guide} + + + +\end{document} + + + + diff --git a/User Guide/User Guide Laser Cooling_old.pdf b/User Guide/User Guide Laser Cooling_old.pdf new file mode 100644 index 0000000..d2c585c Binary files /dev/null and b/User Guide/User Guide Laser Cooling_old.pdf differ diff --git a/User Guide/User Guide Laser Cooling_old.tex b/User Guide/User Guide Laser Cooling_old.tex new file mode 100644 index 0000000..443b59f --- /dev/null +++ b/User Guide/User Guide Laser Cooling_old.tex @@ -0,0 +1,1422 @@ +% Template article for preprint document class `elsart' +% SP 2001/01/05 +% and 2 sets of keywords - 21.05.03 - file called phys-english.tex +% Modified CG (ESME) for Model 4, single column, 2 titles, abstract/rÈsumÈ, +% English Version for Physique (CRAS series 4, now COMREN) - a Note in English +% Revamped, CG, 18.08.04, adding header, dates, +% and name of presenter + +\documentclass[amsmath,amssymb]{revtex4} + +\usepackage[toc,page]{appendix} + +\usepackage{xcolor} + + +%\def\journal@prl{prl}% +%$@$ifx{$@$journal\journal@prl}{% + + +\def\cpl{Chem. Phys. Lett.} +\def\aj{{AJ}} +\def\araa{{ARA\&A}} +\def\apj{{ApJ}} +\def\apjl{{ApJ}} +\def\apjs{{ApJS}} +\def\ao{{Appl.~Opt.}} +\def\apss{{Ap\&SS}} +\def\aap{{A\&A}} +\def\aapr{{A\&A~Rev.}} +\def\aaps{{A\&AS}} +\def\azh{{AZh}} +\def\baas{{BAAS}} +\def\jrasc{{JRASC}} +\def\memras{{MmRAS}} +\def\mnras{{MNRAS}} +\def\pra{{Phys.~Rev.~A}} +\def\prb{{Phys.~Rev.~B}} +\def\prc{{Phys.~Rev.~C}} +\def\prd{{Phys.~Rev.~D}} +\def\pre{{Phys.~Rev.~E}} +\def\prl{{Phys.~Rev.~Lett.}} +\def\pasp{{PASP}} +\def\pasj{{PASJ}} +\def\qjras{{QJRAS}} +\def\skytel{{S\&T}} +\def\solphys{{Sol.~Phys.}} +\def\sovast{{Soviet~Ast.}} +\def\ssr{{Space~Sci.~Rev.}} +\def\zap{{ZAp}} +\def\nat{{Nature}} +\def\iaucirc{{IAU~Circ.}} +\def\aplett{{Astrophys.~Lett.}} +\def\apspr{{Astrophys.~Space~Phys.~Res.}} +\def\bain{{Bull.~Astron.~Inst.~Netherlands}} +\def\fcp{{Fund.~Cosmic~Phys.}} +\def\gca{{Geochim.~Cosmochim.~Acta}} +\def\grl{{Geophys.~Res.~Lett.}} +\def\jcp{{J.~Chem.~Phys.}} +\def\jgr{{J.~Geophys.~Res.}} +\def\jqsrt{{J.~Quant.~Spec.~Radiat.~Transf.}} +\def\memsai{{Mem.~Soc.~Astron.~Italiana}} +\def\nphysa{{Nucl.~Phys.~A}} +\def\physrep{{Phys.~Rep.}} +\def\physscr{{Phys.~Scr}} +\def\planss{{Planet.~Space~Sci.}} +\def\procspie{{Proc.~SPIE}} +\def\icarus{{Icarus}} +\let\astap=\aap +\let\apjlett=\apjl +\let\apjsupp=\apjs +\let\applopt=\ao + + +\usepackage{isomath} +% Scientific organisations like IUPAP\_, IUPAC\_, NIST\_, BIPM\_, and others recommend typesetting math according to the International Standard ISO 31`Quantities and units` [ISO-31] + +\usepackage{upgreek} % to have roman greek letter + + + + +\usepackage{graphicx}% Include figure files +\usepackage{mathtools}% For \MoveEqLeft +\usepackage{dcolumn}% Align table columns on decimal point +\usepackage{bm}% bold math +\usepackage{rotating} +\usepackage{color} +\usepackage{amssymb} +\usepackage[latin1]{inputenc} +%\nofiles +%\usepackage{epstopdf} +\DeclareGraphicsRule{.tif}{png}{.png}{`convert \#1 `basename \#1 .tif`.png} + + +\begin{document} + +\title{USER GUIDE For the simulation of Laser cooling of particles} +\author{Daniel Comparat} +\affiliation{Laboratoire Aim\'e Cotton, CNRS, Univ Paris-Sud, B\^at. 505, 91405 Orsay, France} + +\date{\today} + + + + +\begin{abstract} +This document gives an introduction to the use of the C++ Laser Cooling code described in PHYSICAL REVIEW A 89, 043410 (2014) + and available on git: https://github.com/dcompara/Laser-interaction-in-fields. +The program solves the rate equations to study laser excitation, forces (scattering + dipolar + magnetic + electric + coulombian interactions). +It has been developed under Code::Blocks and Windows. +The inputs are 2 external files describing the levels (with information about their energy + linear or quadratic Stark, Zeeman effect) and the + transitions lines (dipole transitions, photodetachement or photoionization cross sections) +Then a file named Liste\_Param.h contains parameters to run the simulation such as sample size, temperature, magnetic fields and for the laser beams (waist size and position, polarisation, power, linewidth, wavelength, ...). +When running, the program calculates at time t all absorption and emission rates. Then a Kinetic Monte Carlo algorithm gives the exact time t+dt for an event (absorption or emission) compare this time to a typical external motion time then it evolves in motion and event. +The output is writen in a file containing relevant information such as population in given levels and statistics about velocities (temperature), potential energy ... +Output is also performed through 3D snapshots. +% An update of the modifications done in the code can be find in Modif\_code\_rate\_eq.txt. +\textbf{Any modifications, bugs, improvement, ... should be refereed to +Daniel.Comparat$@$u-psud.fr} +\end{abstract} + + +\maketitle + + + + + +\section{Introduction} +The program solves the rate equations, for spontaneous, absorption and stimulated-emission. It studies laser excitation and motion under external forces (scattering + dipolar + magnetic + electric + gravity) and take into account N-body coulombian interactions and Lorentz forces if charged particles. The momentum recoil is also implemented. +The algorithm and detail of some calculations can be found on the appendix of \cite{comparat2014molecular}, thus I will not recall it here. + But to run the code you do not need to read it! + +% The programm can be download at: https://www.dropbox.com/sh/8iivh04gvf0vk6p/AAA0dtvHDgeZQSjZ7oJJ7zlWa + +In brief it requires: Windows (Linux might be possible but I did not write this guide for it) and Code::Blocks. + +Then the program requires: + + + +\begin{enumerate} + \item input files + + +\begin{itemize} + \item levels: containing their energy + linear or quadratic Stark, Zeeman effects. + \item lines: containing the dipole transitions or some cross sections such as for photodetachement or photodissociation. + + +\end{itemize} + +\item File with parameters (named Liste\_Param.h): contains parameters needed to run the code (sample size, temperature, magnetic fields, laser parameters, ...) + + The file Liste\_Param.h contains a lot of lines with comments, \textbf{so read them carefully!}. As a single example, if you do not change the initialization of the random number generator in this file, the simulation will always be the same when you run a new simulation (which is good for debug!). + +Liste\_Param.h is not an header file and it will not be compiled when compiling the project files. The .h is here simply because it is opened by the text editor. + + + + \item Laser Shaping + + If needed (for optical pumping of molecules for instance) + each laser can be spectrally shaped using files such as Laser\_Spectrum[1].dat for the second laser. + + \item Output: + + A 3D visual output help to see in "real" time the evolution of the sample. But informations at given time intervals are writen in a file (donnee\_Mol.dat). + + + You will probably have to modify the file Sortie\_donnee.cpp depending on what output you want. + + + +\end{enumerate} + + + + +To run the code it is not required to understand it. But briefly, at time t: the program calculates all absorption and emission rates for all particles (so the most important part of the code is the function rates\_molecule). Then Kinetic Monte Carlo algorithm gives exact time t+dt for event (absorption or emission) compare this time to the time for the external motion. Finally it evolves all particles in motion to realize the event. A more detailed explanation is given at the end of this guide in section \ref{section_algorithm}? + + +An update on the modifications done in the code can be find in Modif\_code\_rate\_eq.txt but you have the last version so in principle you do not have to read it. + + +In the following section you will have more informations about each files. + +\section{Code::blocks Installation} + + + + +You first need to install Code::Blocks (also called Codeblocks) the free C++ IDE, +as well as some scientific and 3D-visual libraries. +Very recently CodeBlocks becomes a pure 64bits. I modify the code to run on 64bit, for the 32bits version see section \ref{32bits}. + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{linker} + \caption{Example of possible installation (in the case of the simple gsl 1-13). To put either in the Settings/Compiler directory, either in the Project/Build options one.} + \label{fig:linker} +\end{figure} + + +If you are not at all familiar with CodeBlock I suggest that you follow a small tutorial such as http://www.codeblocks.org/user-manual. + +\subsection{64bits} + +The steps are: + + +\begin{enumerate} + \item Install last stable version of codeblocks: a mingw-setup.exe binary file from www.codeblocks.org/ + + It will install the codeblocks in a directory such as C:\textbackslash{}Program Files\textbackslash{}CodeBlocks (see note \footnote{For the 32bits the mingw-32bit-setup.exe it will be installed in C:\textbackslash{}Program Files (x86)\textbackslash{}CodeBlocks where the (x86) is here to say that it is a 32bits file but on a 64bits computer. All other "normal" cases will be on C:\textbackslash{}Program Files (that is 32bits on 32system or 64bits files or 64 computer)}). + + + +\textbf{ Then we need to install useful extra files. This will always be the same idea for all packages (GLUT, GSL, Eigen, ...): put the headers (.h) in an \textbackslash{}include, the .lib (or .a) in a \textbackslash{}lib and the .dll files of the packages in a \textbackslash{}bin directory + that the code and the compiler will find for instance by configuring the project $\rightarrow$ build option.} + +Therefore you will hae to adapt the following names for your own installation. + + +\item OPEN\_GL + GLUT (for graphic) + + +So for example from the github CodeBlocks\_Install repository put + +glut32.lib in the sub Directory of Code::Blocks \textbackslash{}MinGW\textbackslash{}lib + +glut.h in \textbackslash{}MinGW\textbackslash{}include\textbackslash{}GL (you may have to create the GL directory). + +Finally put the glut32.dll in c:\textbackslash{}windows\textbackslash{}system + +\item Eigen Library + +To be able to diagonalize an hamiltonian, we need to install the very good library http://eigen.tuxfamily.org +package and unzip it. + +Then depending on your location you will have to modify the search directories in the Project Build Options. For me it is +C:\textbackslash{}Program Files\textbackslash{}Common Files\textbackslash{}eigen-3.3.7\textbackslash{}Eigen + + +\item GNU Scientific Library (GSL) + +The simplest way is to install Gsl-1.13-1.exe. then always the same modify from the Search directories in the Project Build Options +the location of the .h files. For me it is +C:\textbackslash{}Program Files (x86)\textbackslash{}GSL-1.13\textbackslash{}include + + +Then, copy all .dll (libgsl.dll and libgslcblas.dll and ...) of the GSL installed directory in Windows\textbackslash{}system + + +GSL has not .dll and so it is a static linkage. For this you need to create a Global Variable +gsl +in settings (global variable) of code::blocks with the address where you have installed GSL and add in the +project $\rightarrow$ build option $\rightarrow$ search directory $\rightarrow$ +linker put: \$(\#gsl.lib) + + + + + +\end{enumerate} + + +\subsection{Just run the code} + +\subsubsection{Codeblocks configuration} +The main think you have to do to make the code compiling is to make sure that codeblocks find the files you want (the Eigen, gsl or GLUT ones), the headers (the .h), the library (the .a or .lib files) and the way for windows to handle (the .dll files). +An example of what should be done is given in Fig. \ref{fig:linker}. + + +The linker option -Wl,--allow-multiple-definition are here to avoid too many comments. The others such as +-lglut32 (but also +-lopengl32, +-lglu32, +-lgsl) +mean that the compiler has to look for a library file such as libglut32.a or glut32.lib + + + +\subsubsection{speed consideration} +Finally, if wanted, you can increase the speed by looking to project $\rightarrow$ Build option $\rightarrow$ Compilator and choose your processor (mine is Intel Core i7). However I almost never find any speed increase (on the contraty so be careful). + +For a speed up, you can also use Ctrl+Alt+del and Process $\rightarrow$ to change priority of the program from Normal to high in Windows. + + +\subsection{Comment on 32 bits more recent version or 64bits codeblocks version.} +\label{32bits} + +All this should work if you use a 32 bit computer. For a 64 bit computer you should install the 64bit GSL version and the 64bits codeblocks version + + +\begin{enumerate} +\item 64bit installer (MSYS2 MinGW) + +The best (because Cygwin leads to a lot of problem) is to get an installer of MSYS2 MinGW w64-bit and run it. Then using the package manager (pacman) do: +\begin{itemize} + \item pacman -Syu + \item pacman -Syu base-devel (then make the selection that avoids pacman: typically 1-39,41-58 that avoids pacman at number 40 in this example) + \item pacman -Syu mingw-w64-x86\_64-toolchain (then choose all) +\end{itemize} + + +\item 64bits GSL + + +Retrieve the last GSL folder for example gsl-2.6, unzip it for instance in C:\textbackslash{}msys64\textbackslash{}home\textbackslash{}daniel and install with MSYS2 : +\begin{itemize} + \item cd gsl-2.6 + \item % ./configure --prefix=C:/msys64/mingw64 (be careful, it's a space then twice - in front of prefix). If this does not work try just + ./configure + \item make + \item make install +\end{itemize} + +Obviously you then need in the codeblocks project to put the proper +Gsl : + +- Settings / Global Variables / base: write the path of the main folder of gsl in msys. For example C:\textbackslash{}msys64\textbackslash{}home\textbackslash{}Daniel\textbackslash{}gsl-2.6 + +- Project / Build options... Select the right compiler (at the very bottom of the list) + +- Project / Build options... / Search directories: fix the path For example + C:\textbackslash{}msys64\textbackslash{}MinGW64\textbackslash{}include + + + + + \item 64bits latest Codeblocks + + So you should download the mingw-setup.exe codeblocks binary file from www.codeblocks.org/ + or if you want the + newest codeblocks version. You can download the last version "out" of Nightly built: http://forums.codeblocks.org/index.php/board,20.0.html + that is download three .7z files, unzip them (you need 7Zip) in CodeBlocks directory by replacing all the old files with them. + + + \item C++ 64bits compiler + + The last version of code blocks has a 64bit compiler so this is not needed + + + + You may need to change to Compiler in codeblocks For this go to Settings/compiler/ and select the default compiler and copy, give a name, for example MSYS2 MINGW64 + Go to Settings/compiler/GlobalCompilerSettings/ToolchainExecutables" to set the path of MinGW64 installed at the beginning: C:/msys64/mingw64. + Put the right file names in the "program files" tab of executable toolchain: change all names (exemple x86\_64-w64-mingw32-gcc.exe instead of mingw32-gcc.exe) except the one for make (you will find the names in the bin folder of mingw64). + + + + +\item GLUT + + + +All this works but the onyl problem is GLUT that has some issues that needs also to be fixed because it is intrinsically 32bit. +The best is probably to use freeglut from https://www.transmissionzero.co.uk/computing/using-glut-with-mingw/ + +First it may be wise to know that 32bits dll in a 64bit system should go to c:\textbackslash{}windows\textbackslash{}SysWOW64. All other standard case go to System32 (I know this is confusing but comes from histrorical reasons like (x86) = 32nits and (x64)=64 bits). + + + + + +Run the Command Prompt in administrator mode (type "cmd" on the start menu + click the Run as administrator" option) then run: \%windir\%\textbackslash{}System32\textbackslash{}regsvr32.exe /u glut32.dll +\ and \ +\%windir\%\textbackslash{}SysWOW64\textbackslash{}regsvr32.exe /u glut32.dll + +\end{enumerate} + + + +\section{Short overview} + +\subsection{Overview of the Program} + +You do not need to know the code in detail, but an overview of its C++ structure is given in the Figures \ref{fig:Class} and \ref{fig:Program_evolution}. + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{classes} + \caption{Schematic of the structure and some basics functions used by the code. The blocks are the different files (.cpp or .h) present with their names in bold and an quick explanation of what they do.} + \label{fig:Class} +\end{figure} + + +Figure \ref{fig:Class} gives the list of the basic structure or classes used such as lasers or fields. Molecules are just seen as Levels, Lines and their positions and velocities. + +Figure \ref{fig:Program_evolution} is the core of the code with the main evolution summarized in the Main\_laser\_cooling.cpp program, that is usually the only code that you may have to modify (with the output one: sortie\_donnee). +As you see the code as still some French in it such as: + +\begin{itemize} + \item donnee = data + \item affichage = plot + \item sortie = output + \item champ = field + \end{itemize} + + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{evolution} + \caption{Schematics of how the code evolve its time. The blocks are the different files (.cpp or .h) present with their names in bold and an quick explanation of what they do.} + \label{fig:Program_evolution} +\end{figure} + + + + + +\subsection{graphics} + + +Once run. You will see two screens appearing as shown in figure +\ref{fig:picture}. + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{picture} + \caption{Snapshot (screen capture) of the code.} + \label{fig:picture} +\end{figure} + + + +If you do not want the graphics you have to change the option in Liste\_Param file. +Some parameters like the screen size are directly part of the code but other ones like size of view of the sample are part of Liste\_Param. + + +For now the graphics do not indicate the lasers locations but show the particles behavior at every time steps, set by the parameter +$@${}dt\_out of Liste\_Param + +The graphics (uses OPEN\_GL library for 3D plotting) represent the particles with the following choices: +\begin{itemize} + \item Red arrow along x, green along y and blue along z (gravity is along -Oz) to see the origin and orientation of the view. Global screen rotations are possible in Liste\_Param, the usual one puts gravity down, but if no rotation is performed we would have x toward the right, y up and z toward the screen. + \item Molecules are represented like diatomic molecules (a line connecting 2 balls) +and depend of their ro-vibronic level and mass. + The length is proportional to the vibrational quantum number $v$, the angle in $x y$ is proportional to the rotational quantum number $J$ and the angle in $x z$ is proportional to its projection (along the local field axis) $M$. + Then the ball size and the color reflects the molecule and its state: Ground state are green, excited state are yellow, dead (photodetachment, ionization, annihilation) are blue (and antiprotons are olive). + +\end{itemize} + + + +Then some statistical data are given like the temperature, positions and velocities of the laser cooled molecules. +As well as the temperature of the second species (if they exist). +Finally the total energy of all molecules is given (it should be conserved in absence of laser cooling). + + +\subsection{Output: Export data in files} + +In addition to the graphics output we have several others possible outputs. + +Mainly Sortie\_donnee\_pop\_vJ gives the population in each $v,j$ levels or simply Sortie\_donnee\_pop\_v gives the population in each $v$ levels. But the standard one is +Sortie\_donnee that gives useful data such as positions, velocities or temperatures. + +The current example Sortie\_donnee (call in main\_Laser\_cooling.cpp in "(t $>$= t\_dia)" section) +gives for each diagnositic time: the parameters that you scan, the time, the position (x,z) and v\_z. + +{\bf You Should probably modify those outputs for your own purpose.} +Use the comment lines to inspire you for your own choice. + + +Finally you can stop the code to run by pressing CTRL+C after if you want to stop before the end or to avoid producing too big files. + +\section{Input files} + + +The code requires source input files +(their locations and names are defined in Liste\_Param). The files are the following: + +\begin{enumerate} +\item Liste\_Param.h (it has to have this exact name) + +Contains all relevant parameters such as number, temperatures, locations of the particles, lasers parameters and some output properties and algorithm choices. +The location of the files are also given in $@${}nom\_file\_Levels, +$@${}nom\_file\_Lines or $@${}nom\_file\_Laser\_Spectrum + + + + \item "Levels". + + Contains informations about the levels of the chosen particle (BaF, Cs$_2$, NH, Cs, CO, Ps, ...). The basic informations are the energy levels and their linear and quadratic Zeeman (and eventually Stark) shifts. + + \item "Lines" . + + Give the dipole transition strength between two levels. + + \item "Laser Spectrum[i]" + + It is optional (if not present no laser attenuation is taken into account and the laser is "normal"). But it can be used to create spectral shaping of a laser. + + + +\end{enumerate} + + +ALL FILES SHOULD NOT contain a return line neither an extra character, like a space, at the end! + + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{laser_axis_polarization} + \caption{Definition of the differents frame: laser axis (for the polarization basis), field axis (that is the quantization because we assume adiabatic following of the states) and lab fixed frame. To go from the lab fix frame to the laser axis one a first rotation is by an angle $\phi$ about the $z$-axis then a second rotation is by an angle $\theta$ about the new $y$-axis + } + \label{fig:laseraxispolarization} +\end{figure} + + + +The structure of the files have been chosen because it is the one given by the Pgopher program: PGOPHER, a Program for Simulating Rotational Structure, C. M. Western, University of Bristol, http://pgopher.chm.bris.ac.uk. See Journal of Quantitative Spectroscopy \& Radiative Transfer 186 (2017) 221, where Pgopher is described. + +A more detail description of all files is now given. + +\subsection{Liste\_Param} + +Liste\_Param.h contains: +\begin{itemize} + \item Particles parameters: numbers, type, temperatures, initial positions and velocities + \item Graphics: size and angle of the field of view, time for each output. + \item Fields. Usually given in 3D up to the second order. We can put Helmholtz coils for the magnetic field. For now we can have a trapping magnetic or electric field but not both. With the exception of a Penning trap where the electric field acts on the charge but is supposed to not produce internal energy shifts. + \item Laser beams: waist sizes and positions, polarisations, powers, linewidths, wavelengths, spectral shapes (Lorentzian, Gaussian, comb lines) and possible coherence (intensity interference to create optical lattice) between them.... The polarization could be purely circular (left=$\sigma^+$ or right=$\sigma^-$) or linear and are defined using the laser propagation axis and a rotation angle cf Fig. \ref{fig:laseraxispolarization}. Linear polarizations are thus possible but (to be checked..) then no interference effects are taken into account. Other 'fictuous' laser types can be invented in order to take into account other rates (such as collisional, field ionization, ...) + \item Algorithm parameters: evolution time and steps. Among them we have +the Kinetic Monte Carlo, the First Reaction Method or the less accurate but faster Random Selection Method or even the Fast Rough Method for the internal state. Verlet or Boris-Buneman for the external motion but with different types: either using the analytical acceleration (and no dipolar force) either using gradient of the potential (the epsilon "size step" has to be manually optimized). A N-body algorithm is also implemented. + +\end{itemize} + + +In principle all parameters are in SI units. If not, the name suggests the value such as Gamma\_L\_MHz or Energy\_cm because all energies are in cm$^{-1}$. + + +All parameters have their name staring with $@$ symbol followed by their value (so no symbol $@$ should be use in this file except for this purpose). + + +A loop on the parameters values can be done if the parameters names are written with a +$@${}SCAN\_ prefix and a "true" value between +BEGIN\_OF\_FITPARAMS +and +END\_OF\_FITPARAMS +at the end of Liste\_Param.h file. + + + + +If needed, a new parameter can be added in the file, and then used, in some files of the program using the sentence + params.LocateParam("Nom\_Parametre")-$>$val +that takes its value. + + + + +\subsection{Levels} + + +The name of the file can be chosen as wanted but then put in the Liste\_Param.h file. + +The columns of the file are the following: + + \bigskip + + \textbf{ Manifold 2M Sym \# population } v 2J 2N 2$\Omega$ \textbf{ E$_{\rm cm}$ $\Delta$ C} + \bigskip + +Columns are separated by tabulation. Points (not coma) are used for decimal separations. + + + \textbf{ manifold, 2M, \#, Sym are the only data used to label a Level}. Thus v, 2J, 2N or 2$\Omega$ are extra data and are here only for a better understanding of the file. They can also be used for an output of the data. + +The detail of the columns are(in bold the data that should absolutely be correct): + +\begin{itemize} +\item \textbf{Manifold}: usually 0 means ground electronical level, 1 is for an excited electronical level, 2 for another one ... Negative values can be used for a "dead" level such as one in a continuum (photo-ionization -1, photodetachement -2, or annihilation -3). + + \item \textbf{2M}: where M is the projection of the total angular momentum. We note 2M and not M to be able to use integer in the code for M=1/2 for instance. + In the code the particle will be assumed to always follow (adiabatically) the local quantification axis given by the local field. + +{\it If you want to simulate states without sub-structure like pure ro-vibrational transition in zero field you coudld impose $M$=0 for all states and use $\pi$ laser polarization.} + +\item \textbf{Sym}: Originally it was the parity of the state but this not the case but it should be +1 or -1 to design bound states and 0 for an continuumm state (that is above the continuum threshold such as for photodetachment or photoionization). + +\item \textbf{\#}: "number" of the state. It lifts the degeneracy between levels having the same 3 parameters: manifold, 2M and \#. Usually it is ordered (0,1,2, ...) by energy but for the vibrational levels you could add 10000v to keep trace of it. + +\item \textbf{population}: This is proportional to the initial population in the levels (that will be taken randomly at the beginning of the run). The sum should not have to be 1. + + +\item v: vibrational level. As said previously this is not used by the code except may be for some output data. + +\item 2J: J = total angular momentum (F if nuclear spin present) + +\item 2N: N = rotational angular momentum, including L (L=electron orbital angular momentum). + +\item 2$\Omega$ : $\Omega$ = Projection of J along the molecular axis. + + +\item \textbf{E$_{\rm cm}$}: energy of the level in cm$^{-1}$. For a continuum state, we put the energy of the threshold, like that we can test if the laser transition reach the continuum or not (but we assume a cross section independent of the energy). + +\item \textbf{$\Delta$ and C} give the energy shift of the level under an electric or magnetic field $F$. + +The formula is $E_{\rm cm}(F)= {E_0}_{\rm cm} + {\rm sign}(C) [-\Delta/2+\sqrt{(\Delta/2)^2+(C F)^2}]$. +Thus if $\Delta = 0$ we have a linear variation $E(F)= E_0 + C F$. +Thus, for the magnetic field case, units are cm$^{-1}$/Tesla for $C$. A magnetic moment of 1 $\mu_{\rm Bohr}$ correspond to a value for $C$ of 0.4668645 cm$^{-1}$/Tesla. + + +\end{itemize} + +If needed, an option exists (is\_File\_FC in Liste\_Param) in order to automatically produce new Levels and Lines files from a file containing only $v_X=0 \rightarrow v_A =0$ transition by reading extra Franck-Condon and vibrational and rotational constant files. + + + +\subsection{Lines} + +The lines file can content more lines than used by the Level file. In this case the program only read the useful ones. + + The columns (separated by tabulation) of the file are the following: + + + + \bigskip + + \textbf{UpperManifold 2M' Sym' \#' LowerManifold 2M'' Sym'' \#''} $\Delta_E$ Intensity E$_{\rm upper}$ E$_{\rm lower}$ \textbf{Strength} + +\bigskip + + \textbf{The first 4 columns design the upper level $|1\rangle$ and the second 4 the lower level $|0\rangle$. +So they have to be the same as in the Level file!} + + The last 5 columns give informations about the transitions between these levels. +But \textbf{only the last column (Strength) is used by the code}. However, usually they are composed on: + +\begin{itemize} + + +\item $\Delta_E$: energy difference between the 2 states $|1\rangle$ and $|0\rangle$. + +\item Intensity: Einstein coefficient = spontaneous emission rate of the transition (this is not the total decay rate of the state $|1\rangle$, because it can decay to several levels). + +\item E$_{\rm upper}$: energy in cm$^{-1}$ of the upper state $|1\rangle$. + +\item E$_{\rm lower}$: energy in cm$^{-1}$ of the lower state $|0\rangle$. + +\item \textbf{Strength}: $S_{\rm pol}=d_{\rm axe}^2/3$, where $d_{\rm axe}$ is the dipole (in Debye) of the transition along the polarization axis that authorize the transition between the sum-Zeeman levels). This notation was used due to historical reasons linked to Pgopher. + +So A=Intensity = $\Gamma = 3 S_{\rm pol} C_{{\rm Debye},s} E_{\rm cm}^3$ +with $C_{{\rm Debye},s} = (8\times 10^6 \pi^2 c^3 {\rm Debye}^2 )/(3. \varepsilon_0 c^3 \hbar) = 3.13618932 \times 10^{-7}$ is the conversion from the dipole (in Debye) to the Einstein's coefficient A (s$^{-1}$) for an energy in cm$^{-1}$. + + + +\end{itemize} + + + +For an continuum transition (so with Sym' = 0), the idea to treat it, is to put a "fake" level: the energy should be just at the ionisation threshold (thus the program can test if the laser wavelength is enough to ionize). But, in this case the $S_{\rm pol}$ column is not $d^2/3$ but $\sigma/$cm$^2$ which is the ionization cross section in cm$^2$. + + + + +\subsection{LASER\_SPECTRUM} + +This file is used only if you want to shape spectrally a laser. If you do not create such a file a default one (containing only one line: 0 1) is created which does not affect the laser intensity. + + +The code reads a file one file per laser (number). +Laser\_spectrum[i] for laser number i+1 +that contains 2 columns: E$_{\rm cm}$ (Energy in cm$^{-1}$) and Attenuation (intensity attenuation coefficient). + + +When a transition should occur at the energy $E_{\rm cm}$. +The program look in this file for the line $i$ such as $E_{\rm cm}[i] \leq E_{\rm cm} < E_{\rm cm}[i+1]$ and then it takes the corresponding value +Attenuation$[i]$. This will be the multiplicative factor for the laser intensity for this transition energy. +So in summary the energy in the file is the energy just below yours and the intensity would thus just be multiplied by the amplitude factor. + + + + +\section{Troubleshooting} + + +Figures \ref{fig:Program_evolution} is the core of the code with the main evolution summarized in the Main\_laser\_cooling.cpp program, that is usually the only part of the code that you have to modify (with the output one: sortie\_donnee). + + +If the program does not run for the first time it is usually a problem of links and library in Code::Blocks. + +But if it usually runs but then bug after some modifications it is 90\% due to an error in the input files: levels or lines! + + +For debugging use the debugger in the Debug file. But you can also use Sortie\_rate which gives all rates, or Sortie\_donnee\_etat\_int\_simple that gives the list of levels, and that are commented on Main\_Laser\_Cooling. You have also Sortie\_laser\_spectrum to check the laser spectrum you make or Sortie\_transition to check the transition per + +\textcolor{red}{The best way to debug is to use a simple two level system and to look for the rates to understand if they are as expected. 95\% of the time the problems comes from the Levels or Lines files} + + +\subsection{CodeBlocks problems} + +If you have not strictly followed the rules you might have the following problems!! + + +If Code::Blocks is installed in the C: directories but you have put your project in D: +this does not work. +Thus, you have to put in +"Settings" $\rightarrow$ "Compiler and Debugger" $\rightarrow$ "Toolchain executeables" $\rightarrow$ "Program files" +some link. +For instance modify "mingw32-g++.exe" in "C:\textbackslash{}MinGW\textbackslash{}bin\textbackslash{}mingw32-gcc.exe" +in the "linker for dynamics libs:"... + +More generally the problems are almost always coming from a bad links. + You can specify them for your global environment or just for your project. + +For global environment : +\begin{itemize} + \item Menu Settings/Compiler and debugger +\item In the Global compiler settings, select the Search directories +\item Add the required paths for compiler and linker. +\end{itemize} + + +For your project : +\begin{itemize} + \item Right click on the project then select Build options +\item Select the Search directories +\item Add the required paths for compiler and linker. +\item Add your specific libraries in the linker tab. +\item Pay attention to project settings and target settings. +\end{itemize} + + + +ALWAYS verify that your modifications of directories affect all the project and not only Debug or Release + +Do not forget to recompile the full code after any modification!! + + +\subsection{Common tests} + + +\begin{itemize} + \item It is always good to go back to a situation where the results are known such as: 1 particle at the center, zero temperature, no lasers, no trapping, single laser at resonance, ... +\item Checking energy conservation is always of good practice! +\item Check for the proper time step (dt\_dyn\_epsilon\_param that is the one for the external motion; eventually choix\_epsilon that is the spatial step to calculate the gradient of the potential in some algorithms). + \item Do not forget to recompile the overall project. + \item The most common mistake comes from errors in the Levels or Lines files + \item A too big number of molecules or Levels or Lines may lead to memory overflow. So check also the use of the memory, for instance by using the Windows resource monitor. + \item You can use the code::blocks debugger or simply write some test lines in the code. A very common test is to uncomment the two lines (just before "if (t >= t\_dia)" in main\_laser\_cooling.cpp) with Sortie\_rate and Sortie\_donnee; this will produce at each time step output of all calculated rates and output data. + +\end{itemize} + + + + + +\section{Algorithm used in the code to calculate the evolution and the rates} +\label{section_algorithm} + +\subsection{Diagonalization} +\label{diagonalization} + +We add the possibility cf parameter is\_Levels\_Lines\_Diagonalized +to diagonalize the hamiltonian in order to calculate the energy and the transitions. This was done for positronium (but this is more general) where we had to use the fact that the levels are mixed in $E$ and $B$ fields and that the velocity create a dynamical Stark effect. + +However we do the diagonalization only for the reactions not for the external motion of the particles! So the particles stays in the same levels during their motion (no level crossing during motion) as shown in Figure \ref{fig:diagonalization}. The light shift is not included also. + +\begin{figure} + \centering + \includegraphics[width=0.6\linewidth]{diagonalization.png} + \caption{Schematics of the Energy level due to recoil momentum. The diagonalization thus works only if the energy levels before and after spontaneous emission have the same order in energy. No other dynamical evolution is taken into account, we assume constant velocity during motion (in the excited states).} + \label{fig:diagonalization} +\end{figure} + + +The matrices (Zeeman, Stark, dipoles\footnote{From a dipole Matrix between all levels the dipole matrices could be calculated using Create\_dipole\_Lines\_from\_Matrices. And thus they are correct for the emission-absorption polarization.}) should be put by hand in diagonalization.cpp and should follow the same ordering than the Levels and Lines (and should be ascending in energies). + + + +The most important is that in the degeneracy number \# of the state should be the number of the state staring from 0 (so Level[\#] is the Level itself) [recall that in C++ the index of the first element of the table is 0]. +% The Lines file should contains all transitions (even the nul ones) between i\_low and j\_up. +The levels are thus always refers as Level[i] that is the (i+1)$^{th}$ in energy level ordering (which is not necessary the order you put originally in your level file, EXCEPT for ground state, cf FIG.{fig:diagonalization}). But, for the "sortie" or analysis Level[i] keeps its characteristics (such as M values) given in the input Level file: only Energy\_cm is updated. + + +% Because the magnetic $m$ quantum number, that defines the quantification of the light, is not anymore a good quantum number, the angular emission pattern for the spontaneous emission is done isotropically. + + \subsection{Overview external versus internal dynamics} + +We do not discuss here the Kinetic Monte Carlo (KMC) neither the N-Body solver used to solve rate equations, this is discussed in PRA 89, 043410 (2014). +But we explain the way how code calculates the evolutions for $N$ particles, in order for interested people to modify it. +The main part is the main.cpp file in the + \textit{ while(velocity\_scaling == false)} +loop (before is a tentative to reach thermal equilibrium is a trap using the Berendsen thermostat Algorithm) and especially the +\textit{ calcul\_rates\_molecules} +function. + +The code calculate a time for an internal state evolution dt\_KMC (typically one over the maximal rate) and compare it to the time for the external state evolution dt\_dyn (that is now fixed and given is a parameter in the liste\_Param, even if a commented line to calculate it can by tried). +Then the internal evolution \textit{do\_reaction} and the external \textit{evolve\_step} evolution +depends on the Choix\_algorithme\_Monte\_Carlo and Choix\_algorithme\_N\_corps parameters chosen in in Liste\_Param. + For instance the Choix\_algorithme\_N\_corps is commented in the Liste\_Param. This can be of importance if Coulomb interactions are present or not, or if the dipolar force is included (not well calculated for spectrally shaped laser for instance) or if we calculate it directly using gradient of the fields analytical formula (if implemented) + or through the potential derivative (this is the most general way fo doing it). + + \subsection{Calcul (internal) rates molecules} + +The \textit{ calcul\_rates\_molecules} +function is the most important one. + +In order to not spent too much time on updating all the rates of all molecules we only recalculate the rate of the molecule (number\_mol) that has evolved internally. All others rates will be updated only after (t\_mise\_a\_jour) the dynamical (external state evolution dt\_dyn) time, so when they have moved enough to be in another environment (laser or fields intensity for instance) where the excitation-deexcitation rates have evolved. + +It is possible to force some rates (like by using Pompage\_optique\_force paramter) but genearly we let the system calculate first the spontaneous emission rate and then the key function is the \textit{ \textbf{rates\_molecule}} function. +It is quite complex but commented, here I simply mention that the local parameters such as local intensity, polarization, dipole moment $d$ etc... are calculate and the rate is calculated in \textit{ \textbf{rates\_single\_molecule\_laser\_level}} that is usually the only function that has to be modified if you want to add a new laser type (such as Black Body one). +The stimulated and absorption rate for an $i\leftrightarrow j$ transition for a laser of polarization vector $\bm \epsilon$ is given by $$\gamma= \frac{\pi ({\bm d}.{\bm \epsilon})^2 I_\upomega \otimes L(\omega+\bm k.\bm v-\omega_{ij}) }{\hbar^2 \epsilon_ 0 c}$$ (cf Formula (B.7) of the PRA 2014 article with the correct $\hbar^2$ factor!). So with a local intensity resulting of the convolution of the laser spectrum $I_\upomega$ with the +transition Lorentzian $L(\delta) = \frac{\Gamma_{ij}}{2\pi}\frac{1}{\left( \frac{\Gamma_{ij}}{2}\right)^2 + \delta^2}$. + +For instance for a laser with a Lorentzian spectrum of FWHM $\Gamma_L$ we have, for the Doppler induced detuning $\delta = \omega+\bm k.\bm v-\omega_{ij}$, the rate: +$\gamma= +I \frac{\pi ({\bm d}.{\bm \epsilon})^2 }{\hbar^2 \epsilon_ 0 c} + \frac{\Gamma_{ij}+\Gamma_L}{2\pi}\frac{1}{\left( \frac{\Gamma_{ij}+\Gamma_L}{2}\right)^2 + \delta^2}$ where $I= \varepsilon_0 E^2 c /2$ is the total laser irradiance (intensity). + + + + \subsection{Calcul (external) motion} + +The \textit{ evolve\_step} is the function that evolves the external degree of freedom depending on the chosen algorithm (Verlet, Boris, ..) and most important on the way we calculated the force. We can use directly the acceleration or the derivative of the potential (depending on the choix\_epsilon parameter typically 10nm). +The fastest is clearly the use of the acceleration calculate in the + the key function is the \textit{ \textbf{new\_acc}} function. But this require that the gradient of the fields are analytically calculated. This is not the case for the dipolar potential neither if there is $N$ body interaction where in this case algorithm use the gradient of the potential to calculate the force through the \textit{ \textbf{new\_pot}} function. The dipolar potential requires to calculate all dipolar transitions (so it calls the rates\_molecule function) and this might be very slow! + + + \subsection{Comments} + +The code has evolved and because it is time consuming ot keep all the time the internal Energy of the molecule correct (especially if dipolar potential is used) we do not use anymore the +set\_pot\_all\_mol function and and we therefore do not +the Internal\_state.Energy\_cm is not correct. It should not be used but (see rates\_molecule) recalculated when needed. + +In order to avoid gigantic storage we have single Levels and Lines files and ALL particles point to this and only the Zeeman , Stark and dipolar shift are added to this. For more complex situation where the internal state quantum numbers are modified for instance we need to use the Levels\_Lines\_Diagonalized + + \subsection{Levels Lines Diagonalized } +This is controled using the is\_Levels\_Lines\_Diagonalized parameter + + \section{Performance test} + + N=100 Hydrogen atoms during 50 microsecond and plot every microsecond. 64.571s with graphics versus 57.502 without and 55.826 without any output + \footnote{ Depending on what the computer is doing meanwhile those times can fluctuate within few percent}. + + + \subsection{Nb of molecules} + + \begin{tabular}{|c|c|} + \hline +Time & Nb atoms \\ +\hline +\hline +0.632 & 1 \\ +\hline + 6.984 & 10 \\ + \hline + 26.362 & 50 \\ + 57.502 & 100 \\ + \hline + \end{tabular} + + So the code is very linear in $N$ which is good news ! This is because the particle are not charged if not probably (to be tested) the variation will be in $N^2$. + + \subsection{Kinetic Monte Carlo algorithm} + +It is be interested to compare them (cf + https://en.wikipedia.org/wiki/Kinetic\_Monte\_Carlo) + because the default one + Kinetic\_Monte\_Carlo + is not the fastest in principle but First\_Reaction\_Method + is also perfect as well as Random\_Selection\_Method if the rate are time independent. + + + + + \begin{tabular}{|c|c|} + \hline + Time & Algorithm \\ + \hline + \hline + 58.604 & Kinetic Monte Carlo (0) \\ + \hline + 132.343 & Random Selection Method (1) \\ + \hline + 73.606 & First Reaction Method (2) \\ + \hline + 6.118 & Fast Rough Method (3) \\ + \hline + 0.537 & No laser included \\ + \hline + \end{tabular} + + So Fast Rough Method (to be tested in more detail) may be a good way to start. + +Random Selection Method has probably a problem in the code to be this slow! + + + + \subsection{Motion algorithm} + + for dt\_dyn\_epsilon\_param = $10^{-7}$ the time (for 100 atoms) is 57.502s whereas for $10^{-8}$ the time is 72.933s. Always choix epsilon is 1e-8. + + For 1e-7 we made test of the algorithm. Obviously the accuracy of higher order are better so dt\_dyn\_epsilon\_param can be reduced if using such algorithm but this gives an idea. + + \begin{tabular}{|c|c|} + \hline + Time & Algorithm \\ + \hline + \hline + \\ + 44.639 & Aucun N corps (-1) \\ + \hline + 49.647 & Verlet acc (sans force dipolaire) (1) \\ + \hline + 252.635 &Verlet pot (avec potentiel dipolaire) (2) \\ + \hline + 86.587 & Yoshida6 acc (3) \\ + \hline + 113.549 & Yoshida6 pot (4) \\ + \hline + 474.885 & Verlet pot gradient high order (6) + \\ + \hline + 49.341 & Boris Buneman (with Magnetic field for charged particles) \\ + \hline + \end{tabular} + + + + + \section{Futur} + Despite the fact that the code could largely be improved to use more C++ spirit (like maps between reaction and rates, ...), a long list of possible improvements exists among them are: + + \begin{itemize} + + \item Use of adaptive time steps (like t\_evol\_ext) for the algorithms (under consideration). + + \item Possibilities to use more general laser beam (Laguerre Gauss, others polarizations). Put the phase given by the polarizations to take into account linear polarisation in the interference lattice case. + + \item Optimize the link between the renew of the rates, the KMC steps and the external evolution steps. For instance if the acceleration is known we do not need to recalculate each time in the evolution algorithms ... + + \item Parallelization of the code. Using OpenMP for multiprocessor seems quite easy: If needed, download the last MinGW 64bits version. + Copy-paste and erase the old one in Codeblock directory. Then in Global Compiler setting (or simply in your project) use in Other option -fopenmp. + Linker settings: Adds the MinGW/bin libgomp-1.dll. Then test using simple program + with \# include + + \# pragma omp parallel + + + \item Combine electric and magnetic field of arbitrary orientations. This is partially done using the diagonalization cf section \ref{diagonalization} + + \item Treat chemical reactions during collisions. + + \item Treat coherent dark states by choosing the proper basis. + + \item Use an ionization or photodetachment cross-section which is dependent on the energy. + + \item For strongly focused lasers, we can put the local wave-vector $\bf k$, not the global one as it is now. + + \item Draw lasers using the hyperbolic function (nor the elliptic one). + + \item Improve the statistical initial distribution. Until now we calculate the trapping field using a linear approximation for the potential energy. + + \item Improve the calculation of the dipolar shift. Until now the dipolar potential is not included in the shift for the transition. This avoids accumulation, but in some cases, it may be good to have it. + + \item Improve performance using GNU Gprof (Code Profiler Pluggin in Code::Blocks) + + + \end{itemize} + + + + \newpage + + \appendix + \section{Use of Pgopher} + + As mentioned before you can use Pgopher (pgopher.chm.bris.ac.uk/) to create your input files. It is in fact recommended because they have been written from it. + + Be sure to have a good simulation. For instance for a single pair of equivalent nuclei (such as in I$_2$) the statistical weights should be SymWt=1, AsymWt = 0, rather than both 1. + Be sure to have enough J but not too much to avoid too big files... + + So read carefully Pgopher manual. + + Then in the Pgopher data use the following options. Hopefully with obvious notations: + + \begin{itemize} + \item + MIXTURE: + Precision 12 + + QuantumNumberFormat 2J. But be careful that all values such as tensor rank, max J are thus doubled, so it is sometimes difficult to follow them. So it is better to do this only at the end, it is just use to produce the "Levels" and "Lines" files. + + BField 1e-10. In order to separate M levels and have all transitions! + + \item SIMULATION: + IntensityUnits: EinsteinA (to have the rate for spontaneous emission) + + + \item SPECIES: + ShowJ, ShowOmega, ShowN, .. all TRUE + + + + \item TO PRODUCE THE "LINES" FILE: Use the following option + File Export Line List .txt (tab separation). Intensity Threshold 1e-8. No "Fit File Format" + + + \item TO HAVE THE ENERGY LEVELS IN FIELDS: + + View, Levels List (To have the energy at each points). Verify to have All symmetry, Omega M values ... + Then use "Track State" and click on "Summary". This gives levels + fit linear + quadratic of the field dependence. So be careful to plot with the proper B field T values (0-1T or 0-1mT for instance) + Save the file in LEVEL. + + + + \item THEN GO TO ORIGIN (http://www.originlab.com/) or to any other data acquisition software (in the Directory Data: Pgopher\_Level\_List.opj) and follow the following procedure. + + Your case can be slightly different if you have more molecules or several vibrational levels or .. so adapt it! + + + \begin{itemize} + + + \item To produce the "LEVELS" file: + + Remove the \% from the LEVEL file + + Use Import Wizard in Origin with 11 headers, 1 subheader (should be recognized). + The name of the columns should be (if not modify by coping this line, or use the example in): + + Molecule Manifold 2M Sym \# g Population Label State 2J 2N 2Omega Fn parity*M Energy Linear Dipole Err Quadratic Err 2\_Level Delta C Dipole2 Err + + + Sometimes Pgopher does not create the first column Molecule neither the last columns of E\_2\_Level ... + + + Then we have to calculate the C and $\Delta$ (that is Delta) coefficients when they are not given, that is if Level Delta C Dipole2 Err columns are missing. + If the effect is not linear but quadratic or more complex then create the 2\_level fit by: + Add one column for numbers, + Sort by 2\_Level. + For those who do not have a 2\_Level then create one (for instance take the Linear and the same energy because C=Linéaire, Delta=0). The intermediate case between linear and quadratic is more complex and an appropriate formula should be derived. + Sort again (a priori the file is sort in M, Sym and \#). It is also possible to sort in Energy + + Duplicate the workbook and keep only the following columns (v is State): + + Manifold 2M Sym \# population v 2J 2N 2Omega Energy Delta C + + + Remark: One possibility to remove "v=" that appears when exporting from Pgopher in "State" and to keep only the vibrational level value is: after the exportation remove "v=" (and change "," in "." if needed) and import again. + + Then use only values not the text, so: + In Manifold use 0 for the X state (lower) et 1, 2, ... for higher Manifold and + +/-1 for Sym. + + If wanted you can sort the workbook in Energy and modify the population column to put the desired one. + Export the Workbook without headers (no Label) and in a file with .dat extension + + Check that the decimal are with "." not "," + Remove the space at the end of the file. + + + + + + \item TO PRODUCE THE "LINES" file: + + Remove the first and last 2 lines of the file LINES.txt + Import it in Origin (using options: delimator, Tab/space). + Change the name of the lines: (copy paste the one below) + + Molecule Upper Manifold 2M' Sym' \#' Lower Manifold 2M" Sym" \#" Position Intensity Eupper Elower Strength A Width Branch LabelUpperManifold state 2J' 2N' 2Omega' Fn' 2M' Sym Upper Manifold state 2J'' 2N'' Omega'' Fn'' 2M'' + + + Duplicate the workbook and keep only the columns: + + UpperManifold 2M' Sym' \#' LowerManifold 2M" Sym" \#" Position Intensity Eupper Elower Strength + + then do the same as for Levels: X=0, Sym =+/-1 ... + + Finally divide by 3 the Strength column and export in .dat file + + \end{itemize} + + \end{itemize} + + + \section{Detail of laser interaction} + +The code is based on \cite{comparat2014molecular}; on \cite{chaneliere2018phase} (supplementary material) for quantization, recoil and Doppler effects; and on +\cite{manual_Steck,varshalovich1988quantum} for vector and angular momenta. +We recall here some important points. The notations differ sometimes from \cite{comparat2014molecular} but are more general and should be preferred, because we use less assumptions here (especially about the reality of some vectors). + + + \subsection{Spherical and helicity vectors } + + We use the notation of \cite{varshalovich1988quantum} such as the (covariant) spherical vectors + $ {\bf e}_0 = {\bf e}_z, {\bf e}_{\pm 1} = \mp \frac{{\bf e}_x \pm + i {\bf e}_y} { \sqrt{2}}$. + Using ${\bf{e}}^q = ({\bf{e}}_q)^* = (-1)^q {\bf{e}}_{-q}$ (that leads to the normalization ${\bf{e}}^p {\bf{e}}_q = \delta_{pq} $) we find for any (complex) vector + $$\bm A = \sum_q A^{q} {\bf{e}}_q = \sum_q (-1)^q A_{-q} {\bf{e}}_q $$ + where + $A_q = \bm A. + {\bf{e}}_q$ so for instance $A_0 = A_z, A_{\pm 1} = \mp (A_x \pm + i A_y)$. + % If $\bm A$ is a \textit{real} vector we have $\bm A = (\bm A)^*$ and $ A^q = A_q^*$ so $\bm A = \sum_q A_q^* {\bf{e}}_q $. + We will often have the case where the $A_q$ or $A^q$ are reals (example of the dipoles or of pure laser polarization) but in general we should keep in mind that the vectors are complex. + + + + \subsection{Lasers using complex notations} + + + + + The electromagnetic field, due to the lasers $\rm L$, can be written + $${\bm E}(\bm r,t) = {\bm E'}(\hat{\bm r},t)+ {\bm E'}^\dag(\hat{\bm r},t) = \frac{1}{2}\sum_{\rm L} \left[ {\bm E}_{\rm L} e^{i( {\bm k}_{\rm L}. {\bm r} - \Phi_{\rm L} + (t))} + {\bm E}_{\rm L}^\ast e^{-i( {\bm k}_{\rm L}. {\bm r} - \Phi_{\rm L} + (t))} \right] $$ + + the irradiance, called improperly intensity, is + $ + I_{\rm L}= \varepsilon_0 |E_{\rm L}|^2 c/2 $. + + + + The Doppler effect, and the laser linewidth, are taken into account by writing $\Phi_{\rm L} (t) = (\omega_{\rm L} - {\bm k}_{\rm L}. {\bm v}) t + \Phi^{\rm L} (t)$. Where $\Phi^{\rm L} (t) $ is a fluctuating phase. + + + As shown in Fig. \ref{fig:laseraxispolarization}, + we use the (covariant polar basis) frame linked with the laser propagation: + $({\bf{e}}'_{\rm x} = {\bf{e}}_{\theta} , {\bf{e}}'_{\rm y} = {\bf{e}}_{\phi}, {\bf{e}}'_{\rm z} = {\bf{e}}'_{\rm r} = \bm{k}/\| \bm{k} \|)$ . + The laser polarization is conveniently described in the (covariant) helicity basis + $ {\bf e}'_0 = {\bf e}'_z, {\bf e}'_{\pm 1} = \mp \frac{{\bf e}'_x \pm + i {\bf e}'_y} { \sqrt{2}}$. + For each laser $\rm L$ + the polarization vector, defined by + $ {\bm E}_{\rm L}(\bm r,t) = E_{\rm L}(\bm r,t) {\bm \epsilon}_{\rm L} $, is $ {\bm \epsilon}_{\rm L} = + \sum_{p= -1,0,+1} \epsilon'^p + {\bf e'}_{p} $. + + + In the code we deal (for simplicity and for calculus speed) only with reals. So for instance + \textbf{the polarisation is coded using only 3 real parameters Pol\_circulaire\_right\_sm ($a_{-}$), Pol\_circulaire\_left\_sp ($a_{+}$) and polar\_angle\_degree ($\Psi$) (in degree in Liste\_Param). These 3 parameters + define + \begin{equation} + {\bm \epsilon}_{\rm L} = {\rm Pol\_circulaire\_right\_sm} \ e^{i \Psi} {\bf e'}_{-1} + {\rm Pol\_circulaire\_left\_sp} \ e^{-i \Psi} + {\bf e'}_{+1} = a_{-} \ e^{i \Psi} {\bf e'}_{-1} + a_{+} \ e^{-i \Psi} + {\bf e'}_{+1} + \end{equation}} + % ${\bf{e}}'_{\rm L,pol} = \{ Pol\_circulaire\_right\_sm = \epsilon'^{-1} e^{-i \Psi}, \epsilon'^0 , Pol\_circulaire\_left\_sp = \epsilon'^{+1} e^{i \Psi} \}$ + + This does not authorize arbitrary polarizations but only pure circular (right with $\epsilon'^{-1} =1$, or left with $\epsilon'^{+1}=1$) or + a pure linear polarization. For example, (cf. Fig. + \ref{fig:laseraxispolarization}) linear polarization turned by an angle $\Psi$ from $ {\bf e'}_{x} $ +is ${\bm \epsilon}_{\rm L} = {\bf e}'_x \cos\Psi + {\bf e}'_y \sin \Psi = + \frac{1}{\sqrt{2}} e^{i \Psi} {\bf e'}_{-1} - \frac{1}{\sqrt{2}} e^{-i \Psi} + {\bf e'}_{+1} $, that is $a_{-} = \frac{1}{\sqrt{2}}, a_{+}= - \frac{1}{\sqrt{2}}$. + % and is thus ${\bf{e}}'_{\rm L,pol} = \{ \frac{1}{\sqrt{2}} e^{i \Psi}, 0 , - \frac{1}{\sqrt{2}} e^{-i \Psi} \}$ which is not real. + + + + \subsection{Transition dipole moment} + + + + The transition dipole moment + ($\bm d = e \bm r$ in the simple case of H, Ps or alkali atoms, and we will use often this simplification for the notation) + between 2 levels is defined (for now in the lab fixed frame but this will be precised in section \ref{pol_vector}) as + $ \bm d_{ij} = \langle i | \bm d | j \rangle = \sum_q (-1)^q d_{ij;q} {\bf{e}}_q = \sum_q d_{ij;q} {\bf{e}}^q $ so $ d_{ij;q} = \bm d_{ij}.{\bf{e}}_q$. The notation $d_{ij}^{(q)} = d_{ij;q}$ is often used but has to be avoided because of possible confusion with the (contravariant) notation $d_{ij}^{q}$. + The correct component that forms an irreductible tensor (rank 1) $\hat d_{1q} = \hat d_{q}$ are $ d_{ij;-1},d_{ij;0},d_{ij;+1} $. + In the code this vector is called + the "polarization" dipole vector $\bm d_{ij} $ and is recorded as $ \{ d_{ij;-1},d_{ij;0},d_{ij;+1} \} $ (obviously in C++ the array number will be respectively dipole[0], dipole[1], dipole[2]). + With the proper (Condon-Shortley's type) convention \cite{varshalovich1988quantum}, these dipoles are reals. + + % We also the polarization dipole vector by ${\bf{e}}_{\rm pol,ij} = \bm d_{ij}/|d_{ij}| = \{ d_{\rm pol,ij}^{-1}, d_{\rm pol,ij}^0 , d_{\rm pol,ij}^{+1} \} $ + + + + + + \subsection{Absorption, stimulated or spontaneous emission} + + For a transition between two states $|j\rangle$ to $|i\rangle$, it is important to known if we deal with absorption (rising level energy) or stimulated or spontaneous emission (lowering level energy) to know which term in the rotating wave approximation shall be used. + + \textbf{ In the following, we assume $E_j> E_i$}. + + \subsubsection{Ordered energy levels and rotating wave approximation} + + +The rotating wave approximation leads (for level $j$ above level $i$: $E_j>E_i$) leads to: + + \begin{equation*} + \hat H = \frac{\bm \hat {\bm p}^j}{2 m} + + V_i(\hat {\bm r},t) |i\rangle\langle i| + V_j(\hat {\bm r},t) |j\rangle \langle j| + - \langle j | q \hat {\bm r}| i \rangle .\bm E' (\hat {\bm r} ,t) |j\rangle \langle i| - \langle i | q \hat {\bm r}| j \rangle . \bm E'^\dag (\hat {\bm r} ,t) |i\rangle \langle j| \label{hamiltonianRWA} + \end{equation*} + + where we have added some potential traps $V_i$ and $V_j$ to be more general. + % where the coupling term is $\displaystyle \hat V = - \bm d .\bm E' (\hat r ,t) = - \frac{\bm d}{j}\sum_{\rm L} {\bm E}_{\rm L}(t) e^{i( {\bm k}_{\rm L}. {\hat{\bm r}} - \omega_{\rm L} t - \Phi_{\rm L}(t) )} = \sum_{\rm L} \hat V_{\rm L} $. + + The recoil effect will be present only after the interaction by a $\hbar \bm k$ term added to the momentum. This is clarified, cf Eq. (9) and (20) of \cite{chaneliere2018phase}, by using the (single plane wave, in a volume $L^3$) + quantized field: + $\displaystyle \hat{\bm{E}} (\bm{r},t) = \sum_{\bm{k},\sigma} i \sqrt{\frac{ \hbar \omega_k}{2 \epsilon_0 L^3} } \left( \hat a_{\bm{k} \sigma} e^{- i \omega_k t} \bm{\epsilon}_{\bm{k}\sigma} {\rm e}^{i \bm{k}.\bm{r} } - \hat a_{\bm{k} \sigma}^\dag e^{ i \omega_k t} \bm{\epsilon}_{\bm{k}\sigma}^\ast {\rm e}^{-i \bm{k}.\bm{r} } \right)$, where $ {\bm \epsilon}_{\bm k \pm 1} = {\bf e}'_{\pm 1}$. We thus have: + \begin{equation*} + \hat H = \frac{\hat{\bm p}^2}{2 m} + + V_i(\hat{\bm r},t) |i\rangle\langle i| + V_j(\hat{\bm r},t) |j\rangle \langle j| \label{eq_base_at} + - \bm d_{ji}. \hat{\bm E'} (\hat{\bm r} ,t) |j\rangle \langle i| + \bm d_{ij} .{\hat{\bm E'}}^\dag (\hat{\bm r} ,t) |i\rangle \langle j| + + \sum_{\bm{k} \sigma} \hbar \omega_k \left( \hat a^\dag_{\bm{k} \sigma} \hat a_{\bm{k} \sigma} + 1/2 \right) + \end{equation*} + where $\bm d_{ji} = \langle j | q \hat {\bm r}| i \rangle = \bm d_{ij}^* $ is the transition dipole element. The quantization clarifies the recoil effect because of + $ + e^{ \pm i \bm k.\hat{\bm r}} | \bm p\rangle = |\bm p \pm \hbar \bm k\rangle$. + + + + Descriptions of the rate equations and forces can be find in the appendix of Ref. \cite{comparat2014molecular,chaneliere2018phase} and are not recalled here. + + + + + + + + \subsubsection{Absorption, Stimulated or spontaneous emission} + + + + Absorption is thus a transition $i \rightarrow j$ ($E_j> E_i$). For absorption + the only relevant term is due to $-\bm d.\bm E'$ through the Rabi frequency\footnote{ For more generality we do not (yet) assume real dipoles and so the notation is different (better here even if careful has to be taken in the $i,j$ order because $\Omega_{ji} =\Omega_{i \rightarrow j} $ ) than in \cite{comparat2014molecular}.} +\begin{equation} +\hbar \Omega_{ji} = E_{\rm L} \langle j, \bm p + \hbar \bm k | \hat{\bm d} . \bm \epsilon_L + e^{ i \bm k.\hat{\bm r}} | i, \bm p\rangle = E_{\rm L} \bm d_{ji} . \bm \epsilon_L = E_{\rm L} + \sum_q d_{ji;q} {\bf{e}}^q . \sum_{p} \epsilon'^p {\bf e'}_{p} + \label{Rabi_frequancy} + \end{equation} + + + + + + The stimulated emission $j \rightarrow i$ with the same laser is govern by the $-\bm d.{\bm E'}^\dag$ term and thus arises with the Rabi frequency +$\hbar \Omega_{ij} = E_{\rm L} \langle i, \bm p - \hbar \bm k | \hat{\bm d} . {\bm \epsilon_L}^\dag + e^{ - i \bm k.\hat{\bm r}} | j, \bm p\rangle = E_{\rm L} \bm d_{ij} . {\bm \epsilon_L }^\dag =\hbar \Omega_{ji}^*$ + + We recover the well known fact that the dipole transition rates are the same (conjugated Rabi frequencies) for spontaneous and for stimulated emission. + + + The simplest (ideal) case is when + \begin{itemize} + \item The quantization axis and laser axis (for the polarization) are equal ${\bf{e}}_q={\bf{e'}}_q$. In this case, the absorption is driven by $\hbar \Omega_{ji} = E_{\rm L} \sum_q d_{ji;q} \epsilon'^q $ + \item The laser is of pure polarization $ \epsilon'^q =1$ for a given $q$ and $0$ for others. So $\hbar \Omega_{ji} = E_{\rm L} d_{ji;q} $ + \item states are pure (that is with well defined magnetic quantum numbers $m_i,m_j$ projection on the quantization axis ${\bf{e}}_0$). So $\hbar \Omega_{ji} = E_{\rm L} d_{ji;q} = E_{\rm L} \langle j | d_{1q} | i \rangle $ will verifies $m_j = q+ m_i $. We recover the fact that + $ q=-1$ for a $\sigma-$, $ q=0$ for a $ \pi$ and + $ q= +1$ for a $\sigma+$ light. + \end{itemize} + + +We now have to treat the most general case where none of these 3 assumption is correct. + \subsection{Rotation matrices} + + We have to deal with three frames: + \begin{itemize} + \item The fixed lab frame $(\bf{e}_{\rm x}, \bf{e}_{\rm y}, \bf{e}_{\rm z} )$ + \item The local (different for each particle position $\bm r$) field $\bm F(\bm r)$ frame, $(\bf{e}_{\rm X}, \bf{e}_{\rm Y}, \bf{e}_{\rm Z})$. It defines the quantization axis. It will also be noted + $(\bf{E}_{\rm X}, \bf{E}_{\rm Y}, \bf{E}_{\rm Z} = \bm{F}/\| \bm{F} \|)$ in order to define ${\bf{E}}_{\pm 1}$ without any confusion with ${\bf{e}}_{\pm 1}$. + \item The laser frame $(\bf{e}'_{\rm x}, \bf{e}'_{\rm y}, \bf{e}'_{\rm z} = \bm{k}/\| \bm{k} \|)$. + \end{itemize} + These frames are defined by their $z,z',Z$ axis, and the angle of rotation around this axis is defined such that (cf Fig. + \ref{fig:laseraxispolarization}), taken the example of the laser $z'$ frame, the frame is the polar frame of which $Oz'$ is the direction and $Ox'$ is the meridian. + + + All this explain that in the code a reaction is coded using the type\_codage\_react reaction=$\{n\_mol; n\_laser; \bm F; \bm \epsilon_L; \bm k; final\_internal\_state\}$ for the particule number $n\_mol$, under the laser number $n\_laser$ (-1 for spontaneous emission). + + \subsubsection{Euler angles} + + To go from one $(\bf{e}_{\rm x}, \bf{e}_{\rm y}, \bf{e}_{\rm z} )$ frame to a new one $(\bf{e}'_{\rm x}, \bf{e}'_{\rm y}, \bf{e}'_{\rm z} )$ it is convenient to use the Euler angles. + Different conventions exists: Mathematica and \cite{varshalovich1988quantum} (1.4 schema A) are in the so called z y z (noted also Z Y Z) convention, whereas Wikipedia is in z x z convention. For completeness, we thus recall here the + Euler rotations angles $(\alpha,\beta,\gamma)$ convention. + For instance in the + z y z convention: + \begin{itemize} + \item the first rotation is by an angle $\alpha$ about the $z$-axis. + \item the second rotation is by an angle $\beta$ about the new $y$-axis + \item the third rotation is by an angle $\gamma$ about the new $z$-axis (now $z'$). + \end{itemize} + + Clearly (Fig. + \ref{fig:laseraxispolarization}) our convention to use + the spherical basis leads simply to + $(\alpha,\beta,\gamma) = (\phi,\theta,0)$ in the + z y z convention, but to $(\alpha,\beta,\gamma) = (\phi+\pi/2,\theta,-\pi/2)$ in the z x z convention. + + The z x z convention is the one used (for historical reason) in the code (cf Euler\_angles function). + The z x z convention is useful to find the polar angle $\phi,\theta$ knowing only the vector ${\bf{e}}'_{\rm z} = x_e {\bf{e}}_{\rm x} + y_e {\bf{e}}_{\rm y} + z_e {\bf{e}}_{\rm z} $ that defines the new frame by: + $\alpha = \phi+\pi/2 = {\rm atan2}(x_e, - y_e)$ and $\beta = \theta = \arccos(z_e)$. + + The main function in the code is thus rotation\_axis\_lab that calculates, using simple notation such as $s_1 = \sin (\alpha)$ or $c_3 = \cos (\gamma)$ , the new coordinates + $$ \begin{pmatrix} x \\ y \\ z + \end{pmatrix} + =\begin{pmatrix}c_{1}c_{3}-c_{2}s_{1}s_{3}&-c_{1}s_{3}-c_{2}c_{3}s_{1}&s_{1}s_{2}\\c_{3}s_{1}+c_{1}c_{2}s_{3}&c_{1}c_{2}c_{3}-s_{1}s_{3}&-c_{1}s_{2}\\s_{2}s_{3}&c_{3}s_{2}&c_{2}\end{pmatrix}. \begin{pmatrix} x' \\ y' \\ z' + \end{pmatrix}$$ + The reverse rotation\_lab\_axis is used to find the laser intensity (cf intensity\_lab\_axis function) at the particle location $\bm r = x {\bf{e}}_{\rm x} + y {\bf{e}}_{\rm y} + z {\bf{e}}_{\rm z} $. + \subsubsection{Polarization vectors} + \label{pol_vector} + + % We can write the laser polarization vector in the two frames as \cite{varshalovich1988quantum} Eq. 1-(49): $ {\bm \epsilon} = \sum_{p'= -1,0,+1} {\epsilon'}^\ast_{p'} {\bf e'}_{p'} = \sum_{p= -1,0,+1} \epsilon_p^\ast {\bf e}_{p} $, with $ \epsilon_{p} = \sum_{p' =0,\pm 1 } (-1)^{p'} \epsilon'_{p'} D_{p p'}^{\ast (1)} (0,\theta,\varphi)$. + + To evaluate Eq. \ref{Rabi_frequancy} we + write the laser polarization vector in the three frames + $ {\bm \epsilon}_{\rm L} = + \sum_p \epsilon'^p + {\bf e'}_{p} = \sum_p \mathcal{E}^p + {\bf E}_{p} = \sum_p \epsilon^p + {\bf e}_{p} + $. + Using $ {\bm \epsilon}^. = \begin{pmatrix} \epsilon^{-1} \\ \epsilon^{0} \\ \epsilon^{+1} + \end{pmatrix}, {\bm e}_. = \begin{pmatrix} {\bf e}_{-1} \, {\bf e}_{0} \, {\bf e}_{+1} + \end{pmatrix}, + {{\bm \epsilon}'}^. = \begin{pmatrix} {\epsilon'}^{-1} \\ {\epsilon'}^{0} \\ {\epsilon'}^{+1} + \end{pmatrix} = \begin{pmatrix}a_{-} \ e^{i \Psi} \\ 0 \\ a_{+} \ e^{-i \Psi} + \end{pmatrix} , {\bm e}'_. = \begin{pmatrix} {\bf e'}_{-1} \, {\bf e'}_{0} \, {\bf e'}_{+1} + \end{pmatrix}, + {\mathcal{\bm E}}^. = \begin{pmatrix} \mathcal{E}^{-1} \\ \mathcal{E}^{0} \\ \mathcal{E}^{+1} + \end{pmatrix}, {\bm E}_. = \begin{pmatrix} {\bf E}_{-1} \, {\bf E}_{0} \, {\bf E}_{+1} + \end{pmatrix}$ we have + $ {\bm \epsilon}_{\rm L} = {\bf e'}_. {\bm \epsilon'}^. = {\bf E}_. \mathcal{\bm E}^. = {\bf e}_. {\bm \epsilon}^. $ + + + + We will note $\phi_{\bm k},\theta_{\bm k}$ the polar angles of ${\bm k}$ (to go from the lab fix frame to the laser frame) and $\phi_{\bm F},\theta_{\bm F}$ the polar angles of ${\bm F}$ (so to go from the lab frame to the field frame). Eq. (1.1 53) of Ref. + \cite{varshalovich1988quantum} gives + $ \sum_p {\bf e}_{p} {\rm D}_{p p'}^{1} (\phi_{\bm k},\theta_{\bm k},0) = {\bf e'}_{p'} $ +that is +$ {\bf e}_. {\rm {\bm D}} (\phi_{\bm k},\theta_{\bm k},0) = {\bf e'}_. \mbox{ and similarly } {\bf e}_. {\rm {\bm D}} (\phi_{\bm F},\theta_{\bm F},0) = {\bf E}_. $ + where + $({\rm {\bm D}})_{ij} = {\rm D}_{i j}^{1} $ is the + WignerD function. + Several conventions exists: Mathematica + WignerD$[\{j,m_1,m_2\},\alpha, \beta, \gamma]= {\rm D}_{m_1,m_2}^j (-\alpha, -\beta, -\gamma)$ of \cite{varshalovich1988quantum}. We use the \cite{varshalovich1988quantum} concention, that is also the one chosen by Wikipedia with: + $ {\rm {\bm D}} (\phi,\theta,0) = + \begin{pmatrix} + \frac{1}{2} e^{i \phi} (1+\cos \theta) &\frac{e^{i \phi} \sin \theta}{\sqrt{2}} & e^{i \phi} \sin^2(\theta/2) \\ + -\frac{\sin \theta}{\sqrt{2}} & \cos \theta & \frac{\sin \theta}{\sqrt{2}} \\ + e^{-i \phi} \sin^2(\theta/2) & -\frac{e^{-i \phi} \sin \theta}{\sqrt{2}} & \frac{1}{2} e^{-i \phi} (1+\cos \theta) \end{pmatrix} + $ with the order $i,j = -1,0,1$ in the lines and columns. + + Because the states $|i\rangle$ are defined with the quantization axis frame ${\bf{E}}_.$ we note + $ \bm d_{ij} = \langle i | \bm d | j \rangle = \sum_q D_{ij;q} {\bf{E}}^q $ with $ D_{ij;q} = \bm d_{ij}.{\bf{E}}_q$. So in matrix notation, with +$ {\bm D_{ij}}_. = \begin{pmatrix}D_{ij;-1} \, D_{ij;0} \, D_{ij;+1} \end{pmatrix} = \begin{pmatrix}D_{-1} \, D_{0} \, D_{+1} \end{pmatrix} $ + and $ {\bm E}^. = \begin{pmatrix} {\bf E}^{-1} \\ {\bf E}^{0} \\ {\bf E}^{+1} + \end{pmatrix}$, we have + $\bm d_{ij} = {\bm D_{ij}}_. {\bf E}^. $ + + We can thus now write Eq. \ref{Rabi_frequancy} as + \begin{equation} + \hbar \Omega_{ji} / E_{\rm L} = \bm d_{ji} . \bm \epsilon_L = [ {\bm D_{ij}}_. {\bf E}^. ].[ {\bf e'}_. {\bm \epsilon'}^. ] + % = [{\bm D_{ij}}_. {\bf E}^. ].[ {\bf E}_. {\rm {\bm D}}^{-1} (\phi_{\bm F},\theta_{\bm F},0) {\rm{ \bm D}} (\phi_{\bm k},\theta_{\bm k},0) {\bm \epsilon'}^. ] + = {\bm D_{ij}}_. {\rm {\bm D}}^{-1} (\phi_{\bm F},\theta_{\bm F},0) + {\rm{ \bm D}} (\phi_{\bm k},\theta_{\bm k},0) \begin{pmatrix}a_{-} \ e^{i \Psi} \\ 0 \\ a_{+} \ e^{-i \Psi} + \end{pmatrix} + \end{equation} + + This formula is used in the code in the effectif\_dipole\_local function and the final result is + \begin{eqnarray*} + & & \hbar \Omega_{ji} / E_{\rm L} = \frac{1}{4} e^{-i + (\psi +{\phi_{\bm F}}+{\phi_{\bm k}})} \times \\ + & & \Big[ \cos ({\theta_{\bm k}}) \left(-{a_+}+{a_-} + e^{2 i \psi }\right) \left(\left(e^{2 i {\phi_{\bm F}}}+e^{2 i + {\phi_{\bm k}}}\right) \left(\sqrt{2} {D_0} \sin ({\theta_{\bm F}})+({D_-}-{D_+}) \cos ({\theta_{\bm F}})\right)-({D_-}+{D_+}) \left(e^{2 i {\phi_{\bm F}}}-e^{2 i + {\phi_{\bm k}}}\right)\right) \\ + & & -2 \sin ({\theta_{\bm k}}) e^{i + ({\phi_{\bm F}}+{\phi_{\bm k}})} \left(-{a_+}+{a_-} e^{2 i \psi }\right) \left(\sqrt{2} {D_0} \cos ({\theta_{\bm F}})+({D_+}-{D_-}) \sin ({\theta_{\bm F}})\right) \\ + & & +\left({a_+}+{a_-} e^{2 i \psi + }\right) \left(({D_-}+{D_+}) \left(e^{2 i {\phi_{\bm F}}}+e^{2 i + {\phi_{\bm k}}}\right)-\left(e^{2 i {\phi_{\bm F}}}-e^{2 i {\phi_{\bm k}}}\right) \left(\sqrt{2} {D_0} \sin ({\theta_{\bm F}})+({D_-}-{D_+}) \cos ({\theta_{\bm F}})\right)\right) \Big] + \end{eqnarray*} + + \subsection{Angular distribution of spontaneous emission: recoil} + + + The spontaneous emission rate between a level $| i \rangle $ and $|j\rangle$ is given by + $\Gamma =\|\rm d_{ij}\|^2 C_{{\rm Debye},s} E_{\rm cm}^3$ (function Gamma\_Level\_from\_diagonalized\_dipole in the code). In order to properly take into account the recoil momentum we need to know the angular distribution of the emitted photon. + For this we have to go back to the calculation of the spontaneous emission rate that originates form the quantized field + so from (Fermi golden rule) + $\sum_{\bm k,\pm 1} | \langle i | \bm d | j \rangle. {\bm \epsilon}_{\bm k \pm 1}|^2 = \sum_{\bm k} \left[ \sum_p | \bm d_{ji} . {{\bm e'}_{\bm k}}_p |^2 - | \bm d_{ji} . {{\bm e'}_{\bm k}}_0 |^2 \right] $. So by defining the + "polarization" vector of the emitted light as ${\bf{e}}_{\rm pol} = \bm d_{ji} /\|\bm d_{ji} \|$ we find that the probability distribution, for + the direction $\bm r = \bm k/k$ of the emitted photon, is + given by + $ \frac{3}{8\pi} [1-|\bm r.{\bf{e}}_{\rm pol}|^2]$, with the proper normalization (to $1$). + We recover Eq. (1.45) (see also Eq. (7.427)) of Ref. \cite{manual_Steck}. In the code (get\_unit\_vector\_spontaneous\_emission function) the photon is taken randomly (with the Von Neumann's acceptance-rejection sampling method) using this distribution. % That is in the quantization axis (field) frame $d_{ji} {\bf{e}}_{\rm pol} = \sum_q D_{ij;q} {\bf{E}}^q $. + + \subsection{Diagonalization of the states} + + + In most of the cases the eigenstates themselves are not changing during the evolution, only the energy changes. However, + as explained in section \ref{diagonalization} + we have the possibility + to diagonalize the hamiltonian, for instance, to calculate Zeeman and Stark effect for the magnetic $\bm B$ and electric $\bm E$ fields more exactly. For this purpose, + we give the bare states $|i\rangle_0$, their energies ${E_i}_0$, and the dipole transition moments + (in the Diagonalization\_Energy\_dipole function) as three matrix $\{ \bm d0_{-1},\bm d0_{0},\bm d0_{+1} \} $ in the quantization frame (so always assuming adiabatic following) with $ + (\bm d0_{q})_{ij} = + d0_{ij;q} = {}_0\langle i | \hat {\bm d} | j \rangle_0 . {\bf{E}}_q $. + + + Then, for each local perturbation $\hat V(\bm B(\bm r), \bm E(\bm r) )$ + (the perturbation $\hat V$ matrix is given in the Diagonalization\_Energy function), + we diagonalized $ \hat H = \hat H_0+\hat V$ to get the new eigenvectors + $| i\rangle = \sum_{i_0} {}_0\langle i_0 | i\rangle |i_0\rangle_0 = \sum_{i_0} {\rm \bm evec}_{i_0 i } |i_0\rangle_0 $ with the eigenvectors matrix ${\rm \bm evec}_{i_0 i } = + {}_0\langle i_0 | i\rangle$. We can then calculate the new dipoles + $ \langle i | \hat d_q | j \rangle = ({\rm \bm evec}^\dag.{\bm d0}_q.{\rm \bm evec})_{ij} $ that is coded with the dipole vector $ \{ d_{ij;-1},d_{ij;0},d_{ij;+1} \} $. + + +\bibliographystyle{unsrt} +\bibliography{bibli_user_guide} + + + +\end{document} + + + + diff --git a/User Guide/User Guide Laser Cooling_v2.pdf b/User Guide/User Guide Laser Cooling_v2.pdf new file mode 100644 index 0000000..3702bbf Binary files /dev/null and b/User Guide/User Guide Laser Cooling_v2.pdf differ diff --git a/User Guide/User Guide Laser Cooling_v2.tex b/User Guide/User Guide Laser Cooling_v2.tex new file mode 100644 index 0000000..11d4af7 --- /dev/null +++ b/User Guide/User Guide Laser Cooling_v2.tex @@ -0,0 +1,1392 @@ +% Template article for preprint document class `elsart' +% SP 2001/01/05 +% and 2 sets of keywords - 21.05.03 - file called phys-english.tex +% Modified CG (ESME) for Model 4, single column, 2 titles, abstract/rÈsumÈ, +% English Version for Physique (CRAS series 4, now COMREN) - a Note in English +% Revamped, CG, 18.08.04, adding header, dates, +% and name of presenter + +\documentclass[amsmath,amssymb]{revtex4} + +\usepackage[toc,page]{appendix} + +\usepackage{xcolor} + + +%\def\journal@prl{prl}% +%$@$ifx{$@$journal\journal@prl}{% + + +\def\cpl{Chem. Phys. Lett.} +\def\aj{{AJ}} +\def\araa{{ARA\&A}} +\def\apj{{ApJ}} +\def\apjl{{ApJ}} +\def\apjs{{ApJS}} +\def\ao{{Appl.~Opt.}} +\def\apss{{Ap\&SS}} +\def\aap{{A\&A}} +\def\aapr{{A\&A~Rev.}} +\def\aaps{{A\&AS}} +\def\azh{{AZh}} +\def\baas{{BAAS}} +\def\jrasc{{JRASC}} +\def\memras{{MmRAS}} +\def\mnras{{MNRAS}} +\def\pra{{Phys.~Rev.~A}} +\def\prb{{Phys.~Rev.~B}} +\def\prc{{Phys.~Rev.~C}} +\def\prd{{Phys.~Rev.~D}} +\def\pre{{Phys.~Rev.~E}} +\def\prl{{Phys.~Rev.~Lett.}} +\def\pasp{{PASP}} +\def\pasj{{PASJ}} +\def\qjras{{QJRAS}} +\def\skytel{{S\&T}} +\def\solphys{{Sol.~Phys.}} +\def\sovast{{Soviet~Ast.}} +\def\ssr{{Space~Sci.~Rev.}} +\def\zap{{ZAp}} +\def\nat{{Nature}} +\def\iaucirc{{IAU~Circ.}} +\def\aplett{{Astrophys.~Lett.}} +\def\apspr{{Astrophys.~Space~Phys.~Res.}} +\def\bain{{Bull.~Astron.~Inst.~Netherlands}} +\def\fcp{{Fund.~Cosmic~Phys.}} +\def\gca{{Geochim.~Cosmochim.~Acta}} +\def\grl{{Geophys.~Res.~Lett.}} +\def\jcp{{J.~Chem.~Phys.}} +\def\jgr{{J.~Geophys.~Res.}} +\def\jqsrt{{J.~Quant.~Spec.~Radiat.~Transf.}} +\def\memsai{{Mem.~Soc.~Astron.~Italiana}} +\def\nphysa{{Nucl.~Phys.~A}} +\def\physrep{{Phys.~Rep.}} +\def\physscr{{Phys.~Scr}} +\def\planss{{Planet.~Space~Sci.}} +\def\procspie{{Proc.~SPIE}} +\def\icarus{{Icarus}} +\let\astap=\aap +\let\apjlett=\apjl +\let\apjsupp=\apjs +\let\applopt=\ao + + +\usepackage{isomath} +% Scientific organisations like IUPAP\_, IUPAC\_, NIST\_, BIPM\_, and others recommend typesetting math according to the International Standard ISO 31`Quantities and units` [ISO-31] + +\usepackage{upgreek} % to have roman greek letter + + + + +\usepackage{graphicx}% Include figure files +\usepackage{mathtools}% For \MoveEqLeft +\usepackage{dcolumn}% Align table columns on decimal point +\usepackage{bm}% bold math +\usepackage{rotating} +\usepackage{color} +\usepackage{amssymb} +\usepackage[latin1]{inputenc} +%\nofiles +%\usepackage{epstopdf} +\DeclareGraphicsRule{.tif}{png}{.png}{`convert \#1 `basename \#1 .tif`.png} + + +\begin{document} + +\title{USER GUIDE For the simulation of Laser cooling of particles} +\author{Daniel Comparat} +\affiliation{Laboratoire Aim\'e Cotton, CNRS, Univ Paris-Sud, B\^at. 505, 91405 Orsay, France} + +\date{\today} + + + + +\begin{abstract} +This document gives an introduction to the use of the C++ Laser Cooling code described in PHYSICAL REVIEW A 89, 043410 (2014) + and available on git: https://github.com/dcompara/Laser-interaction-in-fields. +The program solves the rate equations to study laser excitation, forces (scattering + dipolar + magnetic + electric + coulombian interactions). +It has been developed under Code::Blocks and Windows. +The inputs are 2 external files describing the levels (with information about their energy + linear or quadratic Stark, Zeeman effect) and the + transitions lines (dipole transitions, photodetachement or photoionization cross sections) +Then a file named Liste\_Param.h contains parameters to run the simulation such as sample size, temperature, magnetic fields and for the laser beams (waist size and position, polarisation, power, linewidth, wavelength, ...). +When running, the program calculates at time t all absorption and emission rates. Then a Kinetic Monte Carlo algorithm gives the exact time t+dt for an event (absorption or emission) compare this time to a typical external motion time then it evolves in motion and event. +The output is writen in a file containing relevant information such as population in given levels and statistics about velocities (temperature), potential energy ... +Output is also performed through 3D snapshots. +% An update of the modifications done in the code can be find in Modif\_code\_rate\_eq.txt. +\textbf{Any modifications, bugs, improvement, ... should be refereed to +Daniel.Comparat$@$u-psud.fr} +\end{abstract} + + +\maketitle + + + + + +\section{Introduction} +The program solves the rate equations, for spontaneous, absorption and stimulated-emission. It studies laser excitation and motion under external forces (scattering + dipolar + magnetic + electric + gravity) and take into account N-body coulombian interactions and Lorentz forces if charged particles. The momentum recoil is also implemented. +The algorithm and detail of some calculations can be found on the appendix of \cite{comparat2014molecular}, thus I will not recall it here. + But to run the code you do not need to read it! + +% The programm can be download at: https://www.dropbox.com/sh/8iivh04gvf0vk6p/AAA0dtvHDgeZQSjZ7oJJ7zlWa + +In brief it requires: Windows (Linux might be possible but I did not write this guide for it) and Code::Blocks. + +Then the program requires: + + + +\begin{enumerate} + \item input files + + +\begin{itemize} + \item levels: containing their energy + linear or quadratic Stark, Zeeman effects. + \item lines: containing the dipole transitions or some cross sections such as for photodetachement or photodissociation. + + +\end{itemize} + +\item File with parameters (named Liste\_Param.h): contains parameters needed to run the code (sample size, temperature, magnetic fields, laser parameters, ...) + + The file Liste\_Param.h contains a lot of lines with comments, \textbf{so read them carefully!}. As a single example, if you do not change the initialization of the random number generator in this file, the simulation will always be the same when you run a new simulation (which is good for debug!). + +Liste\_Param.h is not an header file and it will not be compiled when compiling the project files. The .h is here simply because it is opened by the text editor. + + + + \item Laser Shaping + + If needed (for optical pumping of molecules for instance) + each laser can be spectrally shaped using files such as Laser\_Spectrum[1].dat for the second laser. + + \item Output: + + A 3D visual output help to see in "real" time the evolution of the sample. But informations at given time intervals are writen in a file (donnee\_Mol.dat). + + + You will probably have to modify the file Sortie\_donnee.cpp depending on what output you want. + + + +\end{enumerate} + + + + +To run the code it is not required to understand it. But briefly, at time t: the program calculates all absorption and emission rates for all particles (so the most important part of the code is the function rates\_molecule). Then Kinetic Monte Carlo algorithm gives exact time t+dt for event (absorption or emission) compare this time to the time for the external motion. Finally it evolves all particles in motion to realize the event. A more detailed explanation is given at the end of this guide in section \ref{section_algorithm}? + + +An update on the modifications done in the code can be find in Modif\_code\_rate\_eq.txt but you have the last version so in principle you do not have to read it. + + +In the following section you will have more informations about each files. + +\section{Code::blocks Installation} + + + + + + +\begin{figure} + \centering + \includegraphics[width=1\linewidth]{linker} + \caption{Example of possible installation (in the case of the simple gsl 1-13). To put either in the Settings/Compiler directory, either in the Project/Build options one.} + \label{fig:linker} +\end{figure} + + +If you are not at all familiar with CodeBlock I suggest that you follow a small tutorial such as http://www.codeblocks.org/user-manual. + + + +You may have to adapt the following names for your own installation. +\textbf{But, you first need to install Code::Blocks (also called Codeblocks) the free C++ IDE, + as well as some scientific and 3D-visual libraries (GLUT, GSL, Eigen, ...). It will always be the same idea for all packages: put the headers (.h) in an \textbackslash{}include, the .lib (or .a) in a \textbackslash{}lib and the .dll files of the packages in a \textbackslash{}bin directory + that the code and the compiler will find. For this we have to configure the project $\rightarrow$ build options as in Fig. \ref{fig:linker}.} + + + + +\subsection{64bits} + + I modify the code to run on 64bits, for the 32bits version see section \ref{32bits}. +The steps are: + + +\begin{enumerate} + \item Install last stable version of codeblocks: a mingw-setup.exe binary file from www.codeblocks.org/ (we need MinGW: a contraction of "Minimalist GNU for Windows"). + It will install the codeblocks in a directory such as C:\textbackslash{}Program Files\textbackslash{}CodeBlocks (see note \footnote{For the 32bits the mingw-32bit-setup.exe it will be installed in C:\textbackslash{}Program Files (x86)\textbackslash{}CodeBlocks where the (x86) is here to say that it is a 32bits file but on a 64bits computer. All other "normal" cases will be on C:\textbackslash{}Program Files (that is 32bits on 32system or 64bits files or 64 computer)}). + + + If you want the +newest codeblocks version you can download the last version from the Nightly built: http://forums.codeblocks.org/index.php/board,20.0.html +: download three .7z files, unzip them (you need 7Zip) in CodeBlocks directory by replacing all the old files with them. + + +\item Eigen Library + +To be able to diagonalize an hamiltonian, we need to install the very good library http://eigen.tuxfamily.org +package and unzip it. + +Then depending on your location you will have to modify the search directories in the Project Build Options. For me it is +C:\textbackslash{}Program Files\textbackslash{}Common Files\textbackslash{}eigen-3.3.7 + + + + \item 64bit installer (MSYS2 MinGW) + + Even if codeblocks is now in 64bits we need MSYS (a contraction of "Minimal SYStem"), and not Cygwin which lead to a lot of problems, to create some pakages (gsl for instance). So get an installer of MSYS2 MinGW w64-bit and run it. Then using the package manager (pacman) do: + \begin{itemize} + \item pacman -Syu + \item pacman -Syu base-devel (then make the selection that avoids pacman: typically 1-39,41-58 that avoids pacman at number 40 in this example) + \item pacman -Syu mingw-w64-x86\_64-toolchain (then choose all) + \end{itemize} + + + \item C++ 64bits compiler + + Codeblocks provide a gcc mingw64 bit compiler but, +because when building packages by msys2 the .h, .lib and .dll will be directly put on msys2 \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin directories it is simpler to use the msys2 compiler because it will automatically find these files. + +To change compiler go to codeblocks Settings/compiler/ and select the default compiler and copy, give a name, for example MSYS2 MINGW64. + Go to Settings/compiler/GlobalCompilerSettings/ToolchainExecutables" to set the path of MinGW64 installed at the beginning: C:/msys64/mingw64. If needed (probably not) change +file names in the "program files" tab of executable toolchain (you will find the names in the bin folder of mingw64). + +Then in Project / Build options... you have to select the right compiler (the MSYS2 MINGW6 should be at the very bottom of the list) + + +\item (free)glut + + +% From the github CodeBlocks\_Install repository \footnote{comes form "Using freeglut or GLUT with MinGW - Transmission Zero"} copy the freeglut directory. Then copy the files from \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin (the ones is \textbackslash{}x64 because we are in 64bits) directories in the correspondings \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin of the C:/msys64/mingw64 directory + +In the +MSYS2 MINGW 64bit window launch + +pacman -S mingw-w64-x86\_64-freeglut + +This automatically copy the files from \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin (the 64bits ones) directories of freeglut in the correspondings \textbackslash{}include, \textbackslash{}lib and \textbackslash{}bin of the C:/msys64/mingw64 directory. + + + \item 64bits gsl= GNU Scientific Library (for 32 bits see note \footnote{For 32 bits the simplest way is to install Gsl-1.13-1.exe. then you would need to modify from the Search directories in the Project Build Options + the location of the .h files + C:\textbackslash{}Program Files (x86)\textbackslash{}GSL-1.13\textbackslash{}include. You need also to modify the location of the global variable}) + + +Retrieve the last GSL folder, for example gsl-2.6, unzip it for instance in C:\textbackslash{}msys64\textbackslash{}home\textbackslash{}daniel and install with MSYS2 : +\begin{itemize} + \item cd gsl-2.6 + \item % ./configure --prefix=C:/msys64/mingw64 (be careful, it's a space then twice - in front of prefix). If this does not work try just + ./configure + \item make + \item make install +\end{itemize} + + For GSL you need to create a Global Variable +gsl +in settings (global variable) of code::blocks with the address where you have installed GSL (for example C:\textbackslash{}msys64\textbackslash{}home\textbackslash{}Daniel\textbackslash{}gsl-2.6) and add in the +project $\rightarrow$ build option $\rightarrow$ search directory $\rightarrow$ +linker \$(\#gsl.lib) + + +Obviously you then need in the + project $\rightarrow$ build options $\rightarrow$ search directories the proper one. + + +\end{enumerate} + + +\subsection{Just run the code} + +\subsubsection{Codeblocks configuration} +The main think you have to do to make the code compiling is to make sure that codeblocks find the files you want (the Eigen, gsl or GLUT ones), the headers (the .h), the library (the .a or .lib files) and the way for windows to handle (the .dll files). +An example of what should be done is given in Fig. \ref{fig:linker}. + + +In the linker option you need to add the needed libraries related to the function you use in the code so +opengl32, +glu32, +gsl, +freeglut. + +For instance for freeglut this +mean that the compiler has to look for a library file such as libfreeglut.a or freeglut.lib + +and for the corresponding .dll + +If you have some problems, may be you need to add your compiler \textbackslash{}bin path (for instance C:\textbackslash{}msys64\textbackslash{}MinGW64\textbackslash{}bin) + to the Path of the System Environment Variables (look at "How to add to the Path on Windows 10") + + +\subsubsection{speed consideration} +Finally, if wanted, you can increase the speed by looking to project $\rightarrow$ Build option $\rightarrow$ Compilator and choose your processor (mine is Intel Core i7). However I almost never find any speed increase (on the contraty so be careful). + +For a speed up, you can also use Ctrl+Alt+del and Process $\rightarrow$ to change priority of the program from Normal to high in Windows. + + +\subsection{Comment on 32 bits codeblocks version.} +\label{32bits} + +All this should work if you use a 64 bit computer. For a 32 bit computer you should use the 32bit GSL version (cf above note and see + https://sourceforge.net/p/mingw-w64/wiki2/GeneralUsageInstructions/ to understant +the complex notations files or directories[you can have a 32 (or 64) bit computer, and use old 32 bit library but at the end produce an executable that work on a 64bit computer] +so names -- such as i686-w64-mingw32, x86\_86-w64-mingw32, gcc-mingw-w64-i686 -- provide this information + i386 or i686 or x32 mean a 32-bit and x64 (or sometimes x86\_64 or) mean a 64-bit. + + + + +\section{Short overview} + +\subsection{Overview of the Program} + +You do not need to know the code in detail, but an overview of its C++ structure is given in the Figures \ref{fig:Class} and \ref{fig:Program_evolution}. + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{classes} + \caption{Schematic of the structure and some basics functions used by the code. The blocks are the different files (.cpp or .h) present with their names in bold and an quick explanation of what they do.} + \label{fig:Class} +\end{figure} + + +Figure \ref{fig:Class} gives the list of the basic structure or classes used such as lasers or fields. Molecules are just seen as Levels, Lines and their positions and velocities. + +Figure \ref{fig:Program_evolution} is the core of the code with the main evolution summarized in the Main\_laser\_cooling.cpp program, that is usually the only code that you may have to modify (with the output one: sortie\_donnee). +As you see the code as still some French in it such as: + +\begin{itemize} + \item donnee = data + \item affichage = plot + \item sortie = output + \item champ = field + \end{itemize} + + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{evolution} + \caption{Schematics of how the code evolve its time. The blocks are the different files (.cpp or .h) present with their names in bold and an quick explanation of what they do.} + \label{fig:Program_evolution} +\end{figure} + + + + + +\subsection{graphics} + + +Once run. You will see two screens appearing as shown in figure +\ref{fig:picture}. + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{picture} + \caption{Snapshot (screen capture) of the code.} + \label{fig:picture} +\end{figure} + + + +If you do not want the graphics you have to change the option in Liste\_Param file. +Some parameters like the screen size are directly part of the code but other ones like size of view of the sample are part of Liste\_Param. + + +For now the graphics do not indicate the lasers locations but show the particles behavior at every time steps, set by the parameter +$@${}dt\_out of Liste\_Param + +The graphics (uses OPEN\_GL library for 3D plotting) represent the particles with the following choices: +\begin{itemize} + \item Red arrow along x, green along y and blue along z (gravity is along -Oz) to see the origin and orientation of the view. Global screen rotations are possible in Liste\_Param, the usual one puts gravity down, but if no rotation is performed we would have x toward the right, y up and z toward the screen. + \item Molecules are represented like diatomic molecules (a line connecting 2 balls) +and depend of their ro-vibronic level and mass. + The length is proportional to the vibrational quantum number $v$, the angle in $x y$ is proportional to the rotational quantum number $J$ and the angle in $x z$ is proportional to its projection (along the local field axis) $M$. + Then the ball size and the color reflects the molecule and its state: Ground state are green, excited state are yellow, dead (photodetachment, ionization, annihilation) are blue (and antiprotons are olive). + +\end{itemize} + + + +Then some statistical data are given like the temperature, positions and velocities of the laser cooled molecules. +As well as the temperature of the second species (if they exist). +Finally the total energy of all molecules is given (it should be conserved in absence of laser cooling). + + +\subsection{Output: Export data in files} + +In addition to the graphics output we have several others possible outputs. + +Mainly Sortie\_donnee\_pop\_vJ gives the population in each $v,j$ levels or simply Sortie\_donnee\_pop\_v gives the population in each $v$ levels. But the standard one is +Sortie\_donnee that gives useful data such as positions, velocities or temperatures. + +The current example Sortie\_donnee (call in main\_Laser\_cooling.cpp in "(t $>$= t\_dia)" section) +gives for each diagnositic time: the parameters that you scan, the time, the position (x,z) and v\_z. + +{\bf You Should probably modify those outputs for your own purpose.} +Use the comment lines to inspire you for your own choice. + + +Finally you can stop the code to run by pressing CTRL+C after if you want to stop before the end or to avoid producing too big files. + +\section{Input files} + + +The code requires source input files +(their locations and names are defined in Liste\_Param). The files are the following: + +\begin{enumerate} +\item Liste\_Param.h (it has to have this exact name) + +Contains all relevant parameters such as number, temperatures, locations of the particles, lasers parameters and some output properties and algorithm choices. +The location of the files are also given in $@${}nom\_file\_Levels, +$@${}nom\_file\_Lines or $@${}nom\_file\_Laser\_Spectrum + + + + \item "Levels". + + Contains informations about the levels of the chosen particle (BaF, Cs$_2$, NH, Cs, CO, Ps, ...). The basic informations are the energy levels and their linear and quadratic Zeeman (and eventually Stark) shifts. + + \item "Lines" . + + Give the dipole transition strength between two levels. + + \item "Laser Spectrum[i]" + + It is optional (if not present no laser attenuation is taken into account and the laser is "normal"). But it can be used to create spectral shaping of a laser. + + + +\end{enumerate} + + +ALL FILES SHOULD NOT contain a return line neither an extra character, like a space, at the end! + + + + +\begin{figure} + \centering + \includegraphics[width=0.7\linewidth]{laser_axis_polarization} + \caption{Definition of the differents frame: laser axis (for the polarization basis), field axis (that is the quantization because we assume adiabatic following of the states) and lab fixed frame. To go from the lab fix frame to the laser axis one a first rotation is by an angle $\phi$ about the $z$-axis then a second rotation is by an angle $\theta$ about the new $y$-axis + } + \label{fig:laseraxispolarization} +\end{figure} + + + +The structure of the files have been chosen because it is the one given by the Pgopher program: PGOPHER, a Program for Simulating Rotational Structure, C. M. Western, University of Bristol, http://pgopher.chm.bris.ac.uk. See Journal of Quantitative Spectroscopy \& Radiative Transfer 186 (2017) 221, where Pgopher is described. + +A more detail description of all files is now given. + +\subsection{Liste\_Param} + +Liste\_Param.h contains: +\begin{itemize} + \item Particles parameters: numbers, type, temperatures, initial positions and velocities + \item Graphics: size and angle of the field of view, time for each output. + \item Fields. Usually given in 3D up to the second order. We can put Helmholtz coils for the magnetic field. For now we can have a trapping magnetic or electric field but not both. With the exception of a Penning trap where the electric field acts on the charge but is supposed to not produce internal energy shifts. + \item Laser beams: waist sizes and positions, polarisations, powers, linewidths, wavelengths, spectral shapes (Lorentzian, Gaussian, comb lines) and possible coherence (intensity interference to create optical lattice) between them.... The polarization could be purely circular (left=$\sigma^+$ or right=$\sigma^-$) or linear and are defined using the laser propagation axis and a rotation angle cf Fig. \ref{fig:laseraxispolarization}. Linear polarizations are thus possible but (to be checked..) then no interference effects are taken into account. Other 'fictuous' laser types can be invented in order to take into account other rates (such as collisional, field ionization, ...) + \item Algorithm parameters: evolution time and steps. Among them we have +the Kinetic Monte Carlo, the First Reaction Method or the less accurate but faster Random Selection Method or even the Fast Rough Method for the internal state. Verlet or Boris-Buneman for the external motion but with different types: either using the analytical acceleration (and no dipolar force) either using gradient of the potential (the epsilon "size step" has to be manually optimized). A N-body algorithm is also implemented. + +\end{itemize} + + +In principle all parameters are in SI units. If not, the name suggests the value such as Gamma\_L\_MHz or Energy\_cm because all energies are in cm$^{-1}$. + + +All parameters have their name staring with $@$ symbol followed by their value (so no symbol $@$ should be use in this file except for this purpose). + + +A loop on the parameters values can be done if the parameters names are written with a +$@${}SCAN\_ prefix and a "true" value between +BEGIN\_OF\_FITPARAMS +and +END\_OF\_FITPARAMS +at the end of Liste\_Param.h file. + + + + +If needed, a new parameter can be added in the file, and then used, in some files of the program using the sentence + params.LocateParam("Nom\_Parametre")-$>$val +that takes its value. + + + + +\subsection{Levels} + + +The name of the file can be chosen as wanted but then put in the Liste\_Param.h file. + +The columns of the file are the following: + + \bigskip + + \textbf{ Manifold 2M Sym \# population } v 2J 2N 2$\Omega$ \textbf{ E$_{\rm cm}$ $\Delta$ C} + \bigskip + +Columns are separated by tabulation. Points (not coma) are used for decimal separations. + + + \textbf{ manifold, 2M, \#, Sym are the only data used to label a Level}. Thus v, 2J, 2N or 2$\Omega$ are extra data and are here only for a better understanding of the file. They can also be used for an output of the data. + +The detail of the columns are(in bold the data that should absolutely be correct): + +\begin{itemize} +\item \textbf{Manifold}: usually 0 means ground electronical level, 1 is for an excited electronical level, 2 for another one ... Negative values can be used for a "dead" level such as one in a continuum (photo-ionization -1, photodetachement -2, or annihilation -3). + + \item \textbf{2M}: where M is the projection of the total angular momentum. We note 2M and not M to be able to use integer in the code for M=1/2 for instance. + In the code the particle will be assumed to always follow (adiabatically) the local quantification axis given by the local field. + +{\it If you want to simulate states without sub-structure like pure ro-vibrational transition in zero field you coudld impose $M$=0 for all states and use $\pi$ laser polarization.} + +\item \textbf{Sym}: Originally it was the parity of the state but this not the case but it should be +1 or -1 to design bound states and 0 for an continuumm state (that is above the continuum threshold such as for photodetachment or photoionization). + +\item \textbf{\#}: "number" of the state. It lifts the degeneracy between levels having the same 3 parameters: manifold, 2M and \#. Usually it is ordered (0,1,2, ...) by energy but for the vibrational levels you could add 10000v to keep trace of it. + +\item \textbf{population}: This is proportional to the initial population in the levels (that will be taken randomly at the beginning of the run). The sum should not have to be 1. + + +\item v: vibrational level. As said previously this is not used by the code except may be for some output data. + +\item 2J: J = total angular momentum (F if nuclear spin present) + +\item 2N: N = rotational angular momentum, including L (L=electron orbital angular momentum). + +\item 2$\Omega$ : $\Omega$ = Projection of J along the molecular axis. + + +\item \textbf{E$_{\rm cm}$}: energy of the level in cm$^{-1}$. For a continuum state, we put the energy of the threshold, like that we can test if the laser transition reach the continuum or not (but we assume a cross section independent of the energy). + +\item \textbf{$\Delta$ and C} give the energy shift of the level under an electric or magnetic field $F$. + +The formula is $E_{\rm cm}(F)= {E_0}_{\rm cm} + {\rm sign}(C) [-\Delta/2+\sqrt{(\Delta/2)^2+(C F)^2}]$. +Thus if $\Delta = 0$ we have a linear variation $E(F)= E_0 + C F$. +Thus, for the magnetic field case, units are cm$^{-1}$/Tesla for $C$. A magnetic moment of 1 $\mu_{\rm Bohr}$ correspond to a value for $C$ of 0.4668645 cm$^{-1}$/Tesla. + + +\end{itemize} + +If needed, an option exists (is\_File\_FC in Liste\_Param) in order to automatically produce new Levels and Lines files from a file containing only $v_X=0 \rightarrow v_A =0$ transition by reading extra Franck-Condon and vibrational and rotational constant files. + + + +\subsection{Lines} + +The lines file can content more lines than used by the Level file. In this case the program only read the useful ones. + + The columns (separated by tabulation) of the file are the following: + + + + \bigskip + + \textbf{UpperManifold 2M' Sym' \#' LowerManifold 2M'' Sym'' \#''} $\Delta_E$ Intensity E$_{\rm upper}$ E$_{\rm lower}$ \textbf{Strength} + +\bigskip + + \textbf{The first 4 columns design the upper level $|1\rangle$ and the second 4 the lower level $|0\rangle$. +So they have to be the same as in the Level file!} + + The last 5 columns give informations about the transitions between these levels. +But \textbf{only the last column (Strength) is used by the code}. However, usually they are composed on: + +\begin{itemize} + + +\item $\Delta_E$: energy difference between the 2 states $|1\rangle$ and $|0\rangle$. + +\item Intensity: Einstein coefficient = spontaneous emission rate of the transition (this is not the total decay rate of the state $|1\rangle$, because it can decay to several levels). + +\item E$_{\rm upper}$: energy in cm$^{-1}$ of the upper state $|1\rangle$. + +\item E$_{\rm lower}$: energy in cm$^{-1}$ of the lower state $|0\rangle$. + +\item \textbf{Strength}: $S_{\rm pol}=d_{\rm axe}^2/3$, where $d_{\rm axe}$ is the dipole (in Debye) of the transition along the polarization axis that authorize the transition between the sum-Zeeman levels). This notation was used due to historical reasons linked to Pgopher. + +So A=Intensity = $\Gamma = 3 S_{\rm pol} C_{{\rm Debye},s} E_{\rm cm}^3$ +with $C_{{\rm Debye},s} = (8\times 10^6 \pi^2 c^3 {\rm Debye}^2 )/(3. \varepsilon_0 c^3 \hbar) = 3.13618932 \times 10^{-7}$ is the conversion from the dipole (in Debye) to the Einstein's coefficient A (s$^{-1}$) for an energy in cm$^{-1}$. + + + +\end{itemize} + + + +For an continuum transition (so with Sym' = 0), the idea to treat it, is to put a "fake" level: the energy should be just at the ionisation threshold (thus the program can test if the laser wavelength is enough to ionize). But, in this case the $S_{\rm pol}$ column is not $d^2/3$ but $\sigma/$cm$^2$ which is the ionization cross section in cm$^2$. + + + + +\subsection{LASER\_SPECTRUM} + +This file is used only if you want to shape spectrally a laser. If you do not create such a file a default one (containing only one line: 0 1) is created which does not affect the laser intensity. + + +The code reads a file one file per laser (number). +Laser\_spectrum[i] for laser number i+1 +that contains 2 columns: E$_{\rm cm}$ (Energy in cm$^{-1}$) and Attenuation (intensity attenuation coefficient). + + +When a transition should occur at the energy $E_{\rm cm}$. +The program look in this file for the line $i$ such as $E_{\rm cm}[i] \leq E_{\rm cm} < E_{\rm cm}[i+1]$ and then it takes the corresponding value +Attenuation$[i]$. This will be the multiplicative factor for the laser intensity for this transition energy. +So in summary the energy in the file is the energy just below yours and the intensity would thus just be multiplied by the amplitude factor. + + + + +\section{Troubleshooting} + + +Figures \ref{fig:Program_evolution} is the core of the code with the main evolution summarized in the Main\_laser\_cooling.cpp program, that is usually the only part of the code that you have to modify (with the output one: sortie\_donnee). + + +If the program does not run for the first time it is usually a problem of links and library in Code::Blocks. + +But if it usually runs but then bug after some modifications it is 90\% due to an error in the input files: levels or lines! + + +For debugging use the debugger in the Debug file. But you can also use Sortie\_rate which gives all rates, or Sortie\_donnee\_etat\_int\_simple that gives the list of levels, and that are commented on Main\_Laser\_Cooling. You have also Sortie\_laser\_spectrum to check the laser spectrum you make or Sortie\_transition to check the transition per + +\textcolor{red}{The best way to debug is to use a simple two level system and to look for the rates to understand if they are as expected. 95\% of the time the problems comes from the Levels or Lines files} + + +\subsection{CodeBlocks problems} + +If you have not strictly followed the rules you might have the following problems!! + + +If Code::Blocks is installed in the C: directories but you have put your project in D: +this does not work. +Thus, you have to put in +"Settings" $\rightarrow$ "Compiler and Debugger" $\rightarrow$ "Toolchain executeables" $\rightarrow$ "Program files" +some link. +For instance modify "mingw32-g++.exe" in "C:\textbackslash{}MinGW\textbackslash{}bin\textbackslash{}mingw32-gcc.exe" +in the "linker for dynamics libs:"... + +More generally the problems are almost always coming from a bad links. + You can specify them for your global environment or just for your project. + +For global environment : +\begin{itemize} + \item Menu Settings/Compiler and debugger +\item In the Global compiler settings, select the Search directories +\item Add the required paths for compiler and linker. +\end{itemize} + + +For your project : +\begin{itemize} + \item Right click on the project then select Build options +\item Select the Search directories +\item Add the required paths for compiler and linker. +\item Add your specific libraries in the linker tab. +\item Pay attention to project settings and target settings. +\end{itemize} + + + +ALWAYS verify that your modifications of directories affect all the project and not only Debug or Release + +Do not forget to recompile the full code after any modification!! + + +\subsection{Common tests} + + +\begin{itemize} + \item It is always good to go back to a situation where the results are known such as: 1 particle at the center, zero temperature, no lasers, no trapping, single laser at resonance, ... +\item Checking energy conservation is always of good practice! +\item Check for the proper time step (dt\_dyn\_epsilon\_param that is the one for the external motion; eventually choix\_epsilon that is the spatial step to calculate the gradient of the potential in some algorithms). + \item Do not forget to recompile the overall project. + \item The most common mistake comes from errors in the Levels or Lines files + \item A too big number of molecules or Levels or Lines may lead to memory overflow. So check also the use of the memory, for instance by using the Windows resource monitor. + \item You can use the code::blocks debugger or simply write some test lines in the code. A very common test is to uncomment the two lines (just before "if (t >= t\_dia)" in main\_laser\_cooling.cpp) with Sortie\_rate and Sortie\_donnee; this will produce at each time step output of all calculated rates and output data. + +\end{itemize} + + + + + +\section{Algorithm used in the code to calculate the evolution and the rates} +\label{section_algorithm} + +\subsection{Diagonalization} +\label{diagonalization} + +We add the possibility cf parameter is\_Levels\_Lines\_Diagonalized +to diagonalize the hamiltonian in order to calculate the energy and the transitions. This was done for positronium (but this is more general) where we had to use the fact that the levels are mixed in $E$ and $B$ fields and that the velocity create a dynamical Stark effect. + +However we do the diagonalization only for the reactions not for the external motion of the particles! So the particles stays in the same levels during their motion (no level crossing during motion) as shown in Figure \ref{fig:diagonalization}. The light shift is not included also. + +\begin{figure} + \centering + \includegraphics[width=0.6\linewidth]{diagonalization.png} + \caption{Schematics of the Energy level due to recoil momentum. The diagonalization thus works only if the energy levels before and after spontaneous emission have the same order in energy. No other dynamical evolution is taken into account, we assume constant velocity during motion (in the excited states).} + \label{fig:diagonalization} +\end{figure} + + +The matrices (Zeeman, Stark, dipoles\footnote{From a dipole Matrix between all levels the dipole matrices could be calculated using Create\_dipole\_Lines\_from\_Matrices. And thus they are correct for the emission-absorption polarization.}) should be put by hand in diagonalization.cpp and should follow the same ordering than the Levels and Lines (and should be ascending in energies). + + + +The most important is that in the degeneracy number \# of the state should be the number of the state staring from 0 (so Level[\#] is the Level itself) [recall that in C++ the index of the first element of the table is 0]. +% The Lines file should contains all transitions (even the nul ones) between i\_low and j\_up. +The levels are thus always refers as Level[i] that is the (i+1)$^{th}$ in energy level ordering (which is not necessary the order you put originally in your level file, EXCEPT for ground state, cf FIG.{fig:diagonalization}). But, for the "sortie" or analysis Level[i] keeps its characteristics (such as M values) given in the input Level file: only Energy\_cm is updated. + + +% Because the magnetic $m$ quantum number, that defines the quantification of the light, is not anymore a good quantum number, the angular emission pattern for the spontaneous emission is done isotropically. + + \subsection{Overview external versus internal dynamics} + +We do not discuss here the Kinetic Monte Carlo (KMC) neither the N-Body solver used to solve rate equations, this is discussed in PRA 89, 043410 (2014). +But we explain the way how code calculates the evolutions for $N$ particles, in order for interested people to modify it. +The main part is the main.cpp file in the + \textit{ while(velocity\_scaling == false)} +loop (before is a tentative to reach thermal equilibrium is a trap using the Berendsen thermostat Algorithm) and especially the +\textit{ calcul\_rates\_molecules} +function. + +The code calculate a time for an internal state evolution dt\_KMC (typically one over the maximal rate) and compare it to the time for the external state evolution dt\_dyn (that is now fixed and given is a parameter in the liste\_Param, even if a commented line to calculate it can by tried). +Then the internal evolution \textit{do\_reaction} and the external \textit{evolve\_step} evolution +depends on the Choix\_algorithme\_Monte\_Carlo and Choix\_algorithme\_N\_corps parameters chosen in in Liste\_Param. + For instance the Choix\_algorithme\_N\_corps is commented in the Liste\_Param. This can be of importance if Coulomb interactions are present or not, or if the dipolar force is included (not well calculated for spectrally shaped laser for instance) or if we calculate it directly using gradient of the fields analytical formula (if implemented) + or through the potential derivative (this is the most general way fo doing it). + + \subsection{Calcul (internal) rates molecules} + +The \textit{ calcul\_rates\_molecules} +function is the most important one. + +In order to not spent too much time on updating all the rates of all molecules we only recalculate the rate of the molecule (number\_mol) that has evolved internally. All others rates will be updated only after (t\_mise\_a\_jour) the dynamical (external state evolution dt\_dyn) time, so when they have moved enough to be in another environment (laser or fields intensity for instance) where the excitation-deexcitation rates have evolved. + +It is possible to force some rates (like by using Pompage\_optique\_force paramter) but genearly we let the system calculate first the spontaneous emission rate and then the key function is the \textit{ \textbf{rates\_molecule}} function. +It is quite complex but commented, here I simply mention that the local parameters such as local intensity, polarization, dipole moment $d$ etc... are calculate and the rate is calculated in \textit{ \textbf{rates\_single\_molecule\_laser\_level}} that is usually the only function that has to be modified if you want to add a new laser type (such as Black Body one). +The stimulated and absorption rate for an $i\leftrightarrow j$ transition for a laser of polarization vector $\bm \epsilon$ is given by $$\gamma= \frac{\pi ({\bm d}.{\bm \epsilon})^2 I_\upomega \otimes L(\omega+\bm k.\bm v-\omega_{ij}) }{\hbar^2 \epsilon_ 0 c}$$ (cf Formula (B.7) of the PRA 2014 article with the correct $\hbar^2$ factor!). So with a local intensity resulting of the convolution of the laser spectrum $I_\upomega$ with the +transition Lorentzian $L(\delta) = \frac{\Gamma_{ij}}{2\pi}\frac{1}{\left( \frac{\Gamma_{ij}}{2}\right)^2 + \delta^2}$. + +For instance for a laser with a Lorentzian spectrum of FWHM $\Gamma_L$ we have, for the Doppler induced detuning $\delta = \omega+\bm k.\bm v-\omega_{ij}$, the rate: +$\gamma= +I \frac{\pi ({\bm d}.{\bm \epsilon})^2 }{\hbar^2 \epsilon_ 0 c} + \frac{\Gamma_{ij}+\Gamma_L}{2\pi}\frac{1}{\left( \frac{\Gamma_{ij}+\Gamma_L}{2}\right)^2 + \delta^2}$ where $I= \varepsilon_0 E^2 c /2$ is the total laser irradiance (intensity). + + + + \subsection{Calcul (external) motion} + +The \textit{ evolve\_step} is the function that evolves the external degree of freedom depending on the chosen algorithm (Verlet, Boris, ..) and most important on the way we calculated the force. We can use directly the acceleration or the derivative of the potential (depending on the choix\_epsilon parameter typically 10nm). +The fastest is clearly the use of the acceleration calculate in the + the key function is the \textit{ \textbf{new\_acc}} function. But this require that the gradient of the fields are analytically calculated. This is not the case for the dipolar potential neither if there is $N$ body interaction where in this case algorithm use the gradient of the potential to calculate the force through the \textit{ \textbf{new\_pot}} function. The dipolar potential requires to calculate all dipolar transitions (so it calls the rates\_molecule function) and this might be very slow! + + + \subsection{Comments} + +The code has evolved and because it is time consuming ot keep all the time the internal Energy of the molecule correct (especially if dipolar potential is used) we do not use anymore the +set\_pot\_all\_mol function and and we therefore do not +the Internal\_state.Energy\_cm is not correct. It should not be used but (see rates\_molecule) recalculated when needed. + +In order to avoid gigantic storage we have single Levels and Lines files and ALL particles point to this and only the Zeeman , Stark and dipolar shift are added to this. For more complex situation where the internal state quantum numbers are modified for instance we need to use the Levels\_Lines\_Diagonalized + + \subsection{Levels Lines Diagonalized } +This is controled using the is\_Levels\_Lines\_Diagonalized parameter + + \section{Performance test} + + N=100 Hydrogen atoms during 50 microsecond and plot every microsecond. 64.571s with graphics versus 57.502 without and 55.826 without any output + \footnote{ Depending on what the computer is doing meanwhile those times can fluctuate within few percent}. + + + \subsection{Nb of molecules} + + \begin{tabular}{|c|c|} + \hline +Time & Nb atoms \\ +\hline +\hline +0.632 & 1 \\ +\hline + 6.984 & 10 \\ + \hline + 26.362 & 50 \\ + 57.502 & 100 \\ + \hline + \end{tabular} + + So the code is very linear in $N$ which is good news ! This is because the particle are not charged if not probably (to be tested) the variation will be in $N^2$. + + \subsection{Kinetic Monte Carlo algorithm} + +It is be interested to compare them (cf + https://en.wikipedia.org/wiki/Kinetic\_Monte\_Carlo) + because the default one + Kinetic\_Monte\_Carlo + is not the fastest in principle but First\_Reaction\_Method + is also perfect as well as Random\_Selection\_Method if the rate are time independent. + + + + + \begin{tabular}{|c|c|} + \hline + Time & Algorithm \\ + \hline + \hline + 58.604 & Kinetic Monte Carlo (0) \\ + \hline + 132.343 & Random Selection Method (1) \\ + \hline + 73.606 & First Reaction Method (2) \\ + \hline + 6.118 & Fast Rough Method (3) \\ + \hline + 0.537 & No laser included \\ + \hline + \end{tabular} + + So Fast Rough Method (to be tested in more detail) may be a good way to start. + +Random Selection Method has probably a problem in the code to be this slow! + + + + \subsection{Motion algorithm} + + for dt\_dyn\_epsilon\_param = $10^{-7}$ the time (for 100 atoms) is 57.502s whereas for $10^{-8}$ the time is 72.933s. Always choix epsilon is 1e-8. + + For 1e-7 we made test of the algorithm. Obviously the accuracy of higher order are better so dt\_dyn\_epsilon\_param can be reduced if using such algorithm but this gives an idea. + + \begin{tabular}{|c|c|} + \hline + Time & Algorithm \\ + \hline + \hline + \\ + 44.639 & Aucun N corps (-1) \\ + \hline + 49.647 & Verlet acc (sans force dipolaire) (1) \\ + \hline + 252.635 &Verlet pot (avec potentiel dipolaire) (2) \\ + \hline + 86.587 & Yoshida6 acc (3) \\ + \hline + 113.549 & Yoshida6 pot (4) \\ + \hline + 474.885 & Verlet pot gradient high order (6) + \\ + \hline + 49.341 & Boris Buneman (with Magnetic field for charged particles) \\ + \hline + \end{tabular} + + + + + \section{Futur} + Despite the fact that the code could largely be improved to use more C++ spirit (like maps between reaction and rates, ...), a long list of possible improvements exists among them are: + + \begin{itemize} + + \item Use of adaptive time steps (like t\_evol\_ext) for the algorithms (under consideration). + + \item Possibilities to use more general laser beam (Laguerre Gauss, others polarizations). Put the phase given by the polarizations to take into account linear polarisation in the interference lattice case. + + \item Optimize the link between the renew of the rates, the KMC steps and the external evolution steps. For instance if the acceleration is known we do not need to recalculate each time in the evolution algorithms ... + + \item Parallelization of the code. Using OpenMP for multiprocessor seems quite easy: If needed, download the last MinGW 64bits version. + Copy-paste and erase the old one in Codeblock directory. Then in Global Compiler setting (or simply in your project) use in Other option -fopenmp. + Linker settings: Adds the MinGW/bin libgomp-1.dll. Then test using simple program + with \# include + + \# pragma omp parallel + + + \item Combine electric and magnetic field of arbitrary orientations. This is partially done using the diagonalization cf section \ref{diagonalization} + + \item Treat chemical reactions during collisions. + + \item Treat coherent dark states by choosing the proper basis. + + \item Use an ionization or photodetachment cross-section which is dependent on the energy. + + \item For strongly focused lasers, we can put the local wave-vector $\bf k$, not the global one as it is now. + + \item Draw lasers using the hyperbolic function (nor the elliptic one). + + \item Improve the statistical initial distribution. Until now we calculate the trapping field using a linear approximation for the potential energy. + + \item Improve the calculation of the dipolar shift. Until now the dipolar potential is not included in the shift for the transition. This avoids accumulation, but in some cases, it may be good to have it. + + \item Improve performance using GNU Gprof (Code Profiler Pluggin in Code::Blocks) + + + \end{itemize} + + + + \newpage + + \appendix + \section{Use of Pgopher} + + As mentioned before you can use Pgopher (pgopher.chm.bris.ac.uk/) to create your input files. It is in fact recommended because they have been written from it. + + Be sure to have a good simulation. For instance for a single pair of equivalent nuclei (such as in I$_2$) the statistical weights should be SymWt=1, AsymWt = 0, rather than both 1. + Be sure to have enough J but not too much to avoid too big files... + + So read carefully Pgopher manual. + + Then in the Pgopher data use the following options. Hopefully with obvious notations: + + \begin{itemize} + \item + MIXTURE: + Precision 12 + + QuantumNumberFormat 2J. But be careful that all values such as tensor rank, max J are thus doubled, so it is sometimes difficult to follow them. So it is better to do this only at the end, it is just use to produce the "Levels" and "Lines" files. + + BField 1e-10. In order to separate M levels and have all transitions! + + \item SIMULATION: + IntensityUnits: EinsteinA (to have the rate for spontaneous emission) + + + \item SPECIES: + ShowJ, ShowOmega, ShowN, .. all TRUE + + + + \item TO PRODUCE THE "LINES" FILE: Use the following option + File Export Line List .txt (tab separation). Intensity Threshold 1e-8. No "Fit File Format" + + + \item TO HAVE THE ENERGY LEVELS IN FIELDS: + + View, Levels List (To have the energy at each points). Verify to have All symmetry, Omega M values ... + Then use "Track State" and click on "Summary". This gives levels + fit linear + quadratic of the field dependence. So be careful to plot with the proper B field T values (0-1T or 0-1mT for instance) + Save the file in LEVEL. + + + + \item THEN GO TO ORIGIN (http://www.originlab.com/) or to any other data acquisition software (in the Directory Data: Pgopher\_Level\_List.opj) and follow the following procedure. + + Your case can be slightly different if you have more molecules or several vibrational levels or .. so adapt it! + + + \begin{itemize} + + + \item To produce the "LEVELS" file: + + Remove the \% from the LEVEL file + + Use Import Wizard in Origin with 11 headers, 1 subheader (should be recognized). + The name of the columns should be (if not modify by coping this line, or use the example in): + + Molecule Manifold 2M Sym \# g Population Label State 2J 2N 2Omega Fn parity*M Energy Linear Dipole Err Quadratic Err 2\_Level Delta C Dipole2 Err + + + Sometimes Pgopher does not create the first column Molecule neither the last columns of E\_2\_Level ... + + + Then we have to calculate the C and $\Delta$ (that is Delta) coefficients when they are not given, that is if Level Delta C Dipole2 Err columns are missing. + If the effect is not linear but quadratic or more complex then create the 2\_level fit by: + Add one column for numbers, + Sort by 2\_Level. + For those who do not have a 2\_Level then create one (for instance take the Linear and the same energy because C=Linéaire, Delta=0). The intermediate case between linear and quadratic is more complex and an appropriate formula should be derived. + Sort again (a priori the file is sort in M, Sym and \#). It is also possible to sort in Energy + + Duplicate the workbook and keep only the following columns (v is State): + + Manifold 2M Sym \# population v 2J 2N 2Omega Energy Delta C + + + Remark: One possibility to remove "v=" that appears when exporting from Pgopher in "State" and to keep only the vibrational level value is: after the exportation remove "v=" (and change "," in "." if needed) and import again. + + Then use only values not the text, so: + In Manifold use 0 for the X state (lower) et 1, 2, ... for higher Manifold and + +/-1 for Sym. + + If wanted you can sort the workbook in Energy and modify the population column to put the desired one. + Export the Workbook without headers (no Label) and in a file with .dat extension + + Check that the decimal are with "." not "," + Remove the space at the end of the file. + + + + + + \item TO PRODUCE THE "LINES" file: + + Remove the first and last 2 lines of the file LINES.txt + Import it in Origin (using options: delimator, Tab/space). + Change the name of the lines: (copy paste the one below) + + Molecule Upper Manifold 2M' Sym' \#' Lower Manifold 2M" Sym" \#" Position Intensity Eupper Elower Strength A Width Branch LabelUpperManifold state 2J' 2N' 2Omega' Fn' 2M' Sym Upper Manifold state 2J'' 2N'' Omega'' Fn'' 2M'' + + + Duplicate the workbook and keep only the columns: + + UpperManifold 2M' Sym' \#' LowerManifold 2M" Sym" \#" Position Intensity Eupper Elower Strength + + then do the same as for Levels: X=0, Sym =+/-1 ... + + Finally divide by 3 the Strength column and export in .dat file + + \end{itemize} + + \end{itemize} + + + \section{Detail of laser interaction} + +The code is based on \cite{comparat2014molecular}; on \cite{chaneliere2018phase} (supplementary material) for quantization, recoil and Doppler effects; and on +\cite{manual_Steck,varshalovich1988quantum} for vector and angular momenta. +We recall here some important points. The notations differ sometimes from \cite{comparat2014molecular} but are more general and should be preferred, because we use less assumptions here (especially about the reality of some vectors). + + + \subsection{Spherical and helicity vectors } + + We use the notation of \cite{varshalovich1988quantum} such as the (covariant) spherical vectors + $ {\bf e}_0 = {\bf e}_z, {\bf e}_{\pm 1} = \mp \frac{{\bf e}_x \pm + i {\bf e}_y} { \sqrt{2}}$. + Using ${\bf{e}}^q = ({\bf{e}}_q)^* = (-1)^q {\bf{e}}_{-q}$ (that leads to the normalization ${\bf{e}}^p {\bf{e}}_q = \delta_{pq} $) we find for any (complex) vector + $$\bm A = \sum_q A^{q} {\bf{e}}_q = \sum_q (-1)^q A_{-q} {\bf{e}}_q $$ + where + $A_q = \bm A. + {\bf{e}}_q$ so for instance $A_0 = A_z, A_{\pm 1} = \mp (A_x \pm + i A_y)$. + % If $\bm A$ is a \textit{real} vector we have $\bm A = (\bm A)^*$ and $ A^q = A_q^*$ so $\bm A = \sum_q A_q^* {\bf{e}}_q $. + We will often have the case where the $A_q$ or $A^q$ are reals (example of the dipoles or of pure laser polarization) but in general we should keep in mind that the vectors are complex. + + + + \subsection{Lasers using complex notations} + + + + + The electromagnetic field, due to the lasers $\rm L$, can be written + $${\bm E}(\bm r,t) = {\bm E'}(\hat{\bm r},t)+ {\bm E'}^\dag(\hat{\bm r},t) = \frac{1}{2}\sum_{\rm L} \left[ {\bm E}_{\rm L} e^{i( {\bm k}_{\rm L}. {\bm r} - \Phi_{\rm L} + (t))} + {\bm E}_{\rm L}^\ast e^{-i( {\bm k}_{\rm L}. {\bm r} - \Phi_{\rm L} + (t))} \right] $$ + + the irradiance, called improperly intensity, is + $ + I_{\rm L}= \varepsilon_0 |E_{\rm L}|^2 c/2 $. + + + + The Doppler effect, and the laser linewidth, are taken into account by writing $\Phi_{\rm L} (t) = (\omega_{\rm L} - {\bm k}_{\rm L}. {\bm v}) t + \Phi^{\rm L} (t)$. Where $\Phi^{\rm L} (t) $ is a fluctuating phase. + + + As shown in Fig. \ref{fig:laseraxispolarization}, + we use the (covariant polar basis) frame linked with the laser propagation: + $({\bf{e}}'_{\rm x} = {\bf{e}}_{\theta} , {\bf{e}}'_{\rm y} = {\bf{e}}_{\phi}, {\bf{e}}'_{\rm z} = {\bf{e}}'_{\rm r} = \bm{k}/\| \bm{k} \|)$ . + The laser polarization is conveniently described in the (covariant) helicity basis + $ {\bf e}'_0 = {\bf e}'_z, {\bf e}'_{\pm 1} = \mp \frac{{\bf e}'_x \pm + i {\bf e}'_y} { \sqrt{2}}$. + For each laser $\rm L$ + the polarization vector, defined by + $ {\bm E}_{\rm L}(\bm r,t) = E_{\rm L}(\bm r,t) {\bm \epsilon}_{\rm L} $, is $ {\bm \epsilon}_{\rm L} = + \sum_{p= -1,0,+1} \epsilon'^p + {\bf e'}_{p} $. + + + In the code we deal (for simplicity and for calculus speed) only with reals. So for instance + \textbf{the polarisation is coded using only 3 real parameters Pol\_circulaire\_right\_sm ($a_{-}$), Pol\_circulaire\_left\_sp ($a_{+}$) and polar\_angle\_degree ($\Psi$) (in degree in Liste\_Param). These 3 parameters + define + \begin{equation} + {\bm \epsilon}_{\rm L} = {\rm Pol\_circulaire\_right\_sm} \ e^{i \Psi} {\bf e'}_{-1} + {\rm Pol\_circulaire\_left\_sp} \ e^{-i \Psi} + {\bf e'}_{+1} = a_{-} \ e^{i \Psi} {\bf e'}_{-1} + a_{+} \ e^{-i \Psi} + {\bf e'}_{+1} + \end{equation}} + % ${\bf{e}}'_{\rm L,pol} = \{ Pol\_circulaire\_right\_sm = \epsilon'^{-1} e^{-i \Psi}, \epsilon'^0 , Pol\_circulaire\_left\_sp = \epsilon'^{+1} e^{i \Psi} \}$ + + This does not authorize arbitrary polarizations but only pure circular (right with $\epsilon'^{-1} =1$, or left with $\epsilon'^{+1}=1$) or + a pure linear polarization. For example, (cf. Fig. + \ref{fig:laseraxispolarization}) linear polarization turned by an angle $\Psi$ from $ {\bf e'}_{x} $ +is ${\bm \epsilon}_{\rm L} = {\bf e}'_x \cos\Psi + {\bf e}'_y \sin \Psi = + \frac{1}{\sqrt{2}} e^{i \Psi} {\bf e'}_{-1} - \frac{1}{\sqrt{2}} e^{-i \Psi} + {\bf e'}_{+1} $, that is $a_{-} = \frac{1}{\sqrt{2}}, a_{+}= - \frac{1}{\sqrt{2}}$. + % and is thus ${\bf{e}}'_{\rm L,pol} = \{ \frac{1}{\sqrt{2}} e^{i \Psi}, 0 , - \frac{1}{\sqrt{2}} e^{-i \Psi} \}$ which is not real. + + + + \subsection{Transition dipole moment} + + + + The transition dipole moment + ($\bm d = e \bm r$ in the simple case of H, Ps or alkali atoms, and we will use often this simplification for the notation) + between 2 levels is defined (for now in the lab fixed frame but this will be precised in section \ref{pol_vector}) as + $ \bm d_{ij} = \langle i | \bm d | j \rangle = \sum_q (-1)^q d_{ij;q} {\bf{e}}_q = \sum_q d_{ij;q} {\bf{e}}^q $ so $ d_{ij;q} = \bm d_{ij}.{\bf{e}}_q$. The notation $d_{ij}^{(q)} = d_{ij;q}$ is often used but has to be avoided because of possible confusion with the (contravariant) notation $d_{ij}^{q}$. + The correct component that forms an irreductible tensor (rank 1) $\hat d_{1q} = \hat d_{q}$ are $ d_{ij;-1},d_{ij;0},d_{ij;+1} $. + In the code this vector is called + the "polarization" dipole vector $\bm d_{ij} $ and is recorded as $ \{ d_{ij;-1},d_{ij;0},d_{ij;+1} \} $ (obviously in C++ the array number will be respectively dipole[0], dipole[1], dipole[2]). + With the proper (Condon-Shortley's type) convention \cite{varshalovich1988quantum}, these dipoles are reals. + + % We also the polarization dipole vector by ${\bf{e}}_{\rm pol,ij} = \bm d_{ij}/|d_{ij}| = \{ d_{\rm pol,ij}^{-1}, d_{\rm pol,ij}^0 , d_{\rm pol,ij}^{+1} \} $ + + + + + + \subsection{Absorption, stimulated or spontaneous emission} + + For a transition between two states $|j\rangle$ to $|i\rangle$, it is important to known if we deal with absorption (rising level energy) or stimulated or spontaneous emission (lowering level energy) to know which term in the rotating wave approximation shall be used. + + \textbf{ In the following, we assume $E_j> E_i$}. + + \subsubsection{Ordered energy levels and rotating wave approximation} + + +The rotating wave approximation leads (for level $j$ above level $i$: $E_j>E_i$) leads to: + + \begin{equation*} + \hat H = \frac{\bm \hat {\bm p}^j}{2 m} + + V_i(\hat {\bm r},t) |i\rangle\langle i| + V_j(\hat {\bm r},t) |j\rangle \langle j| + - \langle j | q \hat {\bm r}| i \rangle .\bm E' (\hat {\bm r} ,t) |j\rangle \langle i| - \langle i | q \hat {\bm r}| j \rangle . \bm E'^\dag (\hat {\bm r} ,t) |i\rangle \langle j| \label{hamiltonianRWA} + \end{equation*} + + where we have added some potential traps $V_i$ and $V_j$ to be more general. + % where the coupling term is $\displaystyle \hat V = - \bm d .\bm E' (\hat r ,t) = - \frac{\bm d}{j}\sum_{\rm L} {\bm E}_{\rm L}(t) e^{i( {\bm k}_{\rm L}. {\hat{\bm r}} - \omega_{\rm L} t - \Phi_{\rm L}(t) )} = \sum_{\rm L} \hat V_{\rm L} $. + + The recoil effect will be present only after the interaction by a $\hbar \bm k$ term added to the momentum. This is clarified, cf Eq. (9) and (20) of \cite{chaneliere2018phase}, by using the (single plane wave, in a volume $L^3$) + quantized field: + $\displaystyle \hat{\bm{E}} (\bm{r},t) = \sum_{\bm{k},\sigma} i \sqrt{\frac{ \hbar \omega_k}{2 \epsilon_0 L^3} } \left( \hat a_{\bm{k} \sigma} e^{- i \omega_k t} \bm{\epsilon}_{\bm{k}\sigma} {\rm e}^{i \bm{k}.\bm{r} } - \hat a_{\bm{k} \sigma}^\dag e^{ i \omega_k t} \bm{\epsilon}_{\bm{k}\sigma}^\ast {\rm e}^{-i \bm{k}.\bm{r} } \right)$, where $ {\bm \epsilon}_{\bm k \pm 1} = {\bf e}'_{\pm 1}$. We thus have: + \begin{equation*} + \hat H = \frac{\hat{\bm p}^2}{2 m} + + V_i(\hat{\bm r},t) |i\rangle\langle i| + V_j(\hat{\bm r},t) |j\rangle \langle j| \label{eq_base_at} + - \bm d_{ji}. \hat{\bm E'} (\hat{\bm r} ,t) |j\rangle \langle i| + \bm d_{ij} .{\hat{\bm E'}}^\dag (\hat{\bm r} ,t) |i\rangle \langle j| + + \sum_{\bm{k} \sigma} \hbar \omega_k \left( \hat a^\dag_{\bm{k} \sigma} \hat a_{\bm{k} \sigma} + 1/2 \right) + \end{equation*} + where $\bm d_{ji} = \langle j | q \hat {\bm r}| i \rangle = \bm d_{ij}^* $ is the transition dipole element. The quantization clarifies the recoil effect because of + $ + e^{ \pm i \bm k.\hat{\bm r}} | \bm p\rangle = |\bm p \pm \hbar \bm k\rangle$. + + + + Descriptions of the rate equations and forces can be find in the appendix of Ref. \cite{comparat2014molecular,chaneliere2018phase} and are not recalled here. + + + + + + + + \subsubsection{Absorption, Stimulated or spontaneous emission} + + + + Absorption is thus a transition $i \rightarrow j$ ($E_j> E_i$). For absorption + the only relevant term is due to $-\bm d.\bm E'$ through the Rabi frequency\footnote{ For more generality we do not (yet) assume real dipoles and so the notation is different (better here even if careful has to be taken in the $i,j$ order because $\Omega_{ji} =\Omega_{i \rightarrow j} $ ) than in \cite{comparat2014molecular}.} +\begin{equation} +\hbar \Omega_{ji} = E_{\rm L} \langle j, \bm p + \hbar \bm k | \hat{\bm d} . \bm \epsilon_L + e^{ i \bm k.\hat{\bm r}} | i, \bm p\rangle = E_{\rm L} \bm d_{ji} . \bm \epsilon_L = E_{\rm L} + \sum_q d_{ji;q} {\bf{e}}^q . \sum_{p} \epsilon'^p {\bf e'}_{p} + \label{Rabi_frequancy} + \end{equation} + + + + + + The stimulated emission $j \rightarrow i$ with the same laser is govern by the $-\bm d.{\bm E'}^\dag$ term and thus arises with the Rabi frequency +$\hbar \Omega_{ij} = E_{\rm L} \langle i, \bm p - \hbar \bm k | \hat{\bm d} . {\bm \epsilon_L}^\dag + e^{ - i \bm k.\hat{\bm r}} | j, \bm p\rangle = E_{\rm L} \bm d_{ij} . {\bm \epsilon_L }^\dag =\hbar \Omega_{ji}^*$ + + We recover the well known fact that the dipole transition rates are the same (conjugated Rabi frequencies) for spontaneous and for stimulated emission. + + + The simplest (ideal) case is when + \begin{itemize} + \item The quantization axis and laser axis (for the polarization) are equal ${\bf{e}}_q={\bf{e'}}_q$. In this case, the absorption is driven by $\hbar \Omega_{ji} = E_{\rm L} \sum_q d_{ji;q} \epsilon'^q $ + \item The laser is of pure polarization $ \epsilon'^q =1$ for a given $q$ and $0$ for others. So $\hbar \Omega_{ji} = E_{\rm L} d_{ji;q} $ + \item states are pure (that is with well defined magnetic quantum numbers $m_i,m_j$ projection on the quantization axis ${\bf{e}}_0$). So $\hbar \Omega_{ji} = E_{\rm L} d_{ji;q} = E_{\rm L} \langle j | d_{1q} | i \rangle $ will verifies $m_j = q+ m_i $. We recover the fact that + $ q=-1$ for a $\sigma-$, $ q=0$ for a $ \pi$ and + $ q= +1$ for a $\sigma+$ light. + \end{itemize} + + +We now have to treat the most general case where none of these 3 assumption is correct. + \subsection{Rotation matrices} + + We have to deal with three frames: + \begin{itemize} + \item The fixed lab frame $(\bf{e}_{\rm x}, \bf{e}_{\rm y}, \bf{e}_{\rm z} )$ + \item The local (different for each particle position $\bm r$) field $\bm F(\bm r)$ frame, $(\bf{e}_{\rm X}, \bf{e}_{\rm Y}, \bf{e}_{\rm Z})$. It defines the quantization axis. It will also be noted + $(\bf{E}_{\rm X}, \bf{E}_{\rm Y}, \bf{E}_{\rm Z} = \bm{F}/\| \bm{F} \|)$ in order to define ${\bf{E}}_{\pm 1}$ without any confusion with ${\bf{e}}_{\pm 1}$. + \item The laser frame $(\bf{e}'_{\rm x}, \bf{e}'_{\rm y}, \bf{e}'_{\rm z} = \bm{k}/\| \bm{k} \|)$. + \end{itemize} + These frames are defined by their $z,z',Z$ axis, and the angle of rotation around this axis is defined such that (cf Fig. + \ref{fig:laseraxispolarization}), taken the example of the laser $z'$ frame, the frame is the polar frame of which $Oz'$ is the direction and $Ox'$ is the meridian. + + + All this explain that in the code a reaction is coded using the type\_codage\_react reaction=$\{n\_mol; n\_laser; \bm F; \bm \epsilon_L; \bm k; final\_internal\_state\}$ for the particule number $n\_mol$, under the laser number $n\_laser$ (-1 for spontaneous emission). + + \subsubsection{Euler angles} + + To go from one $(\bf{e}_{\rm x}, \bf{e}_{\rm y}, \bf{e}_{\rm z} )$ frame to a new one $(\bf{e}'_{\rm x}, \bf{e}'_{\rm y}, \bf{e}'_{\rm z} )$ it is convenient to use the Euler angles. + Different conventions exists: Mathematica and \cite{varshalovich1988quantum} (1.4 schema A) are in the so called z y z (noted also Z Y Z) convention, whereas Wikipedia is in z x z convention. For completeness, we thus recall here the + Euler rotations angles $(\alpha,\beta,\gamma)$ convention. + For instance in the + z y z convention: + \begin{itemize} + \item the first rotation is by an angle $\alpha$ about the $z$-axis. + \item the second rotation is by an angle $\beta$ about the new $y$-axis + \item the third rotation is by an angle $\gamma$ about the new $z$-axis (now $z'$). + \end{itemize} + + Clearly (Fig. + \ref{fig:laseraxispolarization}) our convention to use + the spherical basis leads simply to + $(\alpha,\beta,\gamma) = (\phi,\theta,0)$ in the + z y z convention, but to $(\alpha,\beta,\gamma) = (\phi+\pi/2,\theta,-\pi/2)$ in the z x z convention. + + The z x z convention is the one used (for historical reason) in the code (cf Euler\_angles function). + The z x z convention is useful to find the polar angle $\phi,\theta$ knowing only the vector ${\bf{e}}'_{\rm z} = x_e {\bf{e}}_{\rm x} + y_e {\bf{e}}_{\rm y} + z_e {\bf{e}}_{\rm z} $ that defines the new frame by: + $\alpha = \phi+\pi/2 = {\rm atan2}(x_e, - y_e)$ and $\beta = \theta = \arccos(z_e)$. + + The main function in the code is thus rotation\_axis\_lab that calculates, using simple notation such as $s_1 = \sin (\alpha)$ or $c_3 = \cos (\gamma)$ , the new coordinates + $$ \begin{pmatrix} x \\ y \\ z + \end{pmatrix} + =\begin{pmatrix}c_{1}c_{3}-c_{2}s_{1}s_{3}&-c_{1}s_{3}-c_{2}c_{3}s_{1}&s_{1}s_{2}\\c_{3}s_{1}+c_{1}c_{2}s_{3}&c_{1}c_{2}c_{3}-s_{1}s_{3}&-c_{1}s_{2}\\s_{2}s_{3}&c_{3}s_{2}&c_{2}\end{pmatrix}. \begin{pmatrix} x' \\ y' \\ z' + \end{pmatrix}$$ + The reverse rotation\_lab\_axis is used to find the laser intensity (cf intensity\_lab\_axis function) at the particle location $\bm r = x {\bf{e}}_{\rm x} + y {\bf{e}}_{\rm y} + z {\bf{e}}_{\rm z} $. + \subsubsection{Polarization vectors} + \label{pol_vector} + + % We can write the laser polarization vector in the two frames as \cite{varshalovich1988quantum} Eq. 1-(49): $ {\bm \epsilon} = \sum_{p'= -1,0,+1} {\epsilon'}^\ast_{p'} {\bf e'}_{p'} = \sum_{p= -1,0,+1} \epsilon_p^\ast {\bf e}_{p} $, with $ \epsilon_{p} = \sum_{p' =0,\pm 1 } (-1)^{p'} \epsilon'_{p'} D_{p p'}^{\ast (1)} (0,\theta,\varphi)$. + + To evaluate Eq. \ref{Rabi_frequancy} we + write the laser polarization vector in the three frames + $ {\bm \epsilon}_{\rm L} = + \sum_p \epsilon'^p + {\bf e'}_{p} = \sum_p \mathcal{E}^p + {\bf E}_{p} = \sum_p \epsilon^p + {\bf e}_{p} + $. + Using $ {\bm \epsilon}^. = \begin{pmatrix} \epsilon^{-1} \\ \epsilon^{0} \\ \epsilon^{+1} + \end{pmatrix}, {\bm e}_. = \begin{pmatrix} {\bf e}_{-1} \, {\bf e}_{0} \, {\bf e}_{+1} + \end{pmatrix}, + {{\bm \epsilon}'}^. = \begin{pmatrix} {\epsilon'}^{-1} \\ {\epsilon'}^{0} \\ {\epsilon'}^{+1} + \end{pmatrix} = \begin{pmatrix}a_{-} \ e^{i \Psi} \\ 0 \\ a_{+} \ e^{-i \Psi} + \end{pmatrix} , {\bm e}'_. = \begin{pmatrix} {\bf e'}_{-1} \, {\bf e'}_{0} \, {\bf e'}_{+1} + \end{pmatrix}, + {\mathcal{\bm E}}^. = \begin{pmatrix} \mathcal{E}^{-1} \\ \mathcal{E}^{0} \\ \mathcal{E}^{+1} + \end{pmatrix}, {\bm E}_. = \begin{pmatrix} {\bf E}_{-1} \, {\bf E}_{0} \, {\bf E}_{+1} + \end{pmatrix}$ we have + $ {\bm \epsilon}_{\rm L} = {\bf e'}_. {\bm \epsilon'}^. = {\bf E}_. \mathcal{\bm E}^. = {\bf e}_. {\bm \epsilon}^. $ + + + + We will note $\phi_{\bm k},\theta_{\bm k}$ the polar angles of ${\bm k}$ (to go from the lab fix frame to the laser frame) and $\phi_{\bm F},\theta_{\bm F}$ the polar angles of ${\bm F}$ (so to go from the lab frame to the field frame). Eq. (1.1 53) of Ref. + \cite{varshalovich1988quantum} gives + $ \sum_p {\bf e}_{p} {\rm D}_{p p'}^{1} (\phi_{\bm k},\theta_{\bm k},0) = {\bf e'}_{p'} $ +that is +$ {\bf e}_. {\rm {\bm D}} (\phi_{\bm k},\theta_{\bm k},0) = {\bf e'}_. \mbox{ and similarly } {\bf e}_. {\rm {\bm D}} (\phi_{\bm F},\theta_{\bm F},0) = {\bf E}_. $ + where + $({\rm {\bm D}})_{ij} = {\rm D}_{i j}^{1} $ is the + WignerD function. + Several conventions exists: Mathematica + WignerD$[\{j,m_1,m_2\},\alpha, \beta, \gamma]= {\rm D}_{m_1,m_2}^j (-\alpha, -\beta, -\gamma)$ of \cite{varshalovich1988quantum}. We use the \cite{varshalovich1988quantum} concention, that is also the one chosen by Wikipedia with: + $ {\rm {\bm D}} (\phi,\theta,0) = + \begin{pmatrix} + \frac{1}{2} e^{i \phi} (1+\cos \theta) &\frac{e^{i \phi} \sin \theta}{\sqrt{2}} & e^{i \phi} \sin^2(\theta/2) \\ + -\frac{\sin \theta}{\sqrt{2}} & \cos \theta & \frac{\sin \theta}{\sqrt{2}} \\ + e^{-i \phi} \sin^2(\theta/2) & -\frac{e^{-i \phi} \sin \theta}{\sqrt{2}} & \frac{1}{2} e^{-i \phi} (1+\cos \theta) \end{pmatrix} + $ with the order $i,j = -1,0,1$ in the lines and columns. + + Because the states $|i\rangle$ are defined with the quantization axis frame ${\bf{E}}_.$ we note + $ \bm d_{ij} = \langle i | \bm d | j \rangle = \sum_q D_{ij;q} {\bf{E}}^q $ with $ D_{ij;q} = \bm d_{ij}.{\bf{E}}_q$. So in matrix notation, with +$ {\bm D_{ij}}_. = \begin{pmatrix}D_{ij;-1} \, D_{ij;0} \, D_{ij;+1} \end{pmatrix} = \begin{pmatrix}D_{-1} \, D_{0} \, D_{+1} \end{pmatrix} $ + and $ {\bm E}^. = \begin{pmatrix} {\bf E}^{-1} \\ {\bf E}^{0} \\ {\bf E}^{+1} + \end{pmatrix}$, we have + $\bm d_{ij} = {\bm D_{ij}}_. {\bf E}^. $ + + We can thus now write Eq. \ref{Rabi_frequancy} as + \begin{equation} + \hbar \Omega_{ji} / E_{\rm L} = \bm d_{ji} . \bm \epsilon_L = [ {\bm D_{ij}}_. {\bf E}^. ].[ {\bf e'}_. {\bm \epsilon'}^. ] + % = [{\bm D_{ij}}_. {\bf E}^. ].[ {\bf E}_. {\rm {\bm D}}^{-1} (\phi_{\bm F},\theta_{\bm F},0) {\rm{ \bm D}} (\phi_{\bm k},\theta_{\bm k},0) {\bm \epsilon'}^. ] + = {\bm D_{ij}}_. {\rm {\bm D}}^{-1} (\phi_{\bm F},\theta_{\bm F},0) + {\rm{ \bm D}} (\phi_{\bm k},\theta_{\bm k},0) \begin{pmatrix}a_{-} \ e^{i \Psi} \\ 0 \\ a_{+} \ e^{-i \Psi} + \end{pmatrix} + \end{equation} + + This formula is used in the code in the effectif\_dipole\_local function and the final result is + \begin{eqnarray*} + & & \hbar \Omega_{ji} / E_{\rm L} = \frac{1}{4} e^{-i + (\psi +{\phi_{\bm F}}+{\phi_{\bm k}})} \times \\ + & & \Big[ \cos ({\theta_{\bm k}}) \left(-{a_+}+{a_-} + e^{2 i \psi }\right) \left(\left(e^{2 i {\phi_{\bm F}}}+e^{2 i + {\phi_{\bm k}}}\right) \left(\sqrt{2} {D_0} \sin ({\theta_{\bm F}})+({D_-}-{D_+}) \cos ({\theta_{\bm F}})\right)-({D_-}+{D_+}) \left(e^{2 i {\phi_{\bm F}}}-e^{2 i + {\phi_{\bm k}}}\right)\right) \\ + & & -2 \sin ({\theta_{\bm k}}) e^{i + ({\phi_{\bm F}}+{\phi_{\bm k}})} \left(-{a_+}+{a_-} e^{2 i \psi }\right) \left(\sqrt{2} {D_0} \cos ({\theta_{\bm F}})+({D_+}-{D_-}) \sin ({\theta_{\bm F}})\right) \\ + & & +\left({a_+}+{a_-} e^{2 i \psi + }\right) \left(({D_-}+{D_+}) \left(e^{2 i {\phi_{\bm F}}}+e^{2 i + {\phi_{\bm k}}}\right)-\left(e^{2 i {\phi_{\bm F}}}-e^{2 i {\phi_{\bm k}}}\right) \left(\sqrt{2} {D_0} \sin ({\theta_{\bm F}})+({D_-}-{D_+}) \cos ({\theta_{\bm F}})\right)\right) \Big] + \end{eqnarray*} + + \subsection{Angular distribution of spontaneous emission: recoil} + + + The spontaneous emission rate between a level $| i \rangle $ and $|j\rangle$ is given by + $\Gamma =\|\rm d_{ij}\|^2 C_{{\rm Debye},s} E_{\rm cm}^3$ (function Gamma\_Level\_from\_diagonalized\_dipole in the code). In order to properly take into account the recoil momentum we need to know the angular distribution of the emitted photon. + For this we have to go back to the calculation of the spontaneous emission rate that originates form the quantized field + so from (Fermi golden rule) + $\sum_{\bm k,\pm 1} | \langle i | \bm d | j \rangle. {\bm \epsilon}_{\bm k \pm 1}|^2 = \sum_{\bm k} \left[ \sum_p | \bm d_{ji} . {{\bm e'}_{\bm k}}_p |^2 - | \bm d_{ji} . {{\bm e'}_{\bm k}}_0 |^2 \right] $. So by defining the + "polarization" vector of the emitted light as ${\bf{e}}_{\rm pol} = \bm d_{ji} /\|\bm d_{ji} \|$ we find that the probability distribution, for + the direction $\bm r = \bm k/k$ of the emitted photon, is + given by + $ \frac{3}{8\pi} [1-|\bm r.{\bf{e}}_{\rm pol}|^2]$, with the proper normalization (to $1$). + We recover Eq. (1.45) (see also Eq. (7.427)) of Ref. \cite{manual_Steck}. In the code (get\_unit\_vector\_spontaneous\_emission function) the photon is taken randomly (with the Von Neumann's acceptance-rejection sampling method) using this distribution. % That is in the quantization axis (field) frame $d_{ji} {\bf{e}}_{\rm pol} = \sum_q D_{ij;q} {\bf{E}}^q $. + + \subsection{Diagonalization of the states} + + + In most of the cases the eigenstates themselves are not changing during the evolution, only the energy changes. However, + as explained in section \ref{diagonalization} + we have the possibility + to diagonalize the hamiltonian, for instance, to calculate Zeeman and Stark effect for the magnetic $\bm B$ and electric $\bm E$ fields more exactly. For this purpose, + we give the bare states $|i\rangle_0$, their energies ${E_i}_0$, and the dipole transition moments + (in the Diagonalization\_Energy\_dipole function) as three matrix $\{ \bm d0_{-1},\bm d0_{0},\bm d0_{+1} \} $ in the quantization frame (so always assuming adiabatic following) with $ + (\bm d0_{q})_{ij} = + d0_{ij;q} = {}_0\langle i | \hat {\bm d} | j \rangle_0 . {\bf{E}}_q $. + + + Then, for each local perturbation $\hat V(\bm B(\bm r), \bm E(\bm r) )$ + (the perturbation $\hat V$ matrix is given in the Diagonalization\_Energy function), + we diagonalized $ \hat H = \hat H_0+\hat V$ to get the new eigenvectors + $| i\rangle = \sum_{i_0} {}_0\langle i_0 | i\rangle |i_0\rangle_0 = \sum_{i_0} {\rm \bm evec}_{i_0 i } |i_0\rangle_0 $ with the eigenvectors matrix ${\rm \bm evec}_{i_0 i } = + {}_0\langle i_0 | i\rangle$. We can then calculate the new dipoles + $ \langle i | \hat d_q | j \rangle = ({\rm \bm evec}^\dag.{\bm d0}_q.{\rm \bm evec})_{ij} $ that is coded with the dipole vector $ \{ d_{ij;-1},d_{ij;0},d_{ij;+1} \} $. + + +\bibliographystyle{unsrt} +\bibliography{bibli_user_guide} + + + +\end{document} + + + + diff --git a/User Guide/bibli_user_guide.bib b/User Guide/bibli_user_guide.bib new file mode 100644 index 0000000..262f82b --- /dev/null +++ b/User Guide/bibli_user_guide.bib @@ -0,0 +1,48 @@ +@article{comparat2014molecular, + title={Molecular cooling via Sisyphus processes}, + author={Comparat, Daniel}, + journal={Physical Review A}, + volume={89}, + number={4}, + pages={043410}, + year={2014}, + publisher={APS} +} + +@article{chaneliere2018phase, + title={Phase-space-density limitation in laser cooling without spontaneous emission}, + author={Chaneli{\`e}re, Thierry and Comparat, Daniel and Lignier, Hans}, + journal={Physical Review A}, + volume={98}, + number={6}, + pages={063432}, + year={2018}, + publisher={APS} +} + + +@article{comparat2020limitations, + title={Limitations for field-enhanced atom interferometry}, + author={Comparat, D}, + journal={Physical Review A}, + volume={101}, + number={2}, + pages={023606}, + year={2020}, + publisher={APS} +} + +@book{varshalovich1988quantum, + title={Quantum theory of angular momentum}, + author={Varshalovich, Dmitri{\u\i}} Aleksandrovich and Moskalev, Anatol{\"\i} Nikolaevitch and Khersonskii, Valerii Kel'manovich}, + year={1988}, + publisher={World Scientific} +} + + +@manual{manual_Steck, + title = {Quantum and Atom Optics}, + author = {Daniel Steck}, + address = {http://atomoptics-nas.uoregon.edu/~dsteck/teaching/quantum-optics/}, + year = 2020 +} \ No newline at end of file diff --git a/User Guide/classes.png b/User Guide/classes.png new file mode 100644 index 0000000..64d02aa Binary files /dev/null and b/User Guide/classes.png differ diff --git a/User Guide/diagonalization.png b/User Guide/diagonalization.png new file mode 100644 index 0000000..4097ce4 Binary files /dev/null and b/User Guide/diagonalization.png differ diff --git a/User Guide/diagonalization_converted_pdf.pdf b/User Guide/diagonalization_converted_pdf.pdf new file mode 100644 index 0000000..cb40eee Binary files /dev/null and b/User Guide/diagonalization_converted_pdf.pdf differ diff --git a/User Guide/evolution.png b/User Guide/evolution.png new file mode 100644 index 0000000..9ac3053 Binary files /dev/null and b/User Guide/evolution.png differ diff --git a/User Guide/laser_axis_polarization.png b/User Guide/laser_axis_polarization.png new file mode 100644 index 0000000..5cf2ac2 Binary files /dev/null and b/User Guide/laser_axis_polarization.png differ diff --git a/User Guide/linker.png b/User Guide/linker.png new file mode 100644 index 0000000..e00b84c Binary files /dev/null and b/User Guide/linker.png differ diff --git a/User Guide/picture.png b/User Guide/picture.png new file mode 100644 index 0000000..fe8ebf3 Binary files /dev/null and b/User Guide/picture.png differ