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BBFootprint

Installation

No particular installation is required, other than copying the twiss/survey as pickle files from https://cernbox.cern.ch/index.php/s/bQqj58FQDVgGUfw

About

The main tools of this backage are found in Backend/Detuning.py and Backend/InteractionPoint.py. One can extract all the relevant HO and LR information for each IPs using:

import pandas as pd
import Backend.InteractionPoint as inp

# Importing twiss/survey files
twiss_b1  = pd.read_pickle('LHC_sequence/lhcb1_opticsfile30_twiss.pkl')
survey_b1 = pd.read_pickle('LHC_sequence/lhcb1_opticsfile30_survey.pkl')

twiss_b2  = pd.read_pickle('LHC_sequence/lhcb2_opticsfile30_twiss.pkl')
survey_b2 = pd.read_pickle('LHC_sequence/lhcb2_opticsfile30_survey.pkl')

# Creating beam objects:    
B1 = inp.Beam('b1',twiss_b1,survey_b1,
          Nb       = 1.15e11,
          E        = 6.8e12,
          emittx_n = 2.5e-6,
          emitty_n = 2.5e-6,
          dp_p0    = 0)
    
B2 = inp.Beam('b2',twiss_b2,survey_b2,
              Nb       = 1.15e11,
              E        = 6.8e12,
              emittx_n = 2.5e-6,
              emitty_n = 2.5e-6,
              dp_p0    = 0)

# Attaching beams to the IPs and extracting the relevant twiss/survey for the IP
IP1 = inp.InteractionPoint('ip1',B1,B2)
IP5 = inp.InteractionPoint('ip5',B1,B2)

From there, IP1.b1.twiss contains all the information necessary, including the coordinates in the lab frame, and IP1.bb/IP1.lr/IP1.ho contains dataframes with the BB parameters computed for All BB/LR only/HO only.

An example of footprint computation is found in demo_detuning.ipynb.

Detuning

The detuning from a given LR (or HO) interaction can be computed analytically following:

import Backend.Detuning as dtune

_bb = IP5.lr.loc['bb_lr.r5b1_13']

DQx,DQy = dtune.DQx_DQy( ax   = coord['x_n'],
                         ay   = coord['y_n'],
                         r    = _bb['r'],
                         dx_n = _bb['dx_n'],
                         dy_n = _bb['dy_n'],
                         A_w_s= _bb['A_w_s'],
                         B_w_s= _bb['B_w_s'],
                         xi   = IP5.b2.xi)

The explanation for the physics and the underlying equations can be found from the papers in: https://cernbox.cern.ch/index.php/s/bQqj58FQDVgGUfw

Note that A_w_s and B_w_s are described in the addendum. These numbers are necessary for the general solution of the detuning, where the optics of the weak beam and the strong beam are not necessarily antisymmetric.