Twiss module
This module allows to calculate the different parameters of Twiss as well as the dispersion based on a propagation matrix. It is possible either to compute the periodic Twiss function of a lattice or to compute the propagation of an initial BetaBlock. The standard uncoupled Twiss parametrization (including off-momentum effects, aka. dispersion) is the default option. Additional formalisms for the parametrization of fully coupled transfer matrices are also available (Parzen, Lebedev and Bogacz). More details about the coupled parametrizations can be found in this paper
Herebelow, there is some examples on how to use the Twiss module.
import os
import pandas as pd
import georges_core
from georges_core.units import ureg as _ureg
from georges_core.sequences import BetaBlock
from georges_core.twiss import Twiss
twiss_init = BetaBlock(BETA11 = 1*_ureg.m,
BETA22 = 2*_ureg.m)
tw = Twiss(twiss_init=twiss_init, with_phase_unrolling=False)
# Load a transfer matrix which can computed with MAD-X or Zgoubidoo.
results_twiss = tw(matrix=matrix)
You can now have acces to the Twiss functions along the line as well as the dispersion:
print(results_twiss)
R11 R12 R13 R14 R15 R16 R21 R22 \
NAME
RING$START 0.653840 3.064809 0 0 0 0.419714 -0.080063 1.154138
MQF1 0.212111 3.205167 0 0 0 0.473953 -0.206385 1.595868
D1 0.108918 3.948641 0 0 0 0.670108 -0.206385 1.699060
MQD 1.185141 4.107119 0 0 0 0.759262 -0.063755 0.622838
D2 1.172390 3.997208 0 0 0 0.798868 -0.063755 0.635589
BD 1.090919 3.077186 0 0 0 0.283823 -0.070761 0.717059
D3 1.076767 3.005244 0 0 0 0.340444 -0.070761 0.731212
MQF2 0.661847 3.015579 0 0 0 0.386506 -0.080063 1.146132
D4 0.653840 3.064809 0 0 0 0.419714 -0.080063 1.154138
RING$END 0.653840 3.064809 0 0 0 0.419714 -0.080063 1.154138
R23 R24 ... GAMMA11 GAMMA22 MU1 MU2 DET1 DET2 \
NAME ...
RING$START 0 0 ... 1.338446 0.231914 1.360609 1.042639 1.0 1.0
MQF1 0 0 ... 2.589389 0.083334 1.504715 0.852012 1.0 1.0
D1 0 0 ... 2.929401 0.101987 1.543220 0.776828 1.0 1.0
MQD 0 0 ... 0.391991 0.606416 1.289870 1.102309 1.0 1.0
D2 0 0 ... 0.408037 0.617991 1.285496 1.116647 1.0 1.0
BD 0 0 ... 0.519181 0.739811 1.230102 1.256677 1.0 1.0
D3 0 0 ... 0.539678 0.752600 1.226750 1.269476 1.0 1.0
MQF2 0 0 ... 1.320029 0.228644 1.354746 1.046370 1.0 1.0
D4 0 0 ... 1.338446 0.231914 1.360609 1.042639 1.0 1.0
RING$END 0 0 ... 1.338446 0.231914 1.360609 1.042639 1.0 1.0
DISP1 DISP2 DISP3 DISP4
NAME
RING$START 0.419714 0.332089 0.0 0.0
MQF1 0.473953 0.392310 0.0 0.0
D1 0.670108 0.392310 0.0 0.0
MQD 0.759262 0.198032 0.0 0.0
D2 0.798868 0.198032 0.0 0.0
BD 0.283823 0.283103 0.0 0.0
D3 0.340444 0.283103 0.0 0.0
MQF2 0.386506 0.332089 0.0 0.0
D4 0.419714 0.332089 0.0 0.0
RING$END 0.419714 0.332089 0.0 0.0
[10 rows x 50 columns]