Twiss Optics

Main Classes Twiss Optics

Module twiss_optics.optics_class

Provides Classes to calculate optics from twiss parameters.

The calculation is based on formulas in [1] and [2].

Only works properly for on-orbit twiss files.

• Resonance Driving Terms: Eq. A8 in [2]
• Linear Dispersion: Eq. 24 in [2]
• Linear Chromaticity: Eq. 31 in [2]
• Chromatic Beating: Eq. 36 in [2]

References

[1]	M. Aiba et al., First simultaneous measurement of sextupolar and octupolar resonance driving terms in a circular accelerator from turn-by-turn beam position monitor data, Phys. Rev. ST Accel. Beams 17, 074001 (2014). https://journals.aps.org/prab/pdf/10.1103/PhysRevSTAB.17.074001

[2]	(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14) A. Franchi et al., Analytic formulas for the rapid evaluation of the orbit response matrix and chromatic functions from lattice parameters in circular accelerators https://arxiv.org/abs/1711.06589

[3]	(1, 2) R. Calaga et al., ‘Betatron coupling: Merging Hamiltonian and matrix approaches’ Phys. Rev. ST Accel. Beams, vol. 8, no. 3, p. 034001, Mar. 2005.

class twiss_optics.optics_class.TwissOptics(model_path_or_df, quick_init=True)

Class for calculating optics parameters from twiss-model.

Parameters:

• model_path_or_df -- Path to twissfile of model or DataFrame of model.
• quick_init -- Initializes without calculating phase advances. Default: False

calc_ac_dipole_driving_terms(order_or_terms, spectral_line, plane, ac_tunes, acd_name)

Calculates the Hamiltonian Terms under Forced Motion.

Parameters:

• order_or_terms -- int, string or list of strings If an int is given all Resonance Driving Terms up to this order will be calculated. The strings are assumed to be the desired driving term names, e.g. “F1001”
• spectral_line -- tuple Needed to determine what phase advance is needed before and after AC dipole location, depends on detal+ and delta-. Sample input: (2,-1)
• plane -- string Either ‘H’ or ‘V’ to determine phase term of AC dipole before and after ACD location.
• ac_tunes -- tuple Contains horizontal and vertical AC dipole tunes, i.e. (0.302, 0.33)

calc_chromatic_beating()

Calculate the Chromatic Beating

Eq. 36 in [2]

calc_chromatic_coupling()

Eq. 47, 48, B77 in [2]

calc_cmatrix()

Calculates C matrix and Coupling and Gamma from it. See [3]

calc_linear_chromaticity()

Calculate the Linear Chromaticity

Eq. 31 in [2]

calc_linear_dispersion()

Calculate the Linear Disperion.

Eq. 24 in [2]

calc_rdts(order_or_rdts)

Calculates the Resonance Driving Terms.

Eq. A8 in [2]

Parameters:order_or_rdts -- int, string or list of strings If an int is given all Resonance Driving Terms up to this order will be calculated. The strings are assumed to be the desired driving term names, e.g. “F1001”

calc_second_order_dispersion()

Eq. 11, 41 - 43 in [2]

define_plot_style(**kwargs)

Edit your desired plot style here

get_chromatic_beating()

Return the Chromatic Beating

Available after calc_chromatic_beating

get_cmatrix()

Return the C-Matrix

get_coupling(method='rdt')

Returns the coupling term.

Warning

This function changes sign of the real part of the RDTs compared to [2] to be consistent with the RDT calculations from [3] .

Parameters:method -- ‘rdt’ - Returns the values calculated by calc_rdts() ‘cmatrix’ - Returns the values calculated by calc_cmatrix()

get_gamma()

Return Gamma values.

get_linear_chromaticity()

Return the Linear Chromaticity

Available after calc_linear_chromaticity

get_linear_dispersion()

Return the Linear Dispersion.

Available after calc_linear_dispersion!

get_phase_adv()

Wrapper for returning the matrix of phase-advances.

get_rdts(rdt_names=None)

Return Resonance Driving Terms.

plot_chromatic_beating(combined=True)

Plot the Chromatic Beating

Available after calc_chromatic_beating

Parameters:combined (bool) -- If ‘True’ plots x and y into the same axes.

plot_linear_dispersion(combined=True)

Plot the Linear Dispersion.

Available after calc_linear_dispersion!

Parameters:combined (bool) -- If ‘True’ plots x and y into the same axes.

plot_phase_advance(combined=True)

Plots the phase advances between two consecutive elements

Parameters:combined (bool) -- If ‘True’ plots x and y into the same axes.

plot_rdts(rdt_names=None, apply_fun=<ufunc 'absolute'>, combined=True)

Plot Resonance Driving Terms

Helpers Twiss Optics

Module twiss_optics.twiss_functions

Common Functions not attached to any class in this module.

twiss_optics.twiss_functions.dphi(data, q)

Return dphi from phase advances in data, see Eq. 8 in [2]

twiss_optics.twiss_functions.get_all_rdts(n)

Returns list of all valid RDTs of order 2 to n

twiss_optics.twiss_functions.get_phase_advances(twiss_df)

Calculate phase advances between all elements

Returns:Matrices similar to DPhi(i,j) = Phi(j) - Phi(i)

twiss_optics.twiss_functions.lower(list_of_strings)

Set all items of list to lowercase

twiss_optics.twiss_functions.rdt_generator(orders, normal=True, skew=True, complex_conj=True)

Generates lists of RDT-4-tuples sorted into a dictionary by order.

Parameters:

• orders (list) -- list of orders to be generated. Orders < 2 raise errors.
• normal (bool) -- calculate normal RDTs (default: True)
• skew (bool) -- calculate skew RDTs (default: True)
• complex_conj (bool) -- Have both, RDT and it’s complex conjugate RDT in the list (default: True)

Returns:

Dictionary with keys of orders containing lists of 4-Tuples for the RDTs of that order.

twiss_optics.twiss_functions.tau(data, q)

Return tau from phase advances in data, see Eq. 16 in [2]

twiss_optics.twiss_functions.upper(list_of_strings)

Set all items of list to uppercase