core.beam_parameters.helper module

Define functions useful for beam parameters calculations.

For more information on the units that are used in this module, see Units and conventions.

envelopes_from_sigma(phase_space_name: str, sigma: ndarray) → ndarray

Compute the envelopes.

Units are \(mm\) for the position envelope in \([z-\delta]\), \([x-x']\), \([y-y']\). Units are \(%\) for the energy envelope in \([z-\delta]\), and \(mrad\) for \([x-x']\) and \([y-y']\).

Parameters:

phase_space_name (str) – Name of the phase space, used to set the proper normalization.
sigma (np.ndarray) – (n, 2, 2) (or (2, 2)) array holding \(\sigma\) beam matrix.

Returns:

envelopes – (n, 2) (or (2, )) array with position envelope in first column, energy envelope in second.

Return type:

np.ndarray

envelopes_from_twiss_eps(twiss: ndarray, eps: ndarray | float) → ndarray

Compute the envelopes from the Twiss parameters and emittance.

Parameters:

twiss (np.ndarray) – (n, 3) (or (3, )) array of Twiss parameters.
eps (np.ndarray) – (n, ) array of emittance. If the phase space is \([\phi-W]\), the emittance should be normalized. Else, it should be un-normalized.

Returns:

envelopes – (n, 2) (or (2, )) array with position envelope in first column, energy envelope in second.

Return type:

np.ndarray

eps_from_other_phase_space(other_phase_space_name: str, phase_space_name: str, eps_other: ndarray, gamma_kin: ndarray, beta_kin: ndarray) → tuple[ndarray, ndarray]

eps_from_other_phase_space(other_phase_space_name: str, phase_space_name: str, eps_other: float, gamma_kin: float, beta_kin: float) → tuple[float, float]

Convert emittance from another phase space.

Output emittance is normalized if input is, and is un-normalized if the input emittance is not normalized.

Warning

old funct returned eps with same normalisation state as given eps_other

Parameters:

other_phase_space_name (str) – Name of the original phase space.
phase_space_name (str) – Name of the phase space, used to ensure correct normalization/denormalization.
eps_other (np.ndarray | float) – (n, ) array (or float) of emittance of starting phase-space.
gamma_kin (np.ndarray | float) – (n, ) array (or float) of Lorentz gamma.
beta_kin (np.ndarray | float) – (n, ) array (or float) of Lorentz beta

Returns:

eps_no_normalisation (np.ndarray | float) – (n, ) array (or float) of emittance, not normalized.
eps_normalized (np.ndarray | float) – (n, ) array (or float) of emittance, normalized.

eps_from_sigma(phase_space_name: str, sigma: ndarray, gamma_kin: ndarray, beta_kin: ndarray) → tuple[ndarray, ndarray]

eps_from_sigma(phase_space_name: str, sigma: ndarray, gamma_kin: float, beta_kin: float) → tuple[float, float]

Compute emittance from \(\sigma\) beam matrix.

In the \([z-\delta]\) phase space, emittance is in \(\pi.\mathrm{mm.\%}\). In the transverse phase spaces, emittance is in \(\pi.\mathrm{mm.mrad}\). \(\sigma\) is always in SI units.

Parameters:

phase_space_name (str) – Name of the phase space, used to apply proper normalization factor.
sigma (np.ndarray) – (n, 2, 2) (or (2, 2)) \(\sigma\) beam matrix in SI units.
gamma_kin (np.ndarray | float) – (n, ) (or float) Lorentz gamma factor.
beta_kin (np.ndarray | float) – (n, ) (or float) Lorentz beta factor.

Returns:

eps_no_normalisation (np.ndarray | float) – (n, ) array (or float) of emittance, not normalized.
eps_normalized (np.ndarray float) – (n, ) array (or float) of emittance, normalized.

mismatch_from_arrays(ref: ndarray, fix: ndarray, transp: bool = False) → ndarray: Compute the mismatch factor between two ellipses.

reconstruct_sigma(phase_space_name: str, sigma_00: ndarray, sigma_01: ndarray, eps: ndarray, tol: float = 1e-08, eps_is_normalized: bool = False, gamma_kin: ndarray | None = None, beta_kin: ndarray | None = None) → ndarray

Set \(\sigma\) matrix from the two top components and emittance.

Inputs are in \(\mathrm{mm}\) and \(\mathrm{mrad}\), but the \(\sigma\) matrix is in SI units (\(\mathrm{m}\) and \(\mathrm{rad}\)).