mbtrack2.tracking.emfields module¶

A package dealing with particles electromagnetic fields. For example, it can be applied to space charge, beam-beam force, electron lenses or beam-ion instabilities. This is largely adapted from a fork of PyHEADTAIL https://github.com/gubaidulinvadim/PyHEADTAIL. Only the fastest Fadeeva implementation of the error function is used here. See Oeftiger, A., de Maria, R., Deniau, L., Li, K., McIntosh, E., Moneta, L., Hegglin, S., Aviral, A. (2016). Review of CPU and GPU Faddeeva Implementations. https://cds.cern.ch/record/2207430/files/wepoy044.pdf

_wofz(x: ndarray[tuple[int, ...], dtype[_ScalarType_co]], y: ndarray[tuple[int, ...], dtype[_ScalarType_co]]) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Compute the Faddeeva function w(z) = exp(-z^2) * erfc(-i*z).

Parameters¶

xfloat: Real part of the argument.
yfloat: Imaginary part of the argument.

Returns¶

tuple: Real and imaginary parts of the Faddeeva function.

_sqrt_sig(sig_x: float, sig_y: float) → float[source]¶

Compute the square root of the difference between the squared transverse rms and vertical rms.

Parameters¶

sig_xfloat: Transverse rms of the distribution.
sig_yfloat: Vertical rms of the distribution.

Returns¶

float: Square root of the difference between the squared transverse rms and vertical rms.

_efieldn_mit(x: ndarray[tuple[int, ...], dtype[_ScalarType_co]], y: ndarray[tuple[int, ...], dtype[_ScalarType_co]], sig_x: float, sig_y: float) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Returns electromagnetic fields as E_x/Q, E_y/Q in (V/m/Coulomb).

Parameters¶

xnp.ndarray: x coordinates in meters.
ynp.ndarray: y coordinates in meters.
sig_xfloat: Transverse rms of the distribution in meters.
sig_yfloat: Vertical rms of the distribution in meters.

Returns¶

tuple: Normalized electromagnetic fields Ex/Q, Ey/Q in the units of (V/m/Coulomb).

efieldn_gauss_round(x: ndarray[tuple[int, ...], dtype[_ScalarType_co]], y: ndarray[tuple[int, ...], dtype[_ScalarType_co]], sig_r: float, sig_r2: None = None) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Computes the electromagnetic field of a round Gaussian distribution.

Parameters¶

xnp.ndarray: x coordinates in meters.
ynp.ndarray: y coordinates in meters.
sig_rfloat: Transverse rms of the distribution in meters.

Returns¶

tuple: Normalized electromagnetic fields Ex/Q, Ey/Q in the units of (V/m/Coulomb).

_efieldn_linearized(x: ndarray[tuple[int, ...], dtype[_ScalarType_co]], y: ndarray[tuple[int, ...], dtype[_ScalarType_co]], sig_x: float, sig_y: float) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Computes linearized electromagnetic field.

Parameters¶

xnp.ndarray: x coordinate in meters.
ynp.ndarray: y coordinate in meters.
sig_xfloat: Vertical rms of the distribution in meters.
sig_yfloat: Vertical rms of the distribution in meters.

Returns¶

tuple: Normalized electromagnetic fields Ex/Q, Ey/Q in the units of (V/m/Coulomb).

add_sigma_check(efieldn: Callable) → Callable[source]¶

Wrapper for a normalized electromagnetic field function. Adds the following actions before calculating the field: 1) Exchange x and y quantities if sig_x < sig_y. 2) Apply round beam field formula when sig_x is close to sig_y.

Parameters¶

efieldnfunction: Function to calculate normalized electromagnetic field.

Returns¶

function: Wrapped function, including round beam and inverted sig_x/sig_y.

get_displaced_efield(efieldn: Callable, xr: ndarray[tuple[int, ...], dtype[_ScalarType_co]], yr: ndarray[tuple[int, ...], dtype[_ScalarType_co]], sig_x: float, sig_y: float, mean_x: float, mean_y: float) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Compute the charge-normalized electric field components of a two-dimensional Gaussian charge distribution.

Parameters¶

efieldnfunction: Calculates electromagnetic field of a given distribution of charges.
xrnp.array: x coordinates in meters.
yrnp.array: y coordinates in meters.
sig_xfloat: Horizontal rms size in meters.
sig_yfloat: Vertical rms size in meters.
mean_xfloat: Horizontal mean of the distribution in meters.
mean_yfloat: Vertical mean of the distribution in meters.

Returns¶

tuple: Charge-normalized electromagnetic fields with a displaced center of the distribution.