mbtrack2.tracking.wakepotential module¶

This module defines the WakePotential and LongRangeResistiveWall classes which deal with the single bunch and multi-bunch wakes.

class WakePotential(ring: Synchrotron, wakefield: WakeField, n_bin: int = 80, interp_on_position: bool = True)[source]¶

Bases: Element

Compute a wake potential from uniformly sampled wake functions by performing a convolution with a bunch charge profile.

Two different time bases are used. The first one is controled by the n_bin parameter and is used to compute the bunch profile. Then the bunch profile is interpolated on the wake function time base which is used to perform the convolution to get the wake potential.

Parameters¶

ring : Synchrotron object wakefield : Wakefield object

Wakefield object which contains the wake functions to be used. The wake functions must be uniformly sampled!

n_binint, optional: Number of bins for constructing the longitudinal bunch profile.
interp_on_positionbool, optional: If True, the computed wake potential is interpolated on the exact particle location. If False, the wake potential is interpolated on the bin center and each particle of the bin get the same value. Default is True.

Attributes¶

rhoarray of shape (n_bin, ): Bunch charge density profile in the unit [1/s].
Wparray: Wake potential profile.
Wp_interparray of shape (mp_number, ): Wake potential, obtained from interpolating Wp, exerted on each macro-particle.

Methods¶

charge_density(bunch): Compute bunch charge density profile in [1/s].
dipole_moment(bunch, plane, tau0): Return the dipole moment of the bunch computed on the same time array as the wake function.
prepare_wakefunction(wake_type): Prepare the wake function of a given wake_type to be used for the wake potential computation.
get_wakepotential(bunch, wake_type): Return the wake potential computed on the wake function time array limited to the bunch profile.
track(bunch): Tracking method for the element.
plot_last_wake(wake_type): Plot the last wake potential of a given type computed during the last call of the track method.
reference_loss(bunch): Calculate the loss factor and kick factor from the wake potential and compare it to a reference value assuming a Gaussian bunch computed in the frequency domain.
check_sampling(): Check if the wake function sampling is uniform.
reduce_sampling(factor): Reduce wake function samping by an integer factor.

__init__(ring: Synchrotron, wakefield: WakeField, n_bin: int = 80, interp_on_position: bool = True)[source]¶

_interp_regular_numpy(x_new: ndarray[tuple[int, ...], dtype[_ScalarType_co]], x_min: float, dx: float, y: ndarray[tuple[int, ...], dtype[_ScalarType_co]]) → ndarray[tuple[int, ...], dtype[_ScalarType_co]][source]¶

Linear interpolation funtion for uniformly sampled input data.

Parameters¶

x_newarray: New interpolation base.
x_minfloat: Minimum value of the original interpolant base.
dxfloat: Step of the original interpolant base.
yarray: Data to interpolate.

Returns¶

resultarray of len(x_new): Data interpolated on x_new coordinates.

charge_density(bunch: Bunch)[source]¶: Compute bunch charge density profile in [1/s].

Parameters¶

bunch : Bunch object

dipole_moment(bunch: Bunch, plane: str, tau0: ndarray[tuple[int, ...], dtype[_ScalarType_co]]) → ndarray[tuple[int, ...], dtype[_ScalarType_co]][source]¶

Return the dipole moment of the bunch computed on the same time array as the wake function.

Parameters¶

bunch : Bunch object plane : str

Plane on which the dipole moment is computed, “x” or “y”.

tau0array: Time array on which the dipole moment will be interpolated, in [s].

Returns¶

dipolearray: Dipole moment of the bunch.

prepare_wakefunction(wake_type: str, tau: ndarray[tuple[int, ...], dtype[_ScalarType_co]], save_data: bool = True) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], float, ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Prepare the wake function of a given wake_type to be used for the wake potential computation.

The new time array keeps the same sampling time as given in the WakeFunction definition but is restricted to the bunch profile time array.

Parameters¶

wake_typestr: Type of the wake function to prepare: “Wlong”, “Wxdip”, …
tauarray: Time domain array of the bunch profile in [s].
save_databool, optional: If True, the results are saved as atributes.

Returns¶

tau0array: Time base of the wake function in [s].
dtau0float: Difference between two points of the wake function time base in [s].
W0array: Wake function array in [V/C] or [V/C/m].

get_wakepotential(bunch: Bunch, wake_type: str) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Return the wake potential computed on the wake function time array limited to the bunch profile.

Parameters¶

bunch : Bunch object wake_type : str

Wake function type: “Wlong”, “Wxdip”, …

Returns¶

tau0array: Time base.
Wparray: Wake potential.

track(bunch: Bunch | Beam)[source]¶: Tracking method for the element. No bunch to bunch interaction, so written for Bunch objects and @Element.parallel is used to handle Beam objects.

Parameters¶

bunch : Bunch or Beam object.

plot_last_wake(wake_type: str, plot_rho: bool = True, plot_dipole: bool = False, plot_wake_function: bool = True, ax: Axes | None = None) → Axes[source]¶

Plot the last wake potential of a given type computed during the last call of the track method.

Parameters¶

wake_typestr: Type of the wake to plot: “Wlong”, “Wxdip”, …
plot_rhobool, optional: Plot the normalised bunch profile. The default is True.
plot_dipolebool, optional: Plot the normalised dipole moment. The default is False.
plot_wake_functionbool, optional: Plot the normalised wake function. The default is True.
axAxes, optional: Axes where the plot is displayed. If None, a new figure is created.

Returns¶

ax : Axes

get_gaussian_wakepotential(sigma: float, wake_type: str, dipole: float = 0.001) → tuple[ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]], ndarray[tuple[int, ...], dtype[_ScalarType_co]]][source]¶

Return the wake potential computed using a perfect gaussian profile.

Parameters¶

sigmafloat: RMS bunch length in [s].
wake_typestr: Wake function type: “Wlong”, “Wxdip”, …
dipolefloat, optional: Dipole moment to consider in [m], (uniform dipole moment).

Returns¶

tau0array: Time base in [s].
W0array: Wake function.
Wparray: Wake potential.
profile0array: Gaussian bunch profile.
dipole0array: Dipole moment.

plot_gaussian_wake(sigma: float, wake_type: str, dipole: float = 0.001, plot_rho: bool = True, plot_dipole: bool = False, plot_wake_function: bool = True, ax: Axes | None = None) → Axes[source]¶

Plot the wake potential of a given type for a perfect gaussian bunch.

Parameters¶

sigmafloat: RMS bunch length in [s].
wake_typestr: Type of the wake to plot: “Wlong”, “Wxdip”, …
dipolefloat, optional: Dipole moment to consider in [m], (uniform dipole moment).
plot_rhobool, optional: Plot the normalised bunch profile. The default is True.
plot_dipolebool, optional: Plot the normalised dipole moment. The default is False.
plot_wake_functionbool, optional: Plot the normalised wake function. The default is True.
axAxes, optional: Axes where the plot is displayed. If None, a new figure is created.

Returns¶

ax : Axes

reference_loss(bunch: Bunch) → DataFrame[source]¶

Calculate the loss factor and kick factor from the wake potential and compare it to a reference value assuming a Gaussian bunch computed in the frequency domain.

Parameters¶

bunch : Bunch object

Returns¶

loss_dataDataFrame: An output showing the loss/kick factors compared to the reference values.

check_sampling()[source]¶: Check if the wake function sampling is uniform.

Raises¶

ValueError

reduce_sampling(factor: int)[source]¶

Reduce wake function samping by an integer factor.

Used to reduce computation time for long bunches.

Parameters¶

factor : int

_set_wakefunction_max_frequency()[source]¶

property wakefunction_max_frequency: float¶: Return the wake function maximum frequency in [Hz].

property binning_max_frequency: float¶: Return the binning maximum frequency in [Hz].

property wakepotential_max_frequency: float¶: Return the wake potential maximum frequency in [Hz].

_abc_impl = <_abc._abc_data object>¶

class LongRangeResistiveWall(ring: Synchrotron, beam: Beam, length: float, rho: float, radius: float, types: list[str] = ['Wlong', 'Wxdip', 'Wydip'], nt: int = 50, x3: float | None = None, y3: float | None = None, x3_quad: float | None = None, y3_quad: float | None = None, average_beta: ndarray[tuple[int, ...], dtype[_ScalarType_co]] | None = None)[source]¶

Bases: Element

Element to deal with multi-bunch and multi-turn wakes from resistive wall using the algorithm defined in [1].

Main approximations:

Bunches are treated as point charge.
Assymptotic expression for the resistive wall wake functions are

used. - Multi-turn wakes are limited to nt turns.

Self-bunch interaction is not included in this element and should be dealed with the WakePotential class.

Parameters¶

ring : Synchrotron object beam : Beam object length : float

Length of the resistive pipe to consider in [m].

rhofloat: Effective resistivity to consider in [ohm.m] as in [1].
radiusfloat: Beam pipe radius to consider in [m].
typesstr or list, optional: Wake types to consider. Available types are: “Wlong”,”Wxdip”,”Wydip”,”Wxquad”,”Wyquad”. The default is [“Wlong”,”Wxdip”,”Wydip”].
ntint or float, optional: Number of turns to consider for the long range wakes. The default is 50.
x3float, optional: Horizontal effective radius of the 3rd power in [m], as Eq.27 in [1]. The default is radius.
y3float, optional: Vertical effective radius of the 3rd power in [m], as Eq.27 in [1]. The default is radius.
x3_quadfloat, optional: Quadrupolar wake horizontal effective radius of the 3rd power in [m]. As given by ResistiveWallModel.resistive_wall_effective_radius_yokoya. The quadrupolar radius can be either be positive (defocusing) or negative (focusing). The default is None.
y3_quadfloat, optional: Quadrupolar wake vertical effective radius of the 3rd power in [m]. As given by ResistiveWallModel.resistive_wall_effective_radius_yokoya. The quadrupolar radius can be either be positive (defocusing) or negative (focusing). The default is None.
average_betaarray-like of shape (2,), optional: Average beta function used for kick normalization in [m]. The transverse kick is normalized by average_beta / local_beta. If None and an AT lattice is loaded, average_beta is computed from the lattice. If None and an AT lattice is not loaded, average_beta is taken to be equal to local_beta, i.e. no normalization. The default is None.

References¶

[1] : Skripka, Galina, et al. “Simultaneous computation of intrabunch and interbunch collective beam motions in storage rings.” NIM.A (2016).

__init__(ring: Synchrotron, beam: Beam, length: float, rho: float, radius: float, types: list[str] = ['Wlong', 'Wxdip', 'Wydip'], nt: int = 50, x3: float | None = None, y3: float | None = None, x3_quad: float | None = None, y3_quad: float | None = None, average_beta: ndarray[tuple[int, ...], dtype[_ScalarType_co]] | None = None)[source]¶

Wlong(t: float) → float[source]¶

Approxmiate expression for the longitudinal resistive wall wake function - Eq.24 of [1].

Parameters¶

tfloat: Time in [s].

Returns¶

wlfloat: Wake function in [V/C].

Wdip(t: float, plane: str) → float[source]¶

Approxmiate expression for the transverse resistive wall wake function - Eq.26 of [1].

Parameters¶

tfloat: Time in [s].
planestr: “x” or “y”.

Returns¶

wdipfloat: Wake function in [V/C/m].

update_tables(beam: Beam)[source]¶

Update tables.

Table tau[i,j] is defined as the time difference of the bunch i center of mass with respect to center of the RF bucket number 0 at turn j. Turn 0 corresponds to the tracked turn.

Positive time corresponds to past events and negative time to future events.

Parameters¶

beam : Beam object

Returns¶

None.

_abc_impl = <_abc._abc_data object>¶

get_kick(rank: int, wake_type: float) → float[source]¶

Compute the wake kick to apply.

Parameters¶

rankint: Rank of the bunch, as defined in Mpi class.
wake_typefloat: Type of the wake to compute.

Returns¶

sum_kickfloat: Sum of the kicks from the different bunches at different turns.

track_bunch(bunch: Bunch, rank: int)[source]¶

Track a bunch.

Should only be used within the track method and not standalone.

Parameters¶

bunch : Bunch object rank : int

Rank of the bunch, as defined in Mpi class.

Returns¶

None.

track(beam: Beam)[source]¶: Track a beam.

Parameters¶

beam : Beam object

Returns¶

None.

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