mbtrack2.utilities.misc module¶
This module defines miscellaneous utilities functions.
- effective_impedance(ring: Synchrotron, imp: Impedance, m: int, mu: int, sigma: float, M: int, tuneS: float, xi: float | None = None, mode: str = 'Hermite')[source]¶
Compute the effective (longitudinal or transverse) impedance. Formulas from Eq. (1) and (2) p238 of [1].
Parameters¶
ring : Synchrotron object imp : Impedance object mu : int
coupled bunch mode number, goes from 0 to (M-1) where M is the number of bunches
- mint
head-tail (or azimutal/synchrotron) mode number
- sigmafloat
RMS bunch length in [s]
- Mint
Number of bunches.
- tuneSfloat
Synchrotron tune.
- xifloat, optional
(non-normalized) chromaticity
- mode: str, optional
type of the mode taken into account for the computation: -“Hermite” modes for Gaussian bunches
Returns¶
- Zefffloat
effective impedance in [ohm] or in [ohm/m] depanding on the impedance type.
References¶
[1] : Handbook of accelerator physics and engineering, 3rd printing.
- head_tail_form_factor(ring: Synchrotron, imp: Impedance, m: int, sigma: float, tuneS: float, xi: float | None = None, mode: str = 'Hermite', mu: int = 0)[source]¶
Compute the head-tail form factor for the effective impedance. Formulas from Eq. (3) p238 of [1]. Parameters ———- ring : Synchrotron object
Synchrotron parameters.
- impImpedance object
Impedance spectrum.
- mint
Head-tail (or azimutal/synchrotron) mode number.
- sigmafloat
RMS bunch length in [s].
- tuneSfloat
Synchrotron tune.
- xifloat, optional
(non-normalized) chromaticity.
- mode: str, optional
Type of the mode taken into account for the computation: -“Hermite” modes for Gaussian bunches.
- muint, optional
Coupled bunch mode number, goes from 0 to (M-1) where M is the number of bunches. Default is 0.
Returns¶
- denfloat
Head-tail form factor in [ohm] or in [ohm/m] depending on the impedance type.
References¶
[1] : Handbook of accelerator physics and engineering, 3rd printing.
- yokoya_elliptic(x_radius: float, y_radius: float) tuple[float, float, float, float, float][source]¶
Compute Yokoya factors for an elliptic beam pipe.
Parameters¶
- x_radiusfloat
Horizontal semi-axis of the ellipse in [m].
- y_radiusfloat
Vertical semi-axis of the ellipse in [m].
Returns¶
- yoklongfloat
Yokoya factor for the longitudinal impedance.
- yokxdipfloat
Yokoya factor for the dipolar horizontal impedance.
- yokydipfloat
Yokoya factor for the dipolar vertical impedance.
- yokxquadfloat
Yokoya factor for the quadrupolar horizontal impedance.
- yokyquadfloat
Yokoya factor for the quadrupolar vertical impedance.
References¶
[1] : M. Migliorati, L. Palumbo, C. Zannini, N. Biancacci, and V. G. Vaccaro, “Resistive wall impedance in elliptical multilayer vacuum chambers.” Phys. Rev. Accel. Beams 22, 121001 (2019). [2] : R.L. Gluckstern, J. van Zeijts, and B. Zotter, “Coupling impedance of beam pipes of general cross section.” Phys. Rev. E 47, 656 (1993).
- beam_loss_factor(impedance: Impedance, frequency: ndarray[tuple[int, ...], dtype[_ScalarType_co]], spectrum: ndarray[tuple[int, ...], dtype[_ScalarType_co]], ring: Synchrotron) float[source]¶
Compute “beam” loss factor using the beam spectrum, uses a sum instead of integral compared to loss_factor [1].
Parameters¶
impedance : Impedance of type “long” frequency : array
Sample points of spectrum.
- spectrumarray
Beam spectrum to consider.
ring : Synchrotron object
Returns¶
- kloss_beamfloat
Beam loss factor in [V/C].
References¶
- [1]Handbook of accelerator physics and engineering, 3rd printing.
Eq (3) p239.