Multipacting analysis of the TESLA mid-cell

This example reproduces the benchmark of the PyMultipact paper (IPAC’24, MOPS27): the mid-cell of the TESLA cavity is meshed, its fundamental (TM$_{010}$) mode is solved with NGSolve, and electrons emitted from the equator region are tracked over a sweep of peak surface electric field levels to locate the multipacting band.

See the Theory page for the governing equations and the definitions of the metrics plotted below.

%matplotlib inline
import numpy as np

from pymultipact.domain import Project, Domain

Domain and eigenmode

A Project names the working folder; the Domain reads the TESLA mid-cell contour, resamples the boundary polyline (~250 points) and meshes it. compute_fields() solves the Maxwell eigenvalue problem with third-order Nédélec elements — the TM$_{010}$ frequency of the mid-cell is 1300 MHz.

proj = Project()
proj.create_project('TESLA')

domain = Domain(proj)
domain.compute_fields()

Boundary polyline resampled: 1049 -> 147 points (n_boundary_points=None keeps the full resolution)
Boundary polyline resampled: 1831 -> 147 points (n_boundary_points=None keeps the full resolution)

0 -2.5135035950784276e-14 freq:  nan MHz
1 742.4614307569854 freq:  1300.1030691666238 MHz
2 2656.757500289286 freq:  2459.329913290589 MHz
../_images/0cb7e9b59ee116e9c53ab9bc60dab61465f313715e11cd35102b8962735ab513.png

Emission sites

Electrons are launched from surface sites in a window on the equator side of the cell (circles below), each over a full turn of initial RF phases.

xrange = [-0.025, 0.0]
domain.show_initial_points(xrange, step=0.002)
../_images/545265124708c2a4e3736aaf41082055914599f44bf8c0c767bc2d0a50dead27.png

Field-level sweep

analyse_multipacting tracks every (site, phase) electron for 10 RF periods at each peak-field value. The sweep is parallelised over the field levels by default (proc_count=None uses the machine’s cores; from a plain script on Windows, call it under if __name__ == '__main__':).

epks = np.linspace(1, 90, 179) * 1e6          # peak surface field [V/m]
phis = np.linspace(0, 2 * np.pi, 72)          # initial phases

domain.analyse_multipacting(mode=1, epks=epks, phis=phis,
                            xrange=xrange, step=0.002, proc_count=12)

Running Epk sweep (179 points) on 12 processes.

Total runtime::  354.7451310157776
Done with multipacting analysis.

Counter function

The fraction of electrons surviving 20 impacts. The TESLA mid-cell shows its well-known two-point multipacting band at roughly 29–59 MV/m plus narrow low-field resonances. launchable_norm=True divides by the ~50% of initial phases that can actually emit (the normalisation MultiPac uses), making the curve directly comparable with MultiPac results.

domain.plot_cf(launchable_norm=True)
../_images/164f53d7d69e43160a2f6f5abefd5fd19c169874850344ec5f35c3144140e87a.png

Final impact energy

The mean final (20th) impact energy of the surviving electrons. The solid red lines are the SEY crossover energies ($\delta = 1$) and the dashed line the peak-SEY energy of the surface data: multipacting sustained at impact energies between the crossovers can multiply.

domain.plot_Ef()
../_images/ce9a4fc28e76d476502a95a9eefbae48d7f9eb59df2da7c58c310e6062942b54.png

Enhanced counter function

Weights every surviving trajectory by the product of its per-impact secondary yields — values above 1 (red line) mean the electron population truly grows.

domain.plot_ef()
../_images/cf6965221b211572943dfb800777d6fc21589c1b92c56354438988e9f00c2bc8.png

Distance map

For one field level inside the band, the distance function $d_{20}$ over (emission site, initial phase): the distance between the launch point and the nearest of the last two impacts (two-point orbits return to the launch side on every other impact). The dark core marks the resonant fixed-point phase; the colour grades with the launch offset from it, and grey cells did not survive to 20 impacts – the same structure as MultiPac’s $d_{20}$ map. Also available: metric='d20_strict' (literal thesis definition from the 20th impact) and metric='closure' (orbit-closure test, 20th vs 18th impact).

i_band = int(np.argmin(np.abs(epks - 43e6)))   # ~43 MV/m
domain.plot_df(i_band)
../_images/2804d35a02a3dc6860cd1ff33fb48fae80f06cac99103551c51bc836111822ad.png

Further exploration

  • domain.plot_trajectories() opens an interactive browser (sliders) over the surviving trajectories of each field level.

  • domain.analyse_multipacting(loss_model=...) switches the treatment of impacts at unfavourable field phase ('field', 'wait', 'always').

  • domain.set_sey(path) loads a different secondary emission yield table.

  • Domain(proj, n_boundary_points=None) keeps the full boundary resolution (the original TESLA contour is preserved in sample_domains/tesla_mid_cell_fine.n).