First-principles simulation of free-electron lasers with the Galilean electromagnetic particle-in-cell method: even harmonics of planar undulators
Abstract
Free-electron laser (FEL) codes average the electron motion over the undulator period and add the radiation harmonics through on-axis coupling factors. This is accurate for the fundamental, but the even harmonics of a planar undulator, which vanish on the axis, are not modelled at all. We show that the Galilean electromagnetic particle-in-cell method (GEM-PIC), which resolves the electron motion within the undulator period and the carrier of the forward radiation field without a Courant limit, simulates FELs on two CPU cores at two to three times the cost of a time-dependent run of the averaged code GENESIS. The quasi-cylindrical code GEM-PIC-RZ reproduces the coherent spontaneous emission of a planar undulator in each azimuthal mode m = 0--3 to within 2\,\% of the radiation integral, and seeded amplifiers to within a few per cent of GENESIS run with the same physics. For a seeded planar FEL at 10.6\,nm it predicts 12\,MW of second-harmonic power at saturation, 1.1×10−3 of the fundamental; this harmonic is absent from the averaged model. The unaveraged code Puffin, which has no space charge, gives a comparable level, 9 to 11\,MW for the space-charge-widened and the initial beam size, and the same transverse structure.
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BibTeX
@misc{pukhov2026firstprinciples,
title = {{First-principles simulation of free-electron lasers with the Galilean electromagnetic particle-in-cell method: even harmonics of planar undulators}},
author = {Alexander Pukhov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01640},
eprint = {2611.01640},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01640},
}
RIS
TY - UNPB
TI - First-principles simulation of free-electron lasers with the Galilean electromagnetic particle-in-cell method: even harmonics of planar undulators
AU - Alexander Pukhov
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01640
UR - https://arxiv.org/abs/2611.01640
AB - Free-electron laser (FEL) codes average the electron motion over the undulator period and add the radiation harmonics through on-axis coupling factors. This is accurate for the fundamental, but the even harmonics of a planar undulator, which vanish on the axis, are not modelled at all. We show that the Galilean electromagnetic particle-in-cell method (GEM-PIC), which resolves the electron motion within the undulator period and the carrier of the forward radiation field without a Courant limit, simulates FELs on two CPU cores at two to three times the cost of a time-dependent run of the averaged code GENESIS. The quasi-cylindrical code GEM-PIC-RZ reproduces the coherent spontaneous emission of a planar undulator in each azimuthal mode m = 0--3 to within 2\,\% of the radiation integral, and seeded amplifiers to within a few per cent of GENESIS run with the same physics. For a seeded planar FEL at 10.6\,nm it predicts 12\,MW of second-harmonic power at saturation, 1.1×10^−3 of the fundamental; this harmonic is absent from the averaged model. The unaveraged code Puffin, which has no space charge, gives a comparable level, 9 to 11\,MW for the space-charge-widened and the initial beam size, and the same transverse structure.
ER -