{
  "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, $1.1\\times10^{-3}$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01640",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Pukhov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c6scdv3r731yw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01640",
  "fulltext_url": null,
  "id": "c6scdv3r731yw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01640",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.plasm-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01640",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c6scdv3r731yw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01640",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01640"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.plasm-ph",
      "subfield": "plasma"
    }
  ],
  "title": "First-principles simulation of free-electron lasers with the Galilean electromagnetic particle-in-cell method: even harmonics of planar undulators",
  "title_text": "First-principles simulation of free-electron lasers with the Galilean electromagnetic particle-in-cell method: even harmonics of planar undulators",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:18Z",
  "url": "https://research.draconitic.com/paper/c6scdv3r731yw",
  "venue": "arXiv",
  "versions": []
}