{
  "annotation_id": "5de7ceb0-f58b-4daf-a3ff-31acfbd3740c",
  "date_created": "2026-03-02T18:00:29.221000Z",
  "date_modified": "2026-03-02T18:00:29.221000Z",
  "file_hash": "55e683cc3c410c9fe7c1fc68716c5428bb848969d536f3637cc82cb1c7c3cd6a",
  "private": false,
  "record": {
    "abstract": "We study the longitudinal motion of beam particles under the action of a\nsingle resonator wave induced by the beam itself. Based on the method of\nmultiple scales we derive a system of coupled amplitude equations for the\nslowly varying part of the longitudinal distribution function and for the\nresonator wave envelope, corresponding to an arbitrary wave number. The\nequation governing the slow evolution of the voltage envelope is show to be of\nGinzburg-Landau type.",
    "arxiv_id": "physics/0001073",
    "authors": [
      "Stephan I. Tzenov"
    ],
    "categories": [
      "physics.acc-ph",
      "nlin.PS",
      "physics.plasm-ph"
    ],
    "doi": "10.1142/9789812792181_0019",
    "title": "Formation of Patterns in Intense Hadron Beams. The Amplitude Equation   Approach",
    "url": "https://arxiv.org/abs/physics/0001073"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "678e33ea-175d-4fd4-8b42-67ff5161ce09",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}