{
  "annotation_id": "6e1e8cf9-206c-4895-ac7b-a7e3c214577f",
  "date_created": "2026-03-02T18:01:00.752000Z",
  "date_modified": "2026-03-02T18:01:00.752000Z",
  "file_hash": "d2f1cb6a258afcf3eac257ca8ff2d010be9e9acfd069faf7d3129951ff09d640",
  "private": false,
  "record": {
    "abstract": "The generation and evolution of nonlinear waves in microwave amplifiers such\nas travelling wave tubes, free electron lasers and klystrons have been studied.\nThe analysis is based on the hydrodynamic and field equations for the\nself-consistent evolution of the beam density distribution, the current\nvelocity and the electromagnetic fields. A system of coupled nonlinear\nSchr\\\"{o}dinger equations for the slowly varying amplitudes of interacting\nbeam-density waves has been derived. Under the approximation of an isolated\nmode neglecting the effect of the rest of the modes, this system reduces to a\nsingle nonlinear Schr\\\"{o}dinger equation for that particular mode.",
    "arxiv_id": "physics/0506226",
    "authors": [
      "Stephan I. Tzenov"
    ],
    "categories": [
      "physics.acc-ph",
      "nlin.PS",
      "physics.plasm-ph"
    ],
    "title": "Generation and Propagation of Nonlinear Waves in Travelling Wave Tubes",
    "url": "https://arxiv.org/abs/physics/0506226"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6ec09cb6-876d-48fd-829c-f77c8b52e7d0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}