{
  "annotation_id": "7ee1fe05-91fb-4328-9d59-2e27f9b8f275",
  "date_created": "2026-03-02T18:01:14.360000Z",
  "date_modified": "2026-03-02T18:01:14.360000Z",
  "file_hash": "1a5f95e03a74c82d41913fec1966038770d4053509fda828d38dca9cf81b5a21",
  "private": false,
  "record": {
    "abstract": "The Collective Beam-Beam interaction is studied in the framework of maps with\na ``kick-lattice\u0027\u0027 model in the 4-D phase space of the transverse motion. A\nnovel approach to the classical method of averaging is used to derive an\napproximate map which is equivalent to a flow within the averaging\napproximation. The flow equation is a continuous-time Vlasov equation which we\ncall the averaged Vlasov equation, the new model of this paper. The power of\nthis approach is evidenced by the fact that the averaged Vlasov equation has\nexact equilibria and the associated linearized equations have uncoupled\nazimuthal Fourier modes. The equation for the Fourier modes leads to a Fredholm\nintegral equation of the third kind and the setting is ready-made for the\ndevelopment of a weakly nonlinear theory to study the coupling of the pi and\nsigma modes. The pi and sigma eigenmodes are calculated from the third kind\nintegral equation. These results are compared with the kick-lattice model using\nour weighted macroparticle tracking code and a newly developed, density\ntracking, parallel, Perron-Frobenius code.",
    "arxiv_id": "physics/0611238",
    "authors": [
      "J. A. Ellison",
      "A. V. Sobol",
      "M Vogt"
    ],
    "categories": [
      "physics.acc-ph"
    ],
    "doi": "10.1088/1367-2630/9/2/032",
    "journal_ref": "NewJ.Phys.9:32,2007",
    "title": "A New Model for the Collective Beam-Beam Interaction",
    "url": "https://arxiv.org/abs/physics/0611238"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6405acb0-2d7c-4290-9b71-522d959b701a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}