{
  "annotation_id": "e542bc16-0f97-49d7-85d1-aa3e5faca959",
  "date_created": "2026-03-02T18:00:32.480000Z",
  "date_modified": "2026-03-02T18:00:32.480000Z",
  "file_hash": "9859557834ebcc8fdbf79270beefa8b64824e6dc268ebeaa15455dfeed9a4c8f",
  "private": false,
  "record": {
    "abstract": "By considering delta function sextupole, octupole, and decapole perturbations\nand using difference action-angle variable equations, we find some useful\nanalytical formulae for the estimation of the dynamic apertures of circular\naccelerators due to single sextupole, single octupole, single decapole (single\n2$m$ pole in general). Their combined effects are derived based on the Chirikov\ncriterion of the onset of stochastic motions. Comparisons with numerical\nsimulations are made, and the agreement is quite satisfactory. These formulae\nhave been applied to determine the beam-beam limited dynamic aperture in a\ncircular collider.",
    "arxiv_id": "physics/0005023",
    "authors": [
      "Jie Gao"
    ],
    "categories": [
      "physics.acc-ph"
    ],
    "doi": "10.1016/S0168-9002(00)00345-4",
    "journal_ref": "Nucl.Instrum.Meth. A451 (2000) 545-557",
    "title": "Analytical estimation of the dynamic apertures of circular accelerators",
    "url": "https://arxiv.org/abs/physics/0005023"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5bee8675-1100-45cd-ad39-fe0ef8ccfa5f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}