{
  "annotation_id": "86fc847c-42a1-4e32-b89f-d06167ce8130",
  "date_created": "2026-03-02T18:01:03.348000Z",
  "date_modified": "2026-03-02T18:01:03.348000Z",
  "file_hash": "b7bdd3db015fd5d722b0dd91ccfd95c4619788a4d4ed2ac2227e0dd624250807",
  "private": false,
  "record": {
    "abstract": "We apply the Smaller ALignment Index (SALI) method to a 4--dimensional\nmapping of accelerator dynamics in order to distinguish rapidly, reliably and\naccurately between ordered and chaotic motion. The main advantage of this index\nis that it tends {\\it exponentially} to zero in the case of chaotic orbits,\nwhile it fluctuates around non--zero values in the case of quasiperiodic\ntrajectories. Thus, it avoids the notorious ambiguities concerning the eventual\nconvergence of (maximum) Lyapunov exponents to (positive) non-zero values.\nExploiting the different behavior of SALI in these two cases we produce phase\nspace `charts\u0027 where regions of chaos and order are clearly identified.\nEvaluating the percentage of chaotic and escaping orbits as a function of the\ndistance from the origin we are able to estimate rapidly and accurately the\nboundaries of the {\\it dynamical aperture} of a proton beam, passing repeatedly\nthrough an array of magnetic focusing elements.",
    "arxiv_id": "physics/0512115",
    "authors": [
      "T. Bountis",
      "Ch. Skokos"
    ],
    "categories": [
      "physics.acc-ph",
      "astro-ph",
      "nlin.CD"
    ],
    "doi": "10.1016/j.nima.2006.01.009",
    "journal_ref": "Nucl.Instrum.Meth.A561:173-179,2006",
    "title": "Application of the SALI chaos detection method to accelerator mappings",
    "url": "https://arxiv.org/abs/physics/0512115"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1f753e84-2358-420b-9b80-8d520dac0d0a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}