{
  "annotation_id": "11d108d6-f946-4e97-8cbd-c94bb35162d7",
  "date_created": "2026-03-02T18:01:24.653000Z",
  "date_modified": "2026-03-02T18:01:24.653000Z",
  "file_hash": "1103c478852deb41edb6357e0642fdf05a44376e88ce2c5f0b9a338abeac2879",
  "private": false,
  "record": {
    "abstract": "The presence of skew quadrupole fields will linearly couple the x and y\nmotions. The x and y motions can then be written as the sum of two normal modes\n\u003e. This paper presents analytical perturbation theory results for the tunes of\nthe normal modes. The results for the normal mode tunes are first found correct\nto lowest order in the skew quadrupole fields. The results are then carried one\nstep further to include the next higher order terms in the skew quadrupole\nfields. These analytical results show that for the higher order shift in the\ntune, the important harmonics of the skew quadrupole field are the harmonics\nnear the sum of the tunes. However the harmonics closest to the sum of the\ntunes do not contribute to the higher order tune splitting, the seperation of\nthe tunes, as they shift the two tunes about equally.This results in a lack of\na dominant harmonic for the higher order part of the tune splitting, which\ncomplicates the understanding and correction of the higher order part of the\ntune splitting.",
    "arxiv_id": "physics/9910047",
    "authors": [
      "G. Parzen"
    ],
    "categories": [
      "physics.acc-ph"
    ],
    "title": "Theory of the tune shift due to linear coupling",
    "url": "https://arxiv.org/abs/physics/9910047"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a5a400dc-ca2d-4f0b-a0b2-b30164d528ca",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}