{
  "id": "1902.00513",
  "version": "v1",
  "published": "2019-02-01T20:29:04.000Z",
  "updated": "2019-02-01T20:29:04.000Z",
  "title": "On the dynamics of a charged particle in magnetic fields with cylindrical symmetry",
  "authors": [
    "Paolo Caldiroli",
    "Gabriele Cora"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.DS",
    "math.FA"
  ],
  "abstract": "We study the motion of a charged particle under the action of a magnetic field with cylindrical symmetry. In particular we consider magnetic fields with constant direction and with magnitude depending on the distance $r$ from the symmetry axis of the form $1 + Ar^{-\\gamma}$ as $r\\to\\infty$, with $A\\ne 0$ and $\\gamma > 1$. With perturbative-variational techniques, we can prove the existence of infinitely many trajectories whose projection on a plane orthogonal to the direction of the field describe bounded curves given by the superposition of two motions: a rotation with constant angular speed at a unit distance about a point which moves along a circumference of large radius $\\rho$ with a slow angular speed $\\varepsilon$. The values $\\rho$ and $\\varepsilon$ are suitably related to each other. This problem has some interest also in the context of planar curves with prescribed curvature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-01T20:29:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic field",
      "cylindrical symmetry",
      "charged particle",
      "constant direction",
      "planar curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}