{
  "id": "2509.03091",
  "version": "v1",
  "published": "2025-09-03T07:38:33.000Z",
  "updated": "2025-09-03T07:38:33.000Z",
  "title": "Diffusive shock acceleration: non-classical model of cosmic ray transport",
  "authors": [
    "A. A. Lagutin"
  ],
  "comment": "17 pages, the 5th International Symposium on Cosmic Rays and Astrophysics (ISCRA-2025)",
  "categories": [
    "astro-ph.HE"
  ],
  "abstract": "In this work the theory of diffusive shock acceleration is extended to the case of non-classical particle transport with L\\'{e}vy flights and L\\'{e}vy traps, when the mean square displacement grows nonlinearly with time. In this approach the Green function is not a Gaussian but it exhibits power-law tails. By using the propagator appropriate for non-classical diffusion, it is found for the first time that energy spectral index of particles accelerated at shock front is $\\gamma = [\\alpha (\\mathrm{r} + 5) - 6 \\beta]/[\\alpha(\\mathrm{r}-1)]$, where $0 < \\alpha < 2$ and $0 <\\beta < 1$ are the exponents of power-law behavior of L\\'{e}vy flights and L\\'{e}vy traps, respectively. We note that this result coincides with standard slope at $\\alpha=2, \\beta=1$ (normal diffusion), and also includes those obtained earlier for the subdiffusion ($\\alpha=2, \\beta<1$) and superdiffusion ($\\alpha<2, \\beta=1$) regimes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-09-03T07:38:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diffusive shock acceleration",
      "cosmic ray transport",
      "non-classical model",
      "mean square displacement grows",
      "energy spectral index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}