2025/09/03 by А. А. Лагутин, Lagutin, A. A.
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Cosmology and Gravitation Theories #Dust and Plasma Wave Phenomena #FOS: Physical sciences #High Energy Astrophysical Phenomena (astro-ph.HE)
paper · pdf · doi:10.48550/arxiv.2509.03091
openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work the theory of diffusive shock acceleration is extended to the case of non-classical particle transport with Lévy flights and Lévy 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 γ= [α(r + 5) - 6 β]/[α(r-1)], where 0 < α< 2 and 0 <β< 1 are the exponents of power-law behavior of Lévy flights and Lévy traps, respectively. We note that this result coincides with standard slope at α=2, β=1 (normal diffusion), and also includes those obtained earlier for the subdiffusion (α=2, β<1) and superdiffusion (α<2, β=1) regimes.