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Title: From Lévy walks to superdiffusive shock acceleration

In this paper, we present a general scenario for nondiffusive transport and we investigate the influence of anomalous, superdiffusive transport on Fermi acceleration processes at shocks. We explain why energetic particle superdiffusion can be described within the Lévy walk framework, which is based on a power-law distribution of free path lengths and on a coupling between free path length and free path duration. A self-contained derivation of the particle mean square displacement, which grows as (Δx {sup 2}) = 2D {sub α} t {sup α} with α > 1, and the particle propagator, is presented for Lévy walks, making use of a generalized version of the Montroll-Weiss equation. We also derive for the first time an explicit expression for the anomalous diffusion coefficient D {sub α} and we discuss how to obtain these quantities from energetic particle observations in space. The results are applied to the case of particle acceleration at an infinite planar shock front. Using the scaling properties of the Lévy walk propagator, the energy spectral indices are found to have values smaller than the ones predicted by the diffusive shock acceleration theory. Furthermore, when applying the results to ions with energies of a few MeV accelerated atmore » the solar wind termination shock, the estimation of the anomalous diffusion coefficient associated with the superdiffusive motion gives acceleration times much smaller than the ones related to normal diffusion.« less
Authors:
;  [1]
  1. Dipartimento di Fisica, Università della Calabria, Ponte P. Bucci, Cubo 31C, I-87036 Arcavacata di Rende (Italy)
Publication Date:
OSTI Identifier:
22342030
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 778; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; COSMIC RADIATION; COUPLING; DIFFUSION; DISTRIBUTION; EQUATIONS; HELIOSPHERE; MEV RANGE; PARTICLES; PROPAGATOR; SCALING; SHOCK WAVES; SOLAR WIND; SPACE; SUN; TURBULENCE