Superdiffusive transport at shocks in space plasmas

Abstract

Superdiffusion is characterized by a nonlinear growth of the mean square deviation with time. Superdiffusive transport can be interpreted in terms of a Lévy random walk, a stochastic process where a power-law distribution of free path lengths is allowed. Considering particles accelerated at interplanetary shocks, it is found that their intensity profile is a power-law in time in the case of superdiffusion, while it is an exponential decay for normal diffusion. Analysis of energetic particle fluxes from the Ulysses spacecraft at about 5AU and from the Voyager 2 spacecraft at the solar wind termination shock shows that superdiffusive transport is found.