Superdiffusive Shock Acceleration

Details Superdiffusive Shock Acceleration Superdiffusive Shock Acceleration

May 2012

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012apj...750...87p&link_type=abstract

The Astrophysical Journal, Volume 750, Issue 2, article id. 87 (2012).

Astronomy and Astrophysics

Astronomy

Acceleration Of Particles, Diffusion, Shock Waves, Turbulence

Scientific paper

The theory of diffusive shock acceleration is extended to the case of superdiffusive transport, i.e., when the mean square deviation grows proportionally to t α, with α > 1. Superdiffusion can be described by a statistical process called Lévy random walk, in which the propagator is not a Gaussian but it exhibits power-law tails. By using the propagator appropriate for Lévy random walk, it is found that the indices of energy spectra of particles are harder than those obtained where a normal diffusion is envisaged, with the spectral index decreasing with the increase of α. A new scaling for the acceleration time is also found, allowing substantially shorter times than in the case of normal diffusion. Within this framework we can explain a number of observations of flat spectra in various astrophysical and heliospheric contexts, for instance, for the Crab Nebula and the termination shock of the solar wind.

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