Research Note

Particle acceleration in thick parallel shocks with high compression ratio

¹ Tuorla Observatory, Väisälä Institute for Space Physics and Astronomy, Väisäläntie 20, 21500 Piikkiö, Finland e-mail: joni.virtanen@utu.fi
² Department of Physical Sciences, PO Box 64, 00014 University of Helsinki, Finland e-mail: rami.vainio@helsinki.fi

Received: 2 May 2005
Accepted: 1 June 2005

Abstract

We report studies on first-order Fermi acceleration in parallel modified shock waves with a large scattering center compression ratio expected from turbulence transmission models. Using a Monte Carlo technique we have modeled particle acceleration in shocks with a velocity ranging from nonrelativistic to ultrarelativistic and a thickness extending from nearly steplike to very wide structures exceeding the particle diffusion length by orders of magnitude. The nonrelativistic diffusion approximation is found to be surprisingly accurate in predicting the spectral index of a thick shock with large compression ratio even in the cases involving relativistic shock speeds.