Evolution of Alfvén waves by three-wave interactions in super-Alfvénic shocks

¹ Department of Physical Sciences, PO Box 64, 00014 University of Helsinki, Finland e-mail: rami.vainio@helsinki.fi
² Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, 44780 Bochum, Germany e-mail: fspanier@tp4.rub.de

Received: 25 November 2004
Accepted: 24 February 2005

Abstract

We calculate the evolution of Alfvén waves in super-Alfvénic flows, such as the downstream region of a fast-mode shock, via three-wave interactions between two Aflvén waves and a sound wave. We show that the process has a significant influence on the evolution of the Alfvén wave spectra, driving the system toward a degenerate normalized cross-helicity, . Typical distances in which the system evolves are evaluated, and the effects of the calculated turbulence evolution on test-particle acceleration in super-Alfvénic quasi-parallel shocks are studied. We show that typically the spectrum of accelerated particles is determined by the first-order Fermi acceleration process as described earlier by Vainio & Schlickeiser (1998, A&A, 331, 793; 1999, A&A, 343, 303), and identify some regions of parameter space, where the earlier results are significantly modified either by changes in the predicted scattering-center compression ratio or by stochastic acceleration in the downstream plasma.