Kinetic study of the ion passage over the solar wind MHD termination shock

Institut für Astrophysik und Extraterrestrische Forschung (now part of the Argelander Institut für Astronomie) der Universität Bonn,
Auf dem Huegel 71, 53121 Bonn, Germany e-mail: msiewert@astro.uni-bonn.de

Accepted: 30 June 2006

Abstract

Aims. We study the classical problem of the transition of a pressure-anisotropic plasma over a hydrodynamical shock using a purely Boltzmann-kinetical treatment.

Methods. We derive the Boltzmann equation for a plasma crossing a shock at a random orientation and evaluate the velocity space integral of the distribution function over the shock analytically. We then try to reproduce the classical MHD behavior and to evaluate the pressures parallel and perpendicular to the magnetic field by integrating the resulting Boltzmann equation over velocity space.

Results.We obtain, for the first time, a completely analytical result for the downstream pressure anisotropy in the case of a perpendicular shock, closing the set of MHD jump conditions. For the parallel shock, it turns out that a single-fluid description without relaxation terms is not sufficient to describe the shock, no matter how much we fine-tune our external parameters. All these results are completely independent of the fine structure of the shock and the upstream distribution function.