Full Boltzmann-kinetical treatment of an ion plasma crossing an MHD shock: parallel and non-parallel cases

Abstract

Aims. We attempt to describe kinetic properties of the solar wind termination shock (and similar MHD shocks in general) using the appropriate form of the kinetic Boltzmann equation, for arbitrary inclinations ΘBn between the magnetic field and the shock normal. Methods. In order to understand the deviations from the perpendicular shock, for which we have already derived an exact solution in an earlier publication, we first prove that our current Boltzmann equation is unable to describe a stationary quasiparallel shock. To ease and open up further research, we derive conditions for the specific form of the relevant Boltzmann equation. Results. We demonstrate that the simplest Boltzmann equation aiming to describe a parallel MHD shock is in conflict with the predictions from pure MHD. We identify several possible reasons for this, and likewise derive conditions based on the mass flow conservation which must be fulfilled for the shock to be stationary. Assuming that a model for (quasi-)stationary shocks does exist, we are able to explain the unchanged power law index at the passage of the solar wind termination shock observed by the Voyager 1 spacecraft in 2004. We also show that different dissipation mechanisms lead to different transition scales for perpendicular and parallel MHD shocks, and that these differences in the dissipation process also need to be included in the case-competent Boltzmann equation.