A kinetic description of the dissipative quasi-parallel solar wind termination shock

Abstract
Context. As a special case of astrophysical MHD shock waves, the solar wind termination shock is typically treated using the MHD jump conditions as they have been determined by Rankine and Hugoniot. A kinetic analysis becomes necessary for both a more detailed view of the governing processes and a deeper understanding of the plasma behaviour.
Aims. In the case of a parallel shock, only an electric field can be considered as the main process decelerating the solar wind ions. This field leads to a strong acceleration for the electrons due to the other sign of their charge and the much lower mass of the electrons than of the ions. This situation enforces a two-stream instability, which is considered to be compensated by wave-particle interactions with electrostatic plasma waves.
Methods. The kinetic approach leads to an equation in Fokker-Planck form, which can be solved by using Ito's calculus for stochastic differential equations.
Results. These two processes (electric field and wave-particle interaction) yield a decelerated subsonic solar wind on the downstream side of the termination shock, showing some new features in the ion distribution function, such as a double-hump structure and a comparatively large number of reflected ions. Within these considerations, we estimate of the spatial size of the shock region.

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