Density jump as a function of magnetic field for switch-on collisionless shocks in pair plasmas

TL;DR

This paper extends a kinetic model to analyze the density jump in switch-on collisionless shocks in pair plasmas, revealing multiple solutions and differences from traditional MHD predictions, especially in the context of magnetic field orientation.

Contribution

The study applies a kinetic model to switch-on shocks, uncovering multiple solutions and highlighting differences from MHD, particularly regarding shock classifications and magnetic field effects.

Findings

The model predicts two solutions for switch-on shocks, unlike the single MHD solution.

The solutions correspond to intermediate and fast shocks, which do not merge as in MHD.

Differences are observed in the range of Alfvén Mach numbers for shock solutions.

Abstract

The properties of collisionless shocks, like the density jump, are usually derived from magnetohydrodynamics (MHD), where isotropic pressures are assumed. Yet, in a collisionless plasma, an external magnetic field can sustain a stable anisotropy. In \cite{BretJPP2018}, we devised a model for the kinetic history of the plasma through the shock front, allowing to self-consistently compute the downstream anisotropy, hence the density jump, in terms of the upstream parameters. This model dealt with the case of a parallel shock, where the magnetic field is normal to the front both in the upstream and the downstream. Yet, MHD also allows for shock solutions, the so-called switch-on solutions, where the field is normal to the front only in the upstream. This article consists in applying our model to these switch-on shocks. While MHD offers only 1 switch-on solution within a limited range of Alfv\'{e}n Mach numbers, our model offers 2 kinds of solutions within a slightly different range of Alfv\'{e}n Mach numbers. These 2 solutions are most likely the outcome of the intermediate and fast MHD shocks under our model. While the intermediate and fast shocks merge in MHD for the parallel case, they do not within our model. For simplicity, the formalism is restricted to non-relativistic shocks in pair plasmas where the upstream is cold.