Density jump for oblique collisionless shocks in pair plasmas: allowed solutions

TL;DR

This paper introduces a kinetic-inspired MHD-like model for collisionless pair plasma shocks, revealing new solutions and density jump behaviors across different magnetic field orientations.

Contribution

It extends previous models to include arbitrary coplanar magnetic fields and identifies novel shock solutions not present in traditional MHD theory.

Findings

Discovery of additional shock solutions outside MHD predictions.

Observation of reduced density jumps in quasi-parallel, highly magnetized regimes.

Development of a mathematical framework for anisotropic, collisionless plasma shocks.

Abstract

Shockwaves in plasma are usually dealt with using Magnetohydrodynamics (MHD). Yet, MHD entails the assumption of a short mean free path, which is not fulfilled in a collisionless plasma. Recently, for pair plasmas, we devised a model allowing to account for kinetic effects within an MHD-like formalism. Its relies on an estimate of the anisotropy generated when crossing the front, with a subsequent assessment of the stability of this anisotropy in the downstream. We solved our model for parallel, perpendicular and switch-on shocks. Here we bridge between all these cases by treating the problem of an arbitrarily, but coplanar, oriented magnetic field. Even though the formalism presented is valid for anisotropic upstream temperatures, only the case of a cold upstream is solved. We find extra solutions which are not part of the MHD catalog, and a density jump that is notably less in the quasi parallel, highly magnetized, regime. Given the complexity of the calculations, this work is mainly devoted to the presentation of the mathematical aspect of our model. A forthcoming article will be devoted to the physics of the shocks here defined.