Density jump as a function of magnetic field strength for parallel collisionless shocks with anisotropic upstream pressure

TL;DR

This paper develops a model to analyze how magnetic field strength influences the density jump in collisionless shocks with anisotropic upstream pressure, especially in parallel shock configurations.

Contribution

It introduces a model that relates downstream anisotropy and shock density jump to upstream conditions, considering upstream anisotropy as a free parameter in parallel pair plasma shocks.

Findings

Upstream anisotropy affects shock density jump behavior.

Strong sonic shocks behave similarly to isotropic cases.

Intermediate sonic Mach numbers show diverse behaviors due to anisotropy.

Abstract

The properties of collisionless shocks are frequently assessed in the magnetohydrodynamics (MHD) model. Yet, in a collisionless plasma, an ambient magnetic field can sustain a stable anisotropy in the upstream or the downstream, resulting in a departure from the MHD predicted behavior. We present a model allowing to derive the downstream anisotropy, hence the shock density jump, in terms of the upstream quantities. For simplicity, the case of a parallel shock in pair plasma is considered. Contrary to previous works where the upstream was assumed isotropic, here the upstream anisotropy $A=T_\perp/T_\parallel$ is a free parameter. The strong sonic shock regime is formally identical to the isotropic upstream case. Yet, for intermediate sonic Mach numbers, a variety of behaviors appear as a result of the anisotropy of the upstream.