Density jump as a function of magnetic field strength for parallel collisionless shocks in pair plasmas

TL;DR

This paper develops a non-relativistic model to understand how magnetic field strength influences the pressure anisotropy in collisionless pair plasma shocks, revealing deviations from traditional magnetohydrodynamics predictions.

Contribution

It introduces a novel model linking downstream pressure anisotropy to magnetic field strength in parallel collisionless shocks in pair plasmas.

Findings

Downstream anisotropy depends on magnetic field strength.

Model predicts conditions for firehose stability or instability.

Provides a full analytical description of plasma behavior across shocks.

Abstract

Collisionless shocks follow the Rankine-Hugoniot jump conditions to a good approximation. However, for a shock propagating parallel to a magnetic field, magnetohydrodynamics states that the shock properties are independent of the field strength, whereas recent Particle-in-Cell simulations reveal a significant departure from magnetohydrodynamics behavior for such shocks in the collisionless regime. This departure is found to be caused by a field-driven anisotropy in the downstream pressure, but the functional dependence of this anisotropy on the field strength is yet to be determined. Here, we present a non-relativistic model of the plasma evolution through the shock front, allowing for a derivation of the downstream anisotropy in terms of the field strength. Our scenario assumes double adiabatic evolution of a pair plasma through the shock front. As a result, the perpendicular temperature is conserved. If the resulting downstream is firehose stable, then the plasma remains in this state. If unstable, it migrates towards the firehose stability threshold. In both cases, the conservation equations, together with the relevant hypothesis made on the temperature, allows a full determination of the downstream anisotropy in terms of the field strength.