Density jump as a function of the field for parallel relativistic collisionless shocks

TL;DR

This paper extends a collisionless shock model to the relativistic regime, revealing significant deviations from MHD predictions in density jumps for strong magnetic fields, supported by Particle-in-Cell simulations.

Contribution

It introduces a relativistic collisionless shock model with zero upstream pressure, showing departures from MHD predictions in density jumps for pair plasmas.

Findings

Density jump scales as 2 + 1/γ_up in strong field regime.

Deviations from MHD predictions are confirmed by simulations.

Results are specific to pair plasmas in relativistic shocks.

Abstract

Collisionless shocks are frequently analyzed using the magnetohydrodynamic formalism (MHD), even though the required collisionality hypothesis is not fulfilled. In a previous work \citep{BretJPP2018}, we presented a model of collisionless shock displaying an important departure from the expected MHD behavior, in the case of a strong flow aligned magnetic field. This model was non-relativistic. Here, it is extended to the relativistic regime, considering zero upstream pressure and upstream Lorentz factor $\gg 1$. The result agrees satisfactorily with Particle-in-Cell simulations and shows a similar, and important, departure from the MHD prediction. In the strong field regime, the density jump $r$, seen in the downstream frame, behaves like $r \sim 2 + 1/\gamma_{\mathrm{up}}$ while MHD predicts 4 ($\gamma_{\mathrm{up}}$ is the Lorentz factor of the upstream measured in the downstream frame). Only pair plasmas are considered.