# Density jump as a function of magnetic field for collisionless shocks in pair plasmas: the perpendicular case

## TL;DR

This paper investigates how the density jump in collisionless pair plasmas depends on magnetic field strength in perpendicular shocks, extending previous parallel shock analysis and highlighting a less pronounced magnetic influence.

## Contribution

It extends the kinetic theory of downstream anisotropy and density jump from parallel to perpendicular shock configurations in collisionless pair plasmas.

## Key findings

- Magnetic field reduces the density jump in perpendicular shocks.
- The magnetic influence on the density jump is less significant in perpendicular shocks than in parallel shocks.
- Theoretical extension to perpendicular shocks provides new insights into plasma anisotropies.

## Abstract

In the absence of frequent binary collisions to isotropize the plasma, the fulfillment of the magnetohydrodynamic (MHD) Rankine-Hugoniot jump conditions by collisionless shocks is not trivial. In particular, the presence of an external magnetic field can allow for stable anisotropies, implying some departures from the isotropic MHD jumps. The functional dependence of such anisotropies in terms of the field is yet to be determined. By hypothesizing a kinetic history of the plasma through the shock front, we recently devised a theory of the downstream anisotropy, hence of the density jump, in terms of the field strength for a parallel shock [J. Plasma Phys. (2018), vol. 84, 905840604]. Here, we extend the analysis to the case of a perpendicular shock. We still find that the field reduces the density jump, but the effect is less pronounced than in the parallel case.