# Simulation study of the formation of a non-relativistic pair shock

## TL;DR

This study uses particle-in-cell simulations to explore how non-relativistic pair shocks form through plasma instabilities, revealing the roles of electrostatic waves, phase space vortices, and the Weibel instability in shock development.

## Contribution

It provides a detailed simulation-based analysis of shock formation mechanisms in pair plasma, highlighting the interplay of electrostatic and magnetowaves in non-relativistic regimes.

## Key findings

- Electrostatic two-stream and oblique modes dominate initial wave growth.
- Phase space vortices facilitate wave saturation and plasma heating.
- Strong magnetowaves develop downstream despite electrostatic shock mediation.

## Abstract

We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed c/5 and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.