Collisionless shock formation, spontaneous electromagnetic fluctuations and streaming instabilities

TL;DR

This paper investigates the initial phase of collisionless shock formation in plasmas, combining simulations and theoretical analysis to understand the role of electromagnetic instabilities, especially Weibel modes, in shock development.

Contribution

It provides a detailed analysis of the instability phase leading to shock formation, deriving an expression for the linear phase duration and linking it to shock onset.

Findings

Weibel modes dominate the linear instability phase.

Derived an expression for the linear phase duration matching simulations.

Saturation time sets a lower bound for shock formation time.

Abstract

Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent numerical simulations and experiments have shown how they can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes govern the linear phase. We derive an expression for the duration of the linear phase in good agreement with the simulations. This saturation time constitutes indeed a lower-bound for the shock formation time.