Fast growing instabilities for non-parallel flows

TL;DR

This paper investigates the growth of instabilities in crossing plasma shells at various angles using a cold fluid model, revealing that all configurations are unstable with specific modes dominating depending on the angle.

Contribution

It provides a detailed analysis of instability growth rates and modes for non-parallel plasma flows, including exact results for certain configurations.

Findings

Parallel flows are slightly more unstable than anti-parallel flows.

The $ heta=rac{ ext{pi}}{2}$ case is as unstable as parallel flows, with oblique fastest-growing modes.

No stable configurations exist for any crossing angle.

Abstract

Unstable modes growing when two plasma shells cross over a background plasma at arbitrary angle $\theta$, are investigated using a non-relativistic three cold fluids model. Parallel flows with $\theta=0$ are slightly more unstable than anti-parallel ones with $\theta=\pi$. The case $\theta=\pi/2$ is as unstable as the $\theta=0$ one, but the fastest growing modes are oblique. While the most unstable wave vector varies with orientation, its growth rate slightly evolves and there is no such thing as a stable configuration. A number of exact results can be derived, especially for the $\theta=\pi/2$ case.