# On the parallel and oblique firehose instability in fluid models

## TL;DR

This paper compares fluid and kinetic models of the proton firehose instability, showing that classical fluid models accurately predict growth rates at large scales but require dispersive effects for stabilization at small scales, with notable differences near the instability threshold.

## Contribution

It demonstrates that the classical CGL fluid model effectively describes the firehose instability's growth rate at large scales and clarifies the differences with kinetic theory near the threshold.

## Key findings

- CGL model accurately predicts growth rates at small wavenumbers
- Dispersive effects stabilize the instability at high wavenumbers
- Differences between fluid and kinetic models are pronounced near the threshold

## Abstract

A brief analysis of the proton parallel and oblique firehose instability is presented from a fluid perspective and the results are compared to kinetic theory solutions obtained by the WHAMP code. It is shown that the classical CGL model very accurately describes the growth rate of these instabilities at sufficiently long spatial scales (small wavenumbers). The required stabilization of these instabilities at small spatial scales (high wavenumbers) naturally requires dispersive effects and the stabilization is due to the Hall term and finite Larmor radius (FLR) corrections to the pressure tensor. Even though the stabilization is not completely accurate since at small spatial scales a relatively strong collisionless damping comes into effect, we find that the main concepts of the maximum growth rate and the stabilization of these instabilities is indeed present in the fluid description. However, there are differences that are quite pronounced when close to the firehose threshold and that clarify the different profiles for marginally stable states with a prescribed maximum growth rate $\gamma_{max}$ in the simple fluid models considered here and the kinetic description.