On the Parallel and Oblique Firehose Instability in Fluid Models

A brief analysis of the proton parallel and oblique firehose instability is presented from a fluid perspective, and the results are compared with 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 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.