The parametric instability of Alfv\'en waves: effects of temperature anisotropy

TL;DR

This paper investigates how temperature anisotropy influences the stability of large amplitude Alfvén waves, revealing new regimes of parametric decay instability that depend on plasma beta and anisotropy levels, with implications for solar wind turbulence.

Contribution

It introduces a detailed analysis of the effects of pressure anisotropy on Alfvén wave stability within a double-adiabatic plasma model, extending understanding beyond classical MHD results.

Findings

Anisotropy broadens the instability range for high $eta_\parallel$ when $\xi > 1$.

A critical anisotropy value $\xi^* \\simeq 2.7$ marks a regime where growth rate becomes independent of $eta_\parallel$.

Instability is suppressed at high $eta_\parallel$ for $\xi < \xi^*$, similar to MHD predictions.

Abstract

We study the stability of large amplitude, circularly polarized Alfv\'en waves in an anisotropic plasma described by the double-adiabatic/CGL closure, and in particular the effect of a background thermal pressure anisotropy on the well-known properties of Alfv\'en wave parametric decay in Magnetohydrodynamics (MHD). Anisotropy allows instability over a much wider range of values of parallel plasma beta ($\beta_\parallel$) when $\xi=p_{0\bot}/p_{0\parallel} > 1$. When the pressure anisotropy exceeds a critical value, $\xi\geq\xi^*$ with $\xi^*\simeq2.7$, there is a new regime in which the parametric instability is no longer quenched at high $\beta_\parallel$ and in the limit $\beta_\parallel\gg1$ the growth rate becomes independent of $\beta_\parallel$. In the opposite case of $\xi< \xi^*$, the instability is strongly suppressed with increasing parallel plasma beta, similarly to the MHD case. We analyze marginal stability conditions for parametric decay in the $(\xi,\,\beta_\parallel)$ parameter space, and discuss possible implications for Alfv\'enic turbulence in the solar wind.