Resonant shear-flow instability in anisotropic supersonic plasmas with heat flux

TL;DR

This paper analyzes how temperature anisotropy and heat flux affect the stability of supersonic shear flows in collisionless plasmas, revealing a resonant instability that diminishes with higher Mach numbers.

Contribution

It provides an exact analytical solution for the resonant shear-flow instability in anisotropic plasmas using 16-moment equations, highlighting the negligible role of heat flux at high Mach numbers.

Findings

Resonant instability peaks when wave phase velocity matches flow velocity.

Heat flux has minimal impact on instability growth rate at high Mach numbers.

Instability disappears in the vortex sheet limit, unlike Kelvin-Helmholtz instability.

Abstract

This work is devoted to the study of the influence of temperature anisotropy and parallel heat flux on the stability of supersonic shear flow in collisionless plasmas. Within a fluid-based framework, we employ the 16-moment transport equations -- derived from the Vlasov-Maxwell system -- to describe the plasma dynamics. By performing a modal analysis we investigate the oblique propagation of linear disturbances within a magnetized plasma characterized by a shear flow of arbitrary profile aligned with the ambient magnetic field. In the unperturbed state, both the plasma density and the magnetic field are assumed to be homogeneous. For a smooth, hyperbolic velocity profile representing supersonic shear, the governing wave equation is reduced to a form amenable to an exact analytical solution. Analytical solutions are expressed in terms of special functions that yield an infinite discrete spectrum of complex eigenfrequencies ($n = 0, 1, 2, \dots$). The instability is identified as resonant, peaking when the wave phase velocity matches the mean flow velocity, with the growth rate decreasing for higher-order modes. The results indicate that, while heat flux exerts a negligible influence under conditions of supersonic flow, the growth rate decreases and approaches an asymptotic value as the Mach number increases. Notably, the instability vanishes in the vortex sheet limit, distinguishing it from the classical Kelvin-Helmholtz mechanism. These findings suggest that this specific instability holds significant potential for explaining the problem of observed boundaries between isotropic and anisotropic proton temperature regions in a low-beta solar wind plasma.