Self-inhibiting thermal conduction in high-beta, whistler-unstable plasma

TL;DR

This paper confirms through simulations that in high-beta, low-collisionality plasmas, whistler instabilities suppress thermal conduction by electron scattering, with the suppression level depending on plasma beta and temperature gradients.

Contribution

The study provides the first numerical confirmation of quasilinear theory predictions for heat flux saturation and suppression in high-beta plasmas, including magnetic perturbation levels and scattering rates.

Findings

Heat flux scales as 1/β and is controlled by electron scattering.

Magnetic perturbations are distributed over a wide range of angles.

Suppression of heat flux can be significant in astrophysical plasmas like galaxy clusters.

Abstract

A heat flux in a high-$\beta$ plasma with low collisionality triggers the whistler instability. Quasilinear theory predicts saturation of the instability in a marginal state characterized by a heat flux that is fully controlled by electron scattering off magnetic perturbations. This marginal heat flux does not depend on the temperature gradient and scales as $1/\beta$. We confirm this theoretical prediction by performing numerical particle-in-cell simulations of the instability. We further calculate the saturation level of magnetic perturbations and the electron scattering rate as functions of $\beta$ and the temperature gradient to identify the saturation mechanism as quasilinear. Suppression of the heat flux is caused by oblique whistlers with magnetic-energy density distributed over a wide range of propagation angles. This result can be applied to high-$\beta$ astrophysical plasmas, such as the intracluster medium, where thermal conduction at sharp temperature gradients along magnetic-field lines can be significantly suppressed. We provide a convenient expression for the amount of suppression of the heat flux relative to the classical Spitzer value as a function of the temperature gradient and $\beta$. For a turbulent plasma, the additional independent suppression by the mirror instability is capable of producing large total suppression factors (several tens in galaxy clusters) in regions with strong temperature gradients.