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

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.

accepted to JPP

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