Abstract
A heat flux in a high-$\unicode[STIX]{x1D6FD}$ 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 $1/\unicode[STIX]{x1D6FD}$. 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 $\unicode[STIX]{x1D6FD}$ 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-$\unicode[STIX]{x1D6FD}$ 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 $\unicode[STIX]{x1D6FD}$. 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.
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