Can conduction induce convection? On the non-linear saturation of buoyancy instabilities in dilute plasmas

Abstract

We study the effects of anisotropic thermal conduction on low-collisionality, astrophysical plasmas using two and three-dimensional magnetohydrodynamic simulations. For weak magnetic fields, dilute plasmas are buoyantly unstable for either sign of the temperature gradient: the heat-flux-driven buoyancy instability (HBI) operates when the temperature increases with radius while the magnetothermal instability (MTI) operates in the opposite limit. In contrast to previous results, we show that, in the presence of a sustained temperature gradient, the MTI drives strong turbulence and operates as an efficient magnetic dynamo (akin to standard, adiabatic convection). Together, the turbulent and magnetic energies contribute up to ~10% of the pressure support in the plasma. In addition, the MTI drives a large convective heat flux, ~1.5% of rho c_s^3. These findings are robust even in the presence of an external source of strong turbulence. Our results on the nonlinear saturation of the HBI are consistent with previous studies but we explain physically why the HBI saturates quiescently by re-orienting the magnetic field (suppressing the conductive heat flux through the plasma), while the MTI saturates by generating sustained turbulence. We also systematically study how an external source of turbulence affects the saturation of the HBI: such turbulence can disrupt the HBI only on scales where the shearing rate of the turbulence is faster than the growth rate of the HBI. In particular, our results provide a simple mapping between the level of turbulence in a plasma and the effective isotropic thermal conductivity. We discuss the astrophysical implications of these findings, with a particular focus on the intracluster medium of galaxy clusters.