Can conduction induce convection? The non-linear saturation of buoyancy
  instabilities in dilute plasmas
  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.
