  In dilute astrophysical plasmas, thermal conduction is primarily along
magnetic field lines, and therefore highly anisotropic. As a result, the usual
convective stability criterion is modified from a condition on entropy to a
condition on temperature. For small magnetic fields or small wavenumbers,
instability occurs in any atmosphere where the temperature and pressure
gradients point in the same direction. We refer to the resulting convective
instability as the magnetothermal instability (MTI). We present fully
three-dimensional simulations of the MTI and show that saturation results in an
atmosphere with different vertical structure, dependent upon the boundary
conditions. When the temperature at the boundary of the unstable layer is
allowed to vary, the temperature gradient relaxes until the unstable region is
almost isothermal. When the temperature at the boundary of the unstable region
is fixed, the magnetic field is reoriented to an almost vertical geometry as a
result of buoyant motions. This case exhibits more vigorous turbulence. In both
cases the resulting saturated heat flux is almost one-half of the value
expected if the conduction were purely isotropic. The action of the MTI results
in dynamical processes that lead to significant transport perpendicular to the
initial direction of the magnetic field. The resulting magnetoconvection in
both cases amplifies the magnetic field until it is almost in equipartition
with sustained subsonic turbulence. These results are relevant to understanding
measurements of the temperature profiles of the intracluster medium of clusters
of galaxies as well as the structure of radiatively inefficient accretion
flows.
