  The intracluster medium of galaxy clusters is a weakly collisional, high-beta
plasma in which the transport of heat and momentum occurs primarily along
magnetic-field lines. Anisotropic heat conduction allows convective
instabilities to be driven by temperature gradients of either sign, the
magnetothermal instability (MTI) in the outskirts of non-isothermal clusters
and the heat-flux buoyancy-driven instability (HBI) in their cooling cores. We
employ the Athena MHD code to investigate the nonlinear evolution of these
instabilities, self-consistently including the effects of anisotropic viscosity
(i.e. Braginskii pressure anisotropy), anisotropic conduction, and radiative
cooling. We highlight the importance of the microscale instabilities that
inevitably accompany and regulate the pressure anisotropies generated by the
HBI and MTI. We find that, in all but the innermost regions of cool-core
clusters, anisotropic viscosity significantly impairs the ability of the HBI to
reorient magnetic-field lines orthogonal to the temperature gradient. Thus,
while radio-mode feedback appears necessary in the central few tens of kpc,
conduction may be capable of offsetting radiative losses throughout most of a
cool core over a significant fraction of the Hubble time. Magnetically-aligned
cold filaments are then able to form by local thermal instability. Viscous
dissipation during the formation of a cold filament produces accompanying hot
filaments, which can be searched for in deep Chandra observations of nearby
cool-core clusters. In the case of the MTI, anisotropic viscosity maintains the
coherence of magnetic-field lines over larger distances than in the inviscid
case, providing a natural lower limit for the scale on which the field can
fluctuate freely. In the nonlinear state, the magnetic field exhibits a folded
structure in which the field-line curvature and field strength are
anti-correlated.
