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.
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