  In weakly-collisional plasmas such as the intracluster medium (ICM), heat and
momentum transport become anisotropic with respect to the local magnetic field
direction. Anisotropic heat conduction causes the slow magnetosonic wave to
become buoyantly unstable to the magnetothermal instability (MTI) when the
temperature increases in the direction of gravity and to the heat-flux--driven
buoyancy instability (HBI) when the temperature decreases in the direction of
gravity. The local changes in magnetic field strength that attend these
instabilities cause pressure anisotropies that viscously damp motions parallel
to the magnetic field. In this paper we employ a linear stability analysis to
elucidate the effects of anisotropic viscosity (i.e. Braginskii pressure
anisotropy) on the MTI and HBI. By stifling the convergence/divergence of
magnetic field lines, pressure anisotropy significantly affects how the ICM
interacts with the temperature gradient. Instabilities which depend upon the
convergence/divergence of magnetic field lines to generate unstable buoyant
motions (the HBI) are suppressed over much of the wavenumber space, whereas
those which are otherwise impeded by field-line convergence/divergence (the
MTI) are strengthened. As a result, the wavenumbers at which the HBI survives
largely unsuppressed in the ICM have parallel components too small to
rigorously be considered local. This is particularly true as the magnetic field
becomes more and more orthogonal to the temperature gradient. In contrast, the
fastest-growing MTI modes are unaffected by anisotropic viscosity. However, we
find that anisotropic viscosity couples slow and Alfven waves in such a way as
to buoyantly destabilise Alfvenic fluctuations when the temperature increases
in the direction of gravity. Consequently, many wavenumbers previously
considered MTI-stable or slow-growing are in fact maximally unstable.
(abridged)
