  Using the transport equations for an ideal anisotropic collisionless plasma
derived from the Vlasov equation by the 16-moment method, we analyse the
influence of pressure anisotropy exhibited by collisionless magnetized plasmas
on the magnetothermal (MTI) and heat-flux-driven buoyancy (HBI) instabilities.
We calculate the dispersion relation and the growth rates for these
instabilities in the presence of a background heat flux and for configurations
with static pressure anisotropy, finding that when the frequency at which heat
conduction acts is much larger than any other frequency in the system (i.e.
weak magnetic field) the pressure anisotropy has no effect on the MTI/HBI,
provided the degree of anisotropy is small. In contrast, when this ordering of
timescales does not apply the instability criteria depend on pressure
anisotropy. Specifically, the growth time of the instabilities in the
anisotropic case can be almost one order of magnitude smaller than its
isotropic counterpart. We conclude that in plasmas where pressure anisotropy is
present the MTI/HBI are modified. However, in environments with low magnetic
fields and small anisotropy such as the ICM the results obtained from the
16-moment equations under the approximations considered are similar to those
obtained from ideal MHD.
