In a low-collisionality plasma with a weak magnetic field, the convective instability requirement changes from an entropy dependence to a combination of the magnetic-field orientation and temperature gradient. In such cases, two instabilities are known to be available, the magnetothermal instability (MTI) and the heat-flux-driven buoyancy instability (HBI). Of particular interest to us is the HBI, which exhibits a number of non-linear effects – such as the restriction of vertical heat transport – that have previously been shown to play a key role in cool-core galaxy clusters, and which may prove to be important within smaller astrophysical bodies.
Here we give a brief overview of both instabilities before presenting initial results from our survey of the parameter regime in which the HBI might operate within smaller bodies; stellar and hot planetary atmospheres. We show that the key requirements for the HBI to operate are satisfied within portions of the outer regions of these atmospheres but that stabilisation by magnetic tension presents a significant obstacle in both cases. Additionally, we give a brief overview of the 2D MHD simulations of the HBI that we have performed to investigate the evolution of the instability in various environments.