A simple hydromagnetic stability problem involving finite conductivity, electron inertia and the hall effect

A study is made of the hydromagnetic stability of a current-carrying fluid whose Ohm's law includes finite conductivity, electron inertia and the Hall effect. The system has previously been shown to be unstable when finite conductivity alone is considered. It is found that the system is still unstable. The introduction of the Hall effect does lead to a reduction in growth rate but electron inertia is a further destabilizing influence. In none of the cases studied is the growth rate reduced by an order of magnitude. It is possible that viscosity (which has not been included) causes a larger reduction in growth rate than the Hall effect.