Effect of finite Larmor radius on the gravitational instability of a conducting plasma layer of finite thickness surrounded by a non-conducting matter

The gravitational instability of an incompressible, infinitely conducting plasma layer of finite thickness surrounded a non-conducting matter has been investigated taking into account the effect of the finite Larmor radius. The magnetic field is assumed to be directed parallel to the interfaces. Only the perturbations transverse to the magnetic field are considered, though both the symmetric and asymmetric nature of the perturbations are taken into account. Using the normal mode technique, dispersion relations are obtained.It is found that the finite larmor radius has, in general, a stabilizing influence on the configuration. Even when the system is thoroughly unstable, it has been shown that there exists a critical value of the wave-number, such that the motion is stabilized for wave-numbers of perturbations exceeding this critical value.