Instability of a Plasma in Porous Medium

The double-diffusive instability of a plasma is considered in the presence of finite Larmor radius effect and porous medium. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the finite Larmor radius, stable solute gradient and magnetic field introduce oscillatory modes in the systems which were non-existent in their absence. For stationary convection case, the finite Larmor radius and stable solute gradient have stabilizing effects on the system. On the other hand, the medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain condition in the presence of finite Larmor radius effect whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively. The sufficient conditions for non-existence of overstability are also obtained.