Effects of Hall Currents on the Self‐Gravitational Instability of a Finitely Conducting Plasma of Variable Density

Abstract

AbstractThe effects of Hall currents have been studied on the hydromagnetic stability of a self‐gravitating, incompressible, viscous and finitely conducting plasma of variable density. For a uniform and horizontal magnetic field which is present, it is shown that the problem is characterized by a variational principle. Making use of this, proper solutions have been obtained for a semi‐infinite plasma in which the density varies one‐dimensionally (exponentially) along the vertical. The dispersion relation has been solved numerically for the different values of the parameters involved. It is found that the growth rate increases with both the Hall currents and resistivity, showing thereby the destabilizing character of these effects. However, the influence of viscosity is found to be stabilizing as the growth rate decreases with viscosity.