The character of equilibrium of an inviscid, infinitely conducting fluid of variable density in the presence of a horizontal magnetic field with Hall-current

Abstract

The character of equilibrium of an inviscid, incompressible, infinitely conducting fluid of variable density in the presence of a horizontal magnetic field has been investigated taking into account the effects of Hall-currents. The solution is shown to be characterized by a variational principle. Making use of the existence of variational principle the solution is developed in the case of continuously stratified fluid of exponentially varying density confined between two horizontal planes at finite distance, from which the necessary and sufficient conditions of stability are obtained. The Hall-currents are found to destabilize the wave-number range which is stable otherwise.