On instability of the magnetic Benard problem with Hall and ion-slip effects

Assuming the validity of the principle of exchange of stabilities, the linear stability of the mechanical equilibrium of a horizontal fluid layer subject to a vertical temperature gradient, a vertical magnetic field, in the presence of Hall and ion-slip effects to normal mode perturbations is studied. The Budiansky-DiPrima method is used to solve the governing boundary value problem for an 11 th order system of ordinary differential equations containing four physical parameters. The exact neutral stability curve was obtained in the form of a series. For truncation to one and two terms the coupled action of Hall and ion-slip currents is found destabilizing. The closed form of the Rayleigh number as a function of the other parameters, defining the neutral curves up the two terms, was obtained. The given problem was split into an even and an odd problem. The computation shows that the odd problem corresponding to odd velocity and temperature perturbations with respect to the vertical coordinate is more appropriate than the even one. (C) 2004 Elsevier Ltd. All rights reserved.