THE EFFECT OF A FINITELY CONDUCTING LAYER IN THE MANTLE ON MAGNETIC INSTABILITY IN THE CORE

The stability of a toroidal magnetic field B = B(s)I-phi (where (s*, phi, z) are cylindrical polar coordinates), in a rapidly rotating cyl indrical annulus with finitely conducting boundaries is investigated. In particular we examine the effect of a conducting layer of thickness epsilon at the base of an insulating mantle. The ratio of magnetic di ffusivity in the layer to that of the outer core is denoted by eta(m): eta(m) --> 0 corresponding to a perfectly conducting layer and eta(m) --> infinity to an insulating one. The inner core/outer core diffusivi ty ratio, eta i, is in most cases taken to be eta(i) = 1. Checks were made on the results by comparisons with results of Lamb (1994), and go od agreement was found in the limit eta(m) --> infinity With his insul ating boundary result. Lowering eta(m), to more realistic values and i ncreasing the thickness of the layer were both found to be destabilizi ng effects. An unexpected result was the continued existence of the Ro berts-Loper exceptional mode, not found in the presence of perfectly c onducting boundaries, in the limit eta(i), eta(m) --> 0 and, with eta( i), eta(m) less than or similar to 1, when E and E(eta) (non-dimension al measures of viscous and inertial effects) --> 0.