THE STABILITY OF TOROIDAL MAGNETIC-FIELDS WITH EQUATORIAL SYMMETRY - IMPLICATIONS FOR THE EARTH MAGNETIC-FIELD

Geophysical observation suggests that the symmetry of the Earth's magn etic field has been predominantly dipolar over the last 2.5 m.y. Given that such an antisymmetric field will vanish at the equatorial plane, we might expect antisymmetry to be a source of magnetic field instabi lity, as the presence of so-called critical surfaces are robust destab ilising features, independent of field morphology. To examine the infl uence of antisymmetry on the stability of magnetic fields a detailed i nvestigation of the stability of model toroidal fields is presented. U sing a cylindrical geometry (s,phi,z*), a basic model field B(s*,z*)< (phi)over cap> is subject to an infinitesimal perturbation which is al lowed to grow (or decay) in the presence of B<(phi)over cap>. The addi tion of an antisymmetric z-dependence to a previously stable s-depende nt field, B'(s)<(phi)over cap>, causes the new field, B(s*,z*)<(phi)o ver cap>, to destabilise; the addition of an antisymmetric z-dependenc e to an already unstable field significantly lowers Lambda(c) (where L ambda(c) is a measure of the critical field strength). The addition of antisymmetric z-dependence gives an extra critical surface at the equ ator (z = 0), which, in turn, gives an extra degree of freedom for fi eld line reconnection, thus leading to a lower Lambda(c). The use of a cylindrical geometry permits examination of the spatial structure and complex growth rate of the instability in the large field strength, s mall ohmic diffusion regime (defined by large Lambda). In this regime, the most unstable perturbations are found to belong to the resistive class: their mechanism is reconnection and breaking of field lines nea r a critical surface. Comparisons between results in cylindrical and s pherical geometry in the low field strength regime are favourable. Res ults are also given for the ideal instability which can exist in the a bsence of diffusion. Our model shows strong localisation of the ideal mode far from the critical surfaces.