Hydromagnetic Waves in a Differentially Rotating Annulus III. The Effect of an Axial Field

The first two papers in this series (Fearn, 1983b, 1984) are concerned with the linear stability of the toroidal magnetic field B(o)(s)(phi) over cap (where (s, phi, z) are cylindrical polar coordinates). The field is confined in a cylindrical annulus and the whole system is rapidly rotating about the axis of symmetry. The present study extends the analysis by adding a uniform axial field B(2)(z) over cap. In a non-rotating system this would have a stabilising influence on ideal instabilities. In the rotating system, a small axial field counteracts the stabilising effect of rotation and so has a destabilising influence. For cases of geophysical interest, larger axial fields are stabilising. Resistive instabilities behave in much the same way as their counterparts in a non-rotating system. The essential requirement for instability is k center dot B(o)=0 (where k is the wave vector). The addition of an axial field may therefore be stabilising or destabilising.