MAGNETIC INSTABILITY IN A RAPIDLY ROTATING CYLINDRICAL ANNULUS WITH AFINITELY CONDUCTING INNER-CORE

We consider the stability of a toroidal magnetic field B = B(s)phi (w here(s,phi,z*) are cylindrical polar coordinates) in a cylindrical an nulus of conducting fluid with inner and outer radii s(i) and s(o) rot ating rapidly about its axis. The outer boundary is taken to be either insulating or perfectly conducting, and the effect of a finite magnet ic diffusivity in the inner core is investigated. The ratio of magneti c diffusivity in the inner core to that of the outer core is denoted b y eta; eta --> 0 corresponding to a perfectly conducting inner core an d eta --> infinity to an insulating one. Comparisons with the results of Fearn (1983b, 1988) were made and a good match found in the limits eta --> 0 and eta --> infinity with his perfectly conducting and insul ating results, respectively. In addition a new mode of instability was found in the eta --> 0 regime. Features of this new mode are low freq uency (both the frequency and growth rate --> 0 as eta --> 0) and pene tration deep into the inner core. Typically it is unstable at lower ma gnetic field strengths than the previously known instabilities.