ON THE ADJUSTMENT TO THE BONDI-GOLD THEOREM IN A SPHERICAL-SHELL FASTDYNAMO

We present a numerical solution of the magnetic induction equation in a spherical fluid shell, with an insulator inside and outside. Prescri bing an axisymmetric, time-dependent, chaotic flow, we find that the m agnetic field appears to grow on the fast advective, rather than on th e slow diffusive time scale. We demonstrate how this may be reconciled with the theorem of Bondi and Gold (1950), that the potential field i n these insulators inside and outside the shell cannot be amplified on the fast lime scale, by having the field become increasingly containe d within the shell with increasing magnetic Reynolds number. Thus, as the Bondi-Gold theorem becomes more and more applicable, there is inde ed less and less external field being amplified. This is in precise ag reement with the conjecture of Radler (1982) that the resolution would be to have an ''invisible dynamo,'' one having no external field. Fin ally, we consider some of the implications of this adjustment for the different symmetries of the field (dipolar versus quadrupolar) and the flow (u versus -u).