Numerical Evidence of Fast Dynamo Action in a Spherical Shell

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Abstract
We consider the evolution of a magnetic field in a spherical shell of highly conducting fluid surrounded by an insulator. We impose an axisymmetric, time-dependent flow, having large regions of chaotic particle paths. This flow appears to yield fast dynamo action, in which the field grows on the fast advective, rather than on the slow diffusive time scale. We demonstrate that the field adjusts to the Bondi-Gold theorem, according to which the field in the insulators inside and outside the shell cannot grow on the fast time scale, by becoming increasingly self-contained within the shell.