Turbulent Magnetic Diffusivity Tensor for Time-Dependent Mean Fields

Abstract

We reexamine the nature of the turbulent magnetic diffusivity tensor of mean field electrodynamics and show that the predicted growth rate of the mean field is, in general, incorrect if the tensor is calculated via consideration of time-independent mean magnetic fields. We describe how the traditional expansion procedure for the mean electromotive force should be extended to include time derivatives of the mean magnetic field, and illustrate the consistency of this approach by means of a perturbation analysis for a mean field varying on long spatial scales. Finally, we examine the magnitude of this new contribution to the magnetic diffusion for a particular flow.