The Turbulent Magnetic Diffusivity Tensor for Time-Dependent Mean Fields

TL;DR

This paper revises the understanding of turbulent magnetic diffusivity in mean field electrodynamics, highlighting the importance of time dependence in calculations to accurately predict magnetic field growth.

Contribution

It introduces an extended expansion method for the mean electromotive force that accounts for time-dependent mean magnetic fields, resolving previous inconsistencies.

Findings

Traditional methods underestimate magnetic diffusion in time-dependent fields.

The extended approach provides more accurate growth rate predictions.

Numerical analysis shows significant impact of the new contribution.

Abstract

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