Problems with kinematic mean field electrodynamics at high magnetic Reynolds numbers

TL;DR

This paper examines the limitations of the kinematic alpha-effect formalism in high magnetic Reynolds number regimes, highlighting issues with calculating and interpreting alpha coefficients due to small-scale dynamo effects.

Contribution

It critically analyzes the applicability of the alpha-effect formalism at high magnetic Reynolds numbers and discusses potential methods for computing alpha coefficients.

Findings

Alpha coefficients are difficult to compute accurately at high Rm.

The interpretation of alpha coefficients in large-scale field evolution may be fundamentally flawed.

Small-scale dynamo activity complicates mean field electrodynamics at high Rm.

Abstract

We discuss the applicability of the kinematic $\alpha$-effect formalism at high magnetic Reynolds numbers. In this regime the underlying flow is likely to be a small-scale dynamo, leading to the exponential growth of fluctuations. Difficulties arise with both the actual calculation of the $\alpha$ coefficients and with its interpretation. We argue that although the former may be circumvented -- and we outline several procedures by which the the $\alpha$ coefficients can be computed in principle -- the interpretation of these quantities in terms of the evolution of the large-scale field may be fundamentally flawed.