Nonlinear magnetic diffusivity and alpha tensors in helical turbulence

TL;DR

This paper investigates how a mean magnetic field influences turbulence properties, revealing that turbulent diffusivity weakly depends on magnetic Reynolds number while the alpha effect diminishes significantly with increasing Rm.

Contribution

It provides the first detailed analysis of nonlinear magnetic diffusivity and alpha tensors in helical turbulence using the testfield method across a wide Rm range.

Findings

Turbulent magnetic diffusivity decreases by a factor of ~5 as Rm increases from 2 to 600.

The alpha effect reduces by a factor of ~14 over the same Rm range.

Fluctuations in alpha and etat are only 10-20% of their kinematic values.

Abstract

The effect of a dynamo-generated mean magnetic field of Beltrami type on the mean electromotive force is studied. In the absence of the mean magnetic field the turbulence is assumed to be homogeneous and isotropic, but it becomes inhomogeneous and anisotropic with this field. Using the testfield method the dependence of the alpha and turbulent diffusivity tensors on the magnetic Reynolds number Rm is determined for magnetic fields that have reached approximate equipartition with the velocity field. The tensor components are characterized by a pseudoscalar alpha and a scalar turbulent magnetic diffusivity etat. Increasing Rm from 2 to 600 reduces etat by a factor ~5, suggesting that the quenching of etat is, in contrast to the 2-dimensional case, only weakly dependent on Rm. Over the same range of Rm, however, alpha is reduced by a factor ~14, which can qualitatively be explained by a corresponding increase of a magnetic contribution to the alpha effect with opposite sign. The level of fluctuations of alpha and etat is only 10% and 20% of the respective kinematic reference values.