The alpha effect with imposed and dynamo-generated magnetic fields

TL;DR

This paper compares two methods for estimating the nonlinear alpha effect in helical turbulence with magnetic fields, highlighting the influence of meso-scale magnetic fields and proposing a technique to recover the kinematic value.

Contribution

It demonstrates the agreement and discrepancies between the imposed-field and test-field methods and introduces a resetting technique to accurately measure the alpha effect.

Findings

Both methods agree for strong fields.

Meso-scale magnetic fields can cause over- or underestimation of alpha.

Resetting the magnetic field to zero recovers the kinematic alpha value.

Abstract

Estimates for the nonlinear alpha effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the test-field method where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where these meso-scale fields can lead to both drastically overestimated and underestimated values of alpha compared with the kinematic case. It is demonstrated that the kinematic value can be recovered by resetting the fluctuating magnetic field to zero in regular time intervals. It is concluded that this is the preferred technique both for the imposed-field and the test-field methods.