The fate of alpha dynamos at large $Rm$

TL;DR

This paper investigates how alpha dynamos behave at high magnetic Reynolds numbers, revealing the limits of mean field theory and proposing new directions for modeling solar and stellar magnetic fields.

Contribution

It introduces a Floquet theory-based framework to precisely quantify mean field effects and determine the validity range of alpha dynamo models at varying Rm.

Findings

Alpha description valid below critical Rm_c

Above Rm_c, large scale growth rates become scale-independent

Large scale energy inversely proportional to square of scale separation

Abstract

At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha-dynamos as the magnetic Reynolds number $Rm$ is increased. Using Floquet theory, we are able to precisely quantify mean field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large scale separations with minimal computational cost. We apply this framework to helical and non-helical flows as well as to random flows with short correlation time. Our results determine that the alpha-description is valid for $Rm$ smaller than a critical value $Rm_c$ at which small scale dynamo instability starts. When $Rm$ is above $Rm_c$ the dynamo ceases to follow the mean field description and the growth rate of the large scale modes becomes independent of the scale separation while the energy in the large scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean field modeling are proposed.