The mean electromotive force resulting from magnetic buoyancy instability

TL;DR

This paper investigates the mean electromotive force generated by magnetic buoyancy instability in stratified, rotating magnetic layers, highlighting the limitations of traditional alpha-beta decomposition and providing analytic and numerical insights into emf dependencies.

Contribution

It introduces a new approach to analyze the mean emf from magnetic buoyancy instability, emphasizing the entire emf over traditional alpha-beta effects, with analytic solutions for ideal MHD cases.

Findings

Derived depth-dependent emf expressions for ideal MHD

Showed emf dependence on rotation rate and latitude

Highlighted limitations of alpha-beta decomposition

Abstract

Motivated both by considerations of the generation of large-scale astrophysical magnetic fields and by potential problems with mean magnetic field generation by turbulent convection, we investigate the mean electromotive force (emf) resulting from the magnetic buoyancy instability of a rotating layer of stratified magnetic field, considering both unidirectional and sheared fields. We discuss why the traditional decomposition into $\alpha$ and $\beta$ effects is inappropriate in this case, and that it is only consideration of the entire mean emf that is meaningful. By considering a weighted average of the unstable linear eigenmodes, and averaging over the horizontal plane, we obtain depth-dependent emfs. For the simplified case of isothermal, ideal MHD we are able to obtain an analytic expression for the emf; more generally the emf has to be determined numerically. We calculate how the emf depends on the various parameters of the problem, particularly the rotation rate and the latitude of the magnetic layer.