Axisymmetric dynamo action produced by differential rotation, with anisotropic electrical conductivity and anisotropic magnetic permeability

TL;DR

This paper analytically investigates how anisotropic electrical conductivity and magnetic permeability influence axisymmetric dynamo action driven by simple differential rotation, revealing a competition between anisotropies that affects dynamo viability.

Contribution

It introduces a fully analytical stability analysis of an axisymmetric dynamo with anisotropic properties, challenging traditional dynamo theory assumptions.

Findings

Dynamo is axisymmetric and driven by simple differential rotation.

Dynamo effect is suppressed when electrical conductivity and magnetic permeability anisotropies are identical.

Anisotropic magnetic permeability can enable dynamo action even with isotropic electrical conductivity.

Abstract

The effect on dynamo action of an anisotropic electrical conductivity conjugated to an anisotropic magnetic permeability is considered. Not only is the dynamo fully axisymmetric, but it requires only a simple differential rotation, which twice challenges the well-established dynamo theory. Stability analysis is conducted entirely analytically, leading to an explicit expression of the dynamo threshold. The results show a competition between the anisotropy of electrical conductivity and that of magnetic permeability, the dynamo effect becoming impossible if the two anisotropies are identical. For isotropic electrical conductivity, Cowling's neutral point argument does imply the absence of an azimuthal component of current density, but does not prevent the dynamo effect as long as the magnetic permeability is anisotropic.