Influence of inner and outer walls electromagnetic properties on the onset of a stationary dynamo

TL;DR

This paper investigates how the electromagnetic properties of inner and outer walls influence the initiation of a stationary dynamo using a simplified 1D model with analytical and numerical solutions.

Contribution

It introduces a 1D model replacing flow with an alpha effect to analyze dynamo onset considering walls with varying electromagnetic properties.

Findings

Walls with different conductivities and permeabilities affect dynamo threshold.

Analytical dispersion equations are derived for various wall properties.

Numerical solutions explore limits of infinite conductivity or permeability.

Abstract

To study the onset of a stationary dynamo in the presence of inner or outer walls of various electromagnetic properties, we propose a simple 1D-model in which the flow is replaced by an alpha effect. The equation of dispersion of the problem is derived analytically. It is solved numerically for walls of different thicknesses and of electric conductivity and magnetic permeability different from those of the fluid in motion. We also consider walls in the limit of infinite conductivity or permeability.