Electromagnetic induction in non-uniform domains

TL;DR

This study uses numerical simulations to analyze how material properties of disks in a conducting fluid influence magnetic field generation, showing that high permeability and conductivity disks significantly alter field geometry and dynamo thresholds.

Contribution

The paper provides a detailed numerical validation of induction models and demonstrates the impact of material properties on dynamo action in VKS-like setups, highlighting the sensitivity of critical parameters.

Findings

Material properties strongly modify magnetic field geometry and growth rates.

High permeability disks reduce the critical magnetic Reynolds number, but not enough for practical VKS applications.

The influence of boundary conditions is minimal compared to internal material properties.

Abstract

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high conducting and high permeability disks that are present in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the high permeability/high conductivity material is localized within a quite thin region. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high permeability disks yields a reduction of the critical magnetic Reynolds number for the onset of dynamo action of the simplest non-axisymmetric field mode. However this decrease is not sufficient to become relevant in the VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by tiny changes in the flow configuration so that the result is not very robust against small modifications of setup and properties of turbulence.