Resistive and ferritic-wall plasma dynamos in a sphere

TL;DR

This study investigates how the electrical conductivity and magnetic permeability of a sphere's wall influence the onset and growth rate of a plasma dynamo, providing insights relevant to experimental setups like MPDX.

Contribution

It introduces a numerical analysis of wall property effects on a spherical plasma dynamo, highlighting the impact of permeability and conductivity on dynamo thresholds and growth rates.

Findings

Higher wall permeability lowers the critical magnetic Reynolds number.

Increased wall conductivity does not change the critical number but reduces growth rate.

Abstract

We numerically study the effects of varying electric conductivity and magnetic permeability of the bounding wall on a kinematic dynamo in a sphere for parameters relevant to Madison plasma dynamo experiment (MPDX). The dynamo is excited by a laminar, axisymmetric flow of von Karman type. The flow is obtained as a solution to the Navier-Stokes equation for an isothermal fluid with a velocity profile specified at the sphere's boundary. The properties of the wall are taken into account as thin-wall boundary conditions imposed on the magnetic field. It is found that an increase in the permeability of the wall reduces the critical magnetic Reynolds number Rm_cr. An increase in the conductivity of the wall leaves Rm_cr unaffected, but reduces the dynamo growth rate.