Electrodynamics of turbulent fluids with fluctuating electric conductivity

TL;DR

This paper investigates how fluctuating electric conductivity in turbulent fluids affects magnetic field behavior, revealing effects like increased decay time, diamagnetic pumping, and alpha effects, but not sufficient for self-sustaining dynamos in planetary or stellar contexts.

Contribution

It introduces a theoretical framework for understanding the impact of conductivity fluctuations on mean-field electrodynamics, including new effects like diamagnetic pumping and alpha effects in turbulent fluids.

Findings

Conductivity fluctuations reduce effective magnetic diffusivity.

Correlated conductivity and flow fluctuations induce diamagnetic pumping.

Alpha effect appears but is insufficient for dynamo action in Earth's core or the Sun.

Abstract

The influence of fluctuating conductivity on the coefficients known from the mean-field electrodynamics is considered. If the conductivity fluctuations are assumed as uncorrelated with the turbulent velocity field then only the effective magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field is increased. If the fluctuations of conductivity and flow are correlated in a certain direction then an additional diamagnetic pumping effect results transporting magnetic field in opposite direction to the resistivity flux vector $\langle \eta'\vec{u}'\rangle$. Even for homogeneous turbulence fields in the presence of rotation an alpha effect appears. With the characteristic values of the outer core of the Earth or the solar convection zone, however, the dynamo number of the alpha effect never reaches supercritical values to operate as an $\alpha^2$-dynamo.