Equatorial magnetic helicity flux in simulations with different gauges

TL;DR

This study investigates magnetic helicity flux in MHD turbulence simulations, demonstrating a diffusive flux law largely independent of gauge choice and discussing implications for alleviating catastrophic quenching at high Reynolds numbers.

Contribution

It introduces a gauge-invariant analysis of magnetic helicity flux and quantifies its diffusive behavior in turbulent MHD simulations with varying gauge conditions.

Findings

Magnetic helicity flux follows a Fickian diffusion law with a nearly gauge-independent diffusion coefficient.

The flux can potentially mitigate catastrophic quenching at high magnetic Reynolds numbers.

Magnetic helicity density and flux are consistent across different gauges in steady state.

Abstract

We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the `resistive gauge' in which the Laplacian of the magnetic vector potential acts as resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges.