The inverse cascade of magnetic helicity in magnetohydrodynamic turbulence

TL;DR

This paper investigates the inverse cascade of magnetic helicity in magnetohydrodynamic turbulence using simulations and theory, revealing a universal balance relation that impacts understanding of magnetic field generation.

Contribution

It revisits and extends statistical closure theory to include kinetic effects, explaining the spectral scaling of magnetic helicity and its role in dynamo processes.

Findings

Spectral scaling of magnetic helicity differs from previous models.

A universal dynamical balance relation is derived.

Implications for nonlinear $$-dynamo effects are discussed.

Abstract

The nonlinear dynamics of magnetic helicity, $H^M$, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of $H^M$ is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. \textbf{77} 321 (1976)]. By revisiting this theory a universal dynamical balance relation is found that includes effects of kinetic helicity, as well as kinetic and magnetic energy on the inverse cascade of $H^M$ and explains the above-mentioned discrepancy. Considering the result in the context of mean-field dynamo theory suggests a nonlinear modification of the $\alpha$-dynamo effect important in the context of magnetic field excitation in turbulent plasmas.