Energetics of turbulence generated by chiral MHD dynamos

TL;DR

This paper investigates the energy dynamics of turbulence driven by chiral magnetic fields in the early Universe, using numerical simulations to understand how initial conditions affect magnetic and kinetic energy ratios.

Contribution

It provides a detailed analysis of the energetics of chiral magnetically driven turbulence and introduces a scaling law for the energy ratio as a function of magnetic Prandtl number.

Findings

The kinetic to magnetic energy ratio Upsilon is approximately 0.064-0.074 in the studied parameter space.

Upsilon decreases as a power law with increasing Pm, approximately Upsilon(Pm)=0.1 Pm^{-0.4}.

The results are applicable to understanding magnetic field evolution in the early Universe.

Abstract

An asymmetry in the number density of left- and right-handed fermions is known to give rise to a new term in the induction equation that can result in a dynamo instability. At high temperatures, when a chiral asymmetry can survive for long enough, this chiral dynamo instability can amplify magnetic fields efficiently, which in turn drive turbulence via the Lorentz force. While it has been demonstrated in numerical simulations that this chiral magnetically driven turbulence exists and strongly affects the dynamics of the magnetic field, the details of this process remain unclear. The goal of this paper is to analyse the energetics of chiral magnetically driven turbulence and its effect on the generation and dynamics of the magnetic field using direct numerical simulations. We study these effects for different initial conditions, including a variation of the initial chiral chemical potential and the magnetic Prandtl number, Pm. In particular, we determine the ratio of kinetic to magnetic energy, Upsilon, in chiral magnetically driven turbulence. Within the parameter space explored in this study, Upsilon reaches a value of approximately 0.064-0.074 -independently of the initial chiral asymmetry and for Pm=1. Our simulations suggest, that Upsilon decreases as a power law when increasing Pm by decreasing the viscosity. While the exact scaling depends on the details of the fitting criteria and the Reynolds number regime, an approximate result of Upsilon(Pm)=0.1 Pm^{-0.4} is reported. Using the findings from our numerical simulations, we analyse the energetics of chiral magnetically driven turbulence in the early Universe.