Chiral magnetohydrodynamics with zero total chirality

TL;DR

This paper investigates the coupled evolution of magnetic fields and chiral fermion asymmetry in chiral magnetohydrodynamics with zero initial total chirality, revealing how inverse cascading and helicity dynamics depend on initial conditions and plasma parameters.

Contribution

It provides a detailed analysis of magnetic and chiral evolution in zero total chirality scenarios, highlighting the roles of CPI and eddy turnover times in inverse cascade processes.

Findings

Magnetic helicity and chirality cancel each other over time.

CPI time scale influences high wave number helicity spectrum.

Eddy turnover time affects inverse cascade onset.

Abstract

We study the evolution of magnetic fields coupled with chiral fermion asymmetry in the framework of chiral magnetohydrodynamics with zero initial total chirality. The initial magnetic field has a turbulent spectrum peaking at a certain characteristic scale and is fully helical with positive helicity. The initial chiral chemical potential is spatially uniform and negative. We consider two opposite cases where the ratio of the length scale of the chiral plasma instability (CPI) to the characteristic scale of the turbulence is smaller and larger than unity. These initial conditions might be realized in cosmological models such as certain types of axion inflation. The magnetic field and chiral chemical potential evolve with inverse cascading in such a way that the magnetic helicity and chirality cancel each other at all times. The CPI time scale is found to determine mainly the time when the magnetic helicity spectrum attains negative values at high wave numbers. The turnover time of the energy-carrying eddies, on the other hand, determines the time when the peak of the spectrum starts to shift to smaller wave numbers via an inverse cascade. The onset of helicity decay is determined by the time when the chiral magnetic effect becomes efficient at the peak of the initial magnetic energy spectrum. When spin flipping is important, the chiral chemical potential vanishes and the magnetic helicity becomes constant, which leads to a faster increase of the correlation length, as expected from magnetic helicity conservation. This also happens when the initial total chirality is imbalanced. Our findings have important implications for baryogenesis after axion inflation.