Anomaly-driven inverse cascade and inhomogeneities in a magnetized chiral plasma in the early Universe

TL;DR

This paper investigates how inhomogeneities and diffusion affect the anomaly-driven inverse cascade of magnetic fields in a chiral plasma, finding that diffusion suppresses inhomogeneities and makes the evolution similar to the homogeneous case.

Contribution

It introduces a simple model to analyze the impact of inhomogeneities and diffusion on magnetic field evolution in a chiral plasma, highlighting the dominant role of diffusion.

Findings

Inhomogeneities do not prevent the inverse cascade.

Diffusion suppresses inhomogeneities and alters cascade dynamics.

In the primordial plasma, diffusion makes the evolution similar to the homogeneous case.

Abstract

By making use of a simple model that captures the key features of the anomalous Maxwell equations, we study the role of inhomogeneities on the evolution of magnetic fields in a chiral plasma. We find that inhomogeneities of the chiral asymmetry by themselves do not prevent the anomaly-driven inverse cascade and, as in the homogeneous case, the magnetic helicity is transferred from shorter to longer wavelength helical modes of the magnetic field. However, we also find that the evolution appears to be sensitive to the effects of diffusion. In the case when diffusion is negligible, the inverse cascade slows down considerably compared to the homogeneous scenario. In the case of the primordial plasma, though, we find that the diffusion is substantial and efficiently suppresses chiral asymmetry inhomogeneities. As a result, the inverse cascade proceeds practically in the same way as in the chirally homogeneous model.