Self-similar inverse cascade of magnetic helicity driven by the chiral anomaly

TL;DR

This paper investigates how the chiral magnetic effect causes an inverse cascade of magnetic helicity, leading to self-similar magnetic field structures and topological transitions, with potential experimental signatures in heavy ion collisions.

Contribution

It demonstrates the self-similar inverse cascade of magnetic helicity driven by the chiral anomaly and explores the topological evolution of gauge fields during this process.

Findings

Inverse cascade of magnetic helicity towards large scales.

Transition from linked electric and magnetic fields to knotted magnetic configurations.

Pulses of CME current accompany magnetic reconnections.

Abstract

For systems with charged chiral fermions, the imbalance of chirality in the presence of magnetic field generates an electric current - this is the Chiral Magnetic Effect (CME). We study the dynamical real-time evolution of electromagnetic fields coupled by the anomaly to the chiral charge density and the CME current by solving the Maxwell-Chern-Simons equations. We find that the CME induces the inverse cascade of magnetic helicity towards the large distances, and that at late times this cascade becomes self-similar, with universal exponents. We also find that in terms of gauge field topology the inverse cascade represents the transition from linked electric and magnetic fields (Hopfions) to the knotted configuration of magnetic field (Chandrasekhar-Kendall states). The magnetic reconnections are accompanied by the pulses of the CME current directed along the magnetic field lines. We devise an experimental signature of these phenomena in heavy ion collisions, and speculate about implications for condensed matter systems.