# Taming instability of magnetic field in chiral medium

## TL;DR

This paper analytically studies the evolution of magnetic fields in chiral media, showing that magnetic instability is suppressed by helicity conservation unless initial helicity is large, leading to a peak in magnetic field strength.

## Contribution

It provides an analytical solution for the time evolution of magnetic fields and chiral conductivity in chiral media, highlighting the role of initial helicity in magnetic field behavior.

## Key findings

- Magnetic field instability is suppressed by helicity conservation.
- A peak in magnetic field occurs only if initial helicity is significant.
- The evolution depends on the initial helicity stored in the medium.

## Abstract

Magnetic field is unstable in a medium with time-independent chiral conductivity. Owing to the chiral anomaly, the electromagnetic field and the medium exchange helicity which results in time-evolution of the chiral conductivity. Using the fastest growing momentum and helicity state of the vector potential as an ansatz, the time-evolution of the chiral conductivity and magnetic field is solved analytically. The solution for the hot and cold equations of state shows that the magnetic field does not develop an instability due to he helicity conservation. Moreover, it develops a peak only if a significant part of the \emph{initial} helicity is stored in the medium. The initial helicity determines the height and position of the peak.