Taming instability of magnetic field in chiral medium

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.