Rotational stability of magnetic field in rotating quark-gluon plasma

TL;DR

This paper investigates how magnetic fields relax in a rotating quark-gluon plasma, identifying unstable modes and calculating growth rates, but finds the instability unlikely to significantly affect magnetic field evolution under typical conditions.

Contribution

It introduces an analysis of magnetic field stability in rotating quark-gluon plasma, identifying unstable modes and quantifying growth rates.

Findings

Infrared modes with specific angular momentum projections are unstable.

Instability onset time and growth rate are computed for standard initial profiles.

Under typical conditions, the instability does not significantly influence magnetic field evolution.

Abstract

Relaxation of the magnetic field in rigidly rotating quark-gluon plasma is studied. It is shown that the infrared modes satisfying $k < |m|\Omega$ and $k< |m\pm 1|\Omega$, where integer $m$ is the projection of the orbital angular momentum along the rotating axis and $\Omega$ is the angular velocity, are unstable. The instability onset time and the magnetic field growth rate are computed for a standard initial profile of the magnetic field. Given the present phenomenological values of $\Omega$ and electrical conductivity $\sigma$ the instability is not expected to be a significant factor in the field's time evolution.