Rotational stability of magnetic field in rotating quark-gluon plasma

Relaxation of the magnetic field in rigidly rotating quark-gluon plasma is studied. It is shown that the infrared modes satisfying $k<\mathrm{\mid }m\mathrm{\mid }\mathrm{\Omega }$ and $k<\mathrm{\mid }m\pm 1\mathrm{\mid }\mathrm{\Omega }$, where integer $m$ is the projection of the orbital angular momentum along the rotating axis and $\mathrm{\Omega }$ 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 $\mathrm{\Omega }$ and electrical conductivity $\sigma$ the instability is not expected to be a significant factor in the field’s time evolution.