On minimal energy states of chiral MHD turbulence

We study the evolution of magnetohydrodynamic turbulence taking into account the chiral anomaly effect. This chiral magnetohydrodynamic description of the plasma is expected to be relevant for temperatures comparable to the electroweak scale, and therefore for the evolution of magnetic fields in the early Universe and young neutron stars. We focus on the case of freely decaying chiral magnetohydrodynamic turbulence and discuss the dissipation of ideal MHD invariants. Using the variational approach we discuss the minimum energy configurations of magnetic field and velocity. As in the case of the standard magnetohydrodynamic turbulence, we find that the natural relaxation state is given by a force-free field, $\nabla \times \mathbf{B} \propto \mathbf{B}$. However, the precise form of this configuration is now determined by parameters describing the chiral anomaly effect, leading to some important differences when compared to the non-chiral turbulence. Using this result we argue that the evolution of velocity and magnetic field will tend to effectively decouple during the transition to this minimal energy state.