Spatial parity violation and the turbulent magnetic Prandtl number

Abstract

Using the field theory renormalization-group technique in the two-loop approximation, we study the influence of helicity (spatial parity violation) on the turbulent magnetic Prandtl number in the model of kinematic magnetohydrodynamic turbulence, where the magnetic field behaves as a passive vector quantity advected by the helical turbulent environment given by the stochastic Navier-Stokes equation. We show that the presence of helicity decreases the value of the turbulent magnetic Prandtl number and that the two-loop helical contribution to the turbulent magnetic Prandtl number is up to 4.2% of its nonhelical value. This result demonstrates the strong stability of the properties of diffusion processes of the magnetic field in turbulent environments with spatial parity violation compared with the corresponding systems without the helicity.