On the evolution of turbulent magnetic fields in a collision dominated plasma

Abstract

In a weakly ionized plasma, in which collisions with the neutral background control the velocity fields of the ions and electrons against pressure gradients and the Lorentz force, it is demonstrated that: (1) The energy density in the turbulent magnetic field declines as time progresses. (2) The rate of decline depends on the amount of 'helicity' present in the turbulent magnetic field. (3) The 'helicity' must either be zero or must take on one of its two possible equipartition values, which are equal and opposite. (4) The effect of helicity is to increase the rate of decay of the long wavelength modes of the turbulent field over the decay rate obtained in its absence. This calculation was done both to illustrate the way in which the non-linear interaction of fluid velocities and magnetic fields influences the temporal evolution of the turbulent magnetic field, and as a directional guide which may, perhaps, eventually indicate a self-consistent method of handling the problem of hydromagnetic turbulence in conducting fluids.