Ion-neutral friction as a model for magnetic relaxation

It is generally admitted that a plasma in the absence of forcing will relax to a minimum energy state compatible with appropriate constraints. Usually this is a force-free state, which, in two dimensions, implies a potential magnetic field except by the possible presence of current sheets. The precise mechanism of this relaxation, and in particular the plasma velocity, are generally ignored. There exists, however, a physically well-defined process that should produce magnetic relaxation: ion-neutral (or ambipolar) friction. While there is no guarantee of the existence of a limit of this process when t -> infinity, there exists a family of sequential limits for whom the Lorentz force tends to zero. To analyze the configuration of these limit states, we study the evolution of several moments of the magnetic energy. We prove that for as long as the enstrophy remains bounded, the current density energy also remains bounded in two dimensions: this excludes all classical configurations of current sheets across which the magnetic field reverses direction. Hence, these sheets cannot be the limit of ion-neutral diffusion unless the flow becomes increasingly irregular over time.