Equilibrium structures in partially ionized rotating plasmas within Hall magnetohydrodynamics

Abstract

The formation of equilibrium structures in partially ionized rotating plasmas, consisting of electrons, ions, and neutral molecules, including the Hall effect, is studied in order to diagnose the possible velocity and the magnetic field configurations in a self-consistent manner. A few simple examples show that the linear and the nonlinear force-free magnetic configurations along with essentially nonlinear Beltrami flow field seem to be the general features of plasmas in the special case of the Keplerian rotation relevant for astrophysical plasmas. Thus rotation along with axial bipolar flows emerges as a natural pattern in gravitationally controlled magnetohydrodynamic systems. However, the equilibrium conditions permit more general flow and the magnetic field profiles that can perhaps be fully explored numerically. A special class of equilibria with unit magnetic Prandtl number and equal values of the fractional ion mass density α = ρi/ρn and the Hall parameter ϵ = λi/L exists where ρ’s are the uniform mass densities, λi is the ion inertial scale, and L is the scale of the equilibrium structure. An approximate scaling law between the ionization fraction and the scale of the structure is found. Further by expressing the not so well known ionization fraction in terms of the temperature of the system, assuming thermal equilibrium, relationships among the extensive parameters such as the scale, the neutral particle density, the flow velocity, the temperature, and the magnetic field of the equilibrium structure can be determined. There seems to be a good overlap between the Hall and the thermal equilibria. The validity of the neglect of the ion dynamics is discussed.