Hall magnetohydrodynamics of partially ionized plasmas

TLDR

The Hall effect in plasmas occurs when electrons drift with the magnetic field while ions do not, a phenomenon that in fully ionized plasmas is confined to frequencies between ion and electron cyclotron frequencies and is usually above the dynamical frequencies of interest. In weakly ionized media, neutral collisions preferentially decouple ions from the magnetic field, enabling the Hall effect at lower frequencies. Consequently, the Hall effect can significantly influence the dynamics of weakly ionized systems such as the Earth's ionosphere and protoplanetary discs.

Abstract

The Hall effect arises in a plasma when electrons are able to drift with the magnetic field but ions cannot. In a fully ionized plasma this occurs for frequencies between the ion and electron cyclotron frequencies because of the larger ion inertia. Typically this frequency range lies well above the frequencies of interest (such as the dynamical frequency of the system under consideration) and can be ignored. In a weakly ionized medium, however, the Hall effect arises through a different mechanism – neutral collisions preferentially decouple ions from the magnetic field. This typically occurs at much lower frequencies and the Hall effect may play an important role in the dynamics of weakly ionized systems such as the Earth's ionosphere and protoplanetary discs.