The Hall instability in inhomogeneous low-density warm plasmas

A two-fluid model in which the Hall term is taken into account in Faraday's law (Hall magnetohydrodynamic - HMHD) for low density inhomogeneous magnetized plasmas with finite pressure is considered. Such a model is valid for frequencies that are larger than the ion cyclotron frequency and smaller than the electron cyclotron frequency. For waves propagating perpendicular to both the density gradient and the ambient magnetic field, the only relevant mode in that regime is the fast magnetosonic wave. Under plasma acceleration and inhomogeneity that mode is split into a fast penetrating electronic whistlerlike mode and a quasi-electrostatic slow mode that may become unstable if the plasma acceleration is strong enough. It is shown that the instability saturates due to the effect of the electrons' inertia, and the maximal growth rate is estimated. The waves of interest that propagate in the direction perpendicular to the density gradient and close to the background magnetic field are the slow magnetosonic waves and the ion cyclotron acoustic waves. It is shown that the spatial gradients of the plasma density split each of those modes into two. In addition, when the inhomogeneity length-scale is small enough, an ion cyclotron acoustic mode and a magneto sound mode merge in order to give rise to an inhomogeneity-driven instability. Unlike the perpendicular propagation case, that instability is confined to a finite wavelengths domain. The threshold for the instability as well as the growth rates are obtained for collisionless plasmas.