Waves and instabilities in weak inhomogeneous ideal Hall- magnetohydrodynamic plasmas

The two-fluid magnetohydrodynamic equations in which the Hall term is taken into account in Faraday's law (Hall magnetohydrodynamic) for low-density magnetized inhomogeneous plasmas with finite pressure, and accounting for the inertial electron and ion dynamics responses are considered for slab geometry. Waves that propagate in the direction perpendicular to the density gradient and close to the direction of the background magnetic field are considered and linear analysis is employed in order to derive a local dispersion relation. It is shown that both the ion-cyclotron acoustic mode as well as the magnetosound mode are susceptible to an instability that is driven by the spatial inhomogeneity of the plasma density. The condition under which unstable waves appear and the growth rate of the unstable modes are obtained for collisionless plasmas. The results of this theoretical investigation can be relevant to instabilities in low-beta fusion plasma devices as well as in various space applications.