Global Non-Axisymmetric Hall Instabilities in a Rotating Plasma

Abstract

Non-axisymmetric, flow-driven instabilities in the incompressible Hall-MHD model are studied in a differentially rotating cylindrical plasma. It is found that in the Hall-MHD regime, both whistler waves and ion-cyclotron waves can extract energy from the flow shear, resulting in two distinct branches of global instability. The non-axisymmetric whistler modes grow significantly faster than non-axisymmetric, ideal MHD modes. A discussion of the global whistler instability mechanism is presented in the large-ion-skin-depth, `electron-MHD' limit. When the magnetic field is azimuthal, a subset of the whistler modes having zero axial wave number are uncovered to be destabilized by the `co-rotation amplifier' mechanism. It is observed that the effect of the Hall term on the non-axisymmetric modes can be appreciable when $d_i$ is on the order of a few \% of the width of the cylindrical annulus. Distinct global modes emerge in the strong Hall-MHD regime at significantly stronger magnetic fields than those required for unstable global MHD modes, as the Hall effect weakens the stabilizing `field-line bending' by decoupling ion motion from the magnetic field. These global non-axisymmetric modes may play an important role in weakly ionized accretion disks.