Magnetorotational instabilities in a dusty plasma

Abstract

The charged dust effect on stability of a magnetized rotating plasma is analysed using approximation of immobile dust. In the presence of the dust, a term with the electric field appears in the one-fluid equation of plasma motion. This electric field affects the equilibrium plasma rotation and also gives rise to a family of instabilities of the rotating plasma called dust-induced rotational instabilities (DRIs). The DRIs are related to the charge imbalance between the plasma ions and electrons because of the charged dust. In contrast to the well-known magnetorotational instability driven by the radially decreasing plasma rotation frequency, the DRI can appear for an arbitrary rotation frequency profile. A mathematical technique for the analysis of the magnetorotational phenomena is presented. It is based on the one-fluid magnetohydrodynamic approach developed for a pure plasma and generalized to include the immobile dust effects. The mode equation and local dispersion relation are derived in terms of the canonical parameters.