Instabilities of inhomogeneous plasmas streaming relative to inhomogeneousdust distributions

Streaming instabilities are studied for an inhomogeneous distribution of du st particles. Such situations are characteristic of stellar neighbourhoods, where the star's plasma wind ploughs through a surrounding dust shell. Thi s should result in the acceleration of dust particles at the expense of the plasma momentum, which may throw light on certain dynamical features of th e dust cloud vis-a-vis the plasma dynamical features. Streaming instabiliti es are a first step towards such a study. Various cases of the relative mag nitudes of the plasma and dust velocities are analysed, and the role of inh omogeneities is highlighted.