The Jeans-Buneman instability in the presence of an ion beam in a dusty plasma and the influence of dust-size distribution

The fluid dispersion relation for the Jeans-Buneman instability is solved f or a three component plasma consisting of warm electrons and ions, and cold dust grains. In our model the electrons are assumed to be in electrostatic equilibrium, merely providing Debye shielding. The Buneman instability is driven by the free energy of the ions drifting relative to the dust grains. The transition from the purely Jeans to the Buneman instability is studied as a function of the ion beam speed, ion to electron temperature ratio and the wave number. The effect of the magnitude of the Jeans frequency in com parison to the dust plasma frequency is also examined. Initially the dust g rains are assumed to be of uniform charge and mass. Thereafter, the influen ce of dust-size distributions following a power law density distribution is investigated.