Low frequency electrostatic instabilities in a two-dust component plasma.
The kinetic dispersion relation for a magnetized dusty plasma comprising of ions, electrons and massive, charged dust particles is solved for low frequency electrostatic instabilities in the dust plasma frequency regime. The free energy is provided by the drifting ion beam. The effect of varying parameters such as ion drift speed, particle densities, ion temperature and magnetic field strength on the real frequency and growth rate is examined. Initially light and heavy dust species of different charge are separately considered. This procedure is then repeated for a four-component plasma in an attempt to study the effect of the presence of both the dust species on low frequency electrostatic phenomena. Using a different plasma model, instabilities generated by an equal E x B drift of both the magnetized ions and electrons relative to the unmagnetized dust grains of both the heavy and light dust species is also investigated. The latter instabilities are applicable to the planetary ring plasmas of Saturn. Throughout our studies, numerical solutions of the full dispersion relation for the real frequency and growth rate are compared with approximate analytical solutions.