Low frequency electrostatic instabilities in a two-dust component plasma.

Abstract

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.