Electrostatic modes in (self-gravitating) dusty plasmas with charge and mass distributions

Abstract

To obtain the mass and charge densities for a dusty plasma containing charged grains with individual identities, either an ensemble of discrete grains can be used, or a continuous distribution in charge and in mass, where the densities are determined from an appropriate kinetic theory. Using the electrostatic and gravitational Poisson’s equations the general electrostatic dispersion law is derived. There occur in a natural way two definitions of the dust plasma frequency, and hence of the dust-acoustic velocity. One is based on the average over all dust grains of the ratio of the square of the charge to the mass, whereas the other one uses the square of the average charge and the average mass. The difference between the two gives rise to a dust distribution mode, which together with the self-gravitational effects influences various dust-acoustic and Jeans modes and instabilities in dusty plasmas. This corroborates earlier results, but also indicates that in dusty plasmas containing grains of opposite charges the dust distribution mode could be much stronger than for mixtures with like dust charges, as previously studied.