Dispersion Relation of Dust Acoustic Wave in Dusty Plasma with Charge Fluctuations

Abstract

The effect of dust charge fluctuations on the existence and propagation of dust acoustic waves in unmagnified dusty plasma is studied. Dispersion relation for the dust acoustic waves with temporal dust charge fluctuations is calculated based on the reductive perturbation technique. It is shown that when the dust charging frequency is comparable to the dust acoustic wave frequency, the condition give rise to collision less damping of two existing normal modes and one purely damped mode. In the limit when the charging frequency is very much higher than the wave frequency, it is then possible to derive a nonlinear Schrödinger type equation with envelope soliton as solution.