Nonlinear dynamics of the dust grain charge and dust acoustic waves in a plasma with an ion beam

The temporal evolution of the dust grain charge is investigated for the first time in a dusty plasma with an ion beam. The grain charge attains to the stationary state after the fluctuation of short time. The dust charge increases as the ion beam temperature and the plasma ion density increase, but decreases as the beam density increases. The speed of the wave increases as the ion density and temperature increase, whereas it decreases as the dust charge increases. The variable dust mass-to-charge and ion-to-electron density ratios govern the existence of dust acoustic waves. The findings of this investigation may be useful in understanding laboratory plasma phenomena.