Stability of a dust cloud in the radio frequency low-pressure gas discharge

Abstract

We analyze stability of a three-dimensional cloud of the dust particles in the low-pressure radio frequency discharge under microgravity conditions. The parameters of such complex plasma are assumed to conform to the recently developed ionization equation of state that includes the effects of the ion–atom collisions on the particle charge and of the ion–particle collisions on the ion mean free path. Propagation of the particle number density perturbation in a cloud is treated using the fluid approach. The equation for dust cloud dynamics allows for the electric and ion drag forces that are not compensated in a nonstationary state and yields the wave equation for the dust acoustic waves with either a positive or negative effective friction coefficient. The resulting dispersion relation defines a condition of the instability onset, which is written for the maximum ambipolar field and dust number density gradient. Analysis of the available experimental data reveals a satisfactory correspondence with the theory. In particular, it is demonstrated that the maximum dust density gradient in the cloud increases with the increase in the particle diameter and in the pressure of plasma-forming gas.