Theory of dust voids in plasmas

Dusty plasmas in a gas discharge often feature a stable void, i.e., a dust- free region inside the dust cloud. This occurs under conditions relevant to both plasma processing discharges and plasma crystal experiments. The void results from a balance of the electrostatic and ion drag forces on a dust particle. The ion drag force is driven by a flow of ions outward from an io nization source and toward the surrounding dust cloud, which has a negative space charge. In equilibrium the force balance for dust particles requires that the boundary with the dust cloud be sharp, provided that the particle s are cold and monodispersive. Numerical solutions of the one-dimensional n onlinear fluid equations are carried out including dust charging and dust-n eutral collisions, but not ion-neutral collisions. The regions of parameter space that allow stable void equilibria are identified. There is a minimum ionization rate that can sustain a void. Spatial profiles of plasma parame ters in the void are reported. In the absence of ion-neutral collisions, th e ion flow enters the dust cloud's edge at Mach number M = 1. Phase diagram s for expanding or contracting voids reveal a stationary point correspondin g to a single stable equilibrium void size, provided the ionization rate is constant. Large voids contract and small voids expand until they attain th is stationary void size. On the other hand, if the ionization rate is not c onstant, the void size can oscillate. Results are compared to recent labora tory and microgravity experiments.