Nonlinear dust equilibria in space and laboratory plasmas

Abstract

This chapter presents the theory of equilibrium nonlinear dissipative structures in dusty plasma. Nonlinear electrostatic and pressure equilibria is analyzed for dust clouds embedded in dust free plasma, dust voids, and dust convection pattern. Homogeneous dusty plasma is shown to be instabile to formation of dust clouds surrounded by dust-free plasma. A single dust structure creates in self-consistent way, the plasma flux toward the structure which compresses and self-confines dust in the structure. Exact solutions of nonlinear equations describing 1D planar and spherical structures are found numerically. The structures are determined by only one parameter—the number of dust particles in the structure. Dust cloud and dust voids have sharp dust boundaries. The chapter also presents the theory of voids in dusty plasma both in the limit where the ion-neutral collisions are negligible and in the case where the ion-neutral collisions are dominant. The void equilibrium position is stable for large deviation from equilibrium for perturbations perpendicular to the void surface and is unstable for disturbances along the void surface, creating convection patterns.