Theory of dust self-organized convection in cylindrical discharges. I. The model and stationary nonlinear dust structures

Abstract

The convection of dust particles in a plasma is related to the spatial gradients of dust charge distributions existing due to different plasma conditions in different parts of dusty structures. For many experiments, the convection appears as a result of convective perturbations of basic nonlinear self-organized states of the dust structures. Here, the set of nonlinear equations is derived suitable for the study of basic stationary dust structures as well as their convective perturbations. On its basis, the stationary nonlinear states of self-organized cylindrical dusty structures in a plasma are investigated. It is demonstrated that there is the broad range of plasma and dust parameters where the self-organized states exist. The characteristics of these basic structures are determined by a limited number of the controlling parameters such as the ion number density in the center of the structure and the plasma ionization level. The derived set of equations also forms the basis for further investigation of the dust convection.