Kinetic theory of dusty plasmas. I. General approach

Abstract

The kinetic theory of dusty plasmas is formulated introducing the dust charge as an independent variable. The Bogoliubov–Klimontovich approach is generalized for the case where the discreetness of the dust grain distribution is described rigorously, while the electrons and ions are described by continuous kinetic equations which take into account their absorption on the highly charged dust grains. The theory is valid for dust densities larger than the critical value where the binary plasma particle collisions can be neglected with respect to the collisions with dust particles. This condition is fulfilled in most dust-plasma experiments and often in space plasmas. The discreetness in the dust distribution leads to both dust fluctuations and plasma particle fluctuations, the latter induced by the dust fluctuations. The dust charge fluctuations alter the interaction appreciably, leading to effective dust charges in interactions which depend on distance and deviate substantially from the equilibrium dust charges. New collision integrals describing the dust charge distribution and inelasticity of dust-plasma particle collisions are found and the problem of dust charging is formulated self-consistently.