Kinetic theory of the charging process in dusty plasmas

On basis of the kinetic equations for dusty plasmas we consider the charging equation for grains. We suggest the local charge approximation, in which the distribution function of the charge variable is a delta function, so the charge becomes a function of position and time. Only with this assumption can the usual form of the charging equation be derived. We also simplify the kinetic equations for dusty plasmas in the case of the local charge approximation and find not only an electrical but also a bombarding force acting on grains. In the case of immobile grains and linear perturbations we find the dielectric function and analyse the influence of the charging process on the wave spectra.