Model of grain charging in collisional plasmas accounting for collisionless layer

Grain charging in collision dominated plasmas is investigated. The transition from a thin collisionless region around the grain, ℓi(e)≪a, to a thick one, ℓi(e)≫a, is studied under the assumptions ℓi(e)≪λD and a≪λD, where ℓi(e) is the ion (electron) mean free path, a is the grain radius, and λD is the plasma screening length. It is also assumed that no ionization and recombination occur in the vicinity of the grain. With these assumptions, the analytical model of grain charging is constructed, the expressions for the ion and electron fluxes to the grain surface are derived, and the grain charge is obtained from their balance. The analytical results are then compared with the available experimental results. The behavior of ion and electron number densities in the vicinity of the grain is briefly discussed.