A kinetic theory of particle charging in the free-molecule regime

The charging of small neutral and charged particles suspended in a weakly ionized plasma is investigated under the assumption that the Coulomb + image forces affect the ion transport in the carrier plasma and define the rate of charging processes. Our approach is based on a solution of the collisionless kinetic equation describing the ion transport in the presence of force fields created by the particle charge and the image force. The exact free-molecule ion distribution over coordinates and velocities is used for calculating the rate of ion deposition onto neutral and charged dielectric particles. Our approach easily reproduces well-known results for metallic particles and allows us to derive rather simple expressions for the charging efficiencies of dielectric particles. Our theory is applicable either for particles whose sizes are much smaller than the ion mean free path (the charging of neutral particles) or when the ion mean free path much exceeds the Coulomb length (the distance at which the ion thermal and Coulomb's energy become comparable (ion-particle recombination)).