Flux-matching theory of particle charging

A new flux-matching theory is formulated and applied to the study of particle charging by ions. Assuming that the ion-particle interaction includes the Coulomb + polarization forces the collisionless kinetic equation is solved and the ion concentration profile in the free-molecule zone (at the distances less than the ion mean free path) is found. This profile is then matched to that derived from the solution of the diffusion equation, which describes the ion transport outside the free-molecule zone. Three matching parameters are introduced: the ion flux, the matching distance, and the ion density at the matching distance; and three conditions are formulated for fixing these parameters: (i) the constancy of the total ion flux, (ii) the continuity of the ion concentration profile, and (iii) the continuity of the derivative of the ion concentration profile. The charging efficiencies are expressed in terms of their free-molecule values, the ion diffusivity in the carrier gas, and the ion thermal velocity. This approach is applied for calculating the efficiencies of particle charging in the transition regime (the particle size is comparable to the ion mean free path and the Coulomb length). The corrections due to ion-carrier gas interaction to the particle-ion recombination rate are shown to remain finite even for very small particles, whereas in the case of particle-ion repulsion the contribution of ion-molecular collisions to the rate of particle charging is suppressed in the free-molecule regime.