Fokker-Planck description of particle charging in ionized gases

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Abstract
We present a Fokker-Planck description of the charging of particles weakly in ionized gases and of the charge fluctuations arising from the statistical nature of this process. Charge fluctuations constitute a Markov process and in the limit of linear charging currents or large particles this process is also Gaussian. The time scale of fluctuations is inversely proportional to the particle size and ion concentration and for small particles it is significantly larger than the particle diffusion time. In this regime Brownian diffusion becomes a mechanism by which charge fluctuations are transported into different regions of the plasma.