Charge fluctuations for particles on a surface exposed to plasma

We develop a stochastic model for the charge fluctuations on a microscopic dust particle resting on a surface exposed to plasma. We find in steady state that the fluctuations are normally distributed with a standard deviation that is proportional to $C{T}_e{)}^{1\mathrm{/}2}$, where $C$ is the particle-surface capacitance and $T_e$ is the plasma electron temperature. The time for an initially uncharged ensemble of particles to reach the steady state distribution is directly proportional to $C{T}_e$.