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 (CTe)1/2, where C is the particle-surface capacitance and Te is the plasma electron temperature. The time for an initially uncharged ensemble of particles to reach the steady state distribution is directly proportional to CTe.