Fluctuations of the charge on a dust grain in a plasma

A dust grain in a plasma acquires an electric charge by collecting electron and ion currents. These currents consist of discrete charges, causing the charge to fluctuate around an equilibrium value ⟨Q⟩. Electrons and ions are collected at random intervals and in a random sequence, with probabilities that depend on the grain´s potential. We developed a model for these probabilities and implemented it in a numerical simulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain´s charge. Electron emission from the grain is not included, although it could be added easily to our method. We obtained the power spectrum and the RMS fluctuation level, as well as the distribution function of the charge. Most of the power in the spectrum lies at frequencies much lower than 1/τ, the inverse charging time. The RMS fractional fluctuation level varies as 0.5 |⟨N⟩|^-1/2, where ⟨N⟩=⟨Q⟩/e is the average number of electron charges on the grain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can experience fluctuations to neutral and positive polarities, even in the absence of electron emission