FLUCTUATIONS OF THE CHARGE ON A DUST GRAIN IN A PLASMA

A dust grain in a plasma acquires an electric charge by Collecting ele ctron and ion currents. These currents consist of discrete charges, ca using the charge to fluctuate around an equilibrium value [Q]. Electro ns 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 sim ulation of the collection of individual ions and electrons, yielding a time series Q(t) for the grain's charge. Electron emission from the g rain is not included, although ft 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/tau, the inverse chargi ng 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 gr ain. This inverse square-root scaling means that fluctuations are most important for small grains. We also show that very small grains can e xperience fluctuations to neutral and positive polarities, even in the absence of electron emission.