Empirical approximation for the ion current to the surface of a dust grain in a weakly ionized gas-discharge plasma

The results from numerical simulation of the dust grain charging process in a weakly ionized gasdischarge plasma are analyzed. An empirical approximate formula for the ion current to the grain surface under conditions close to those in laboratory experiments with dusty plasmas is derived. Investigations show that the approximation proposed greatly simplifies determination of the grain charge by avoiding laborious calculations for different grain sizes and different parameters of the surrounding plasma.