Charge state fluctuations: a master equation approach

Abstract

A stochastic theory of charge exchange fluctuations in ion transport is introduced based on a master equation for the probability of finding ions in appropriate phase space locations. When energy losses are absent, a forward master equation is obtained which is solved exactly in the binary charge state case. The equilibrium probability distribution is shown to be a binomial distribution and differs from that at small depths. In the more general case a backward master equation is derived for the multi-point probability distribution function, from which an equation for the average charge state is obtained.