  A master equation is formulated to model the states of the grain charge in a
general multi-component plasma, where there are electrons and various kinds of
positive or negative ions that are singly or multiply charged. A Fokker-Planck
equation is developed from the master equation through the system-size
expansion method. The Fokker-Planck equation has a Gaussian solution with a
mean and variance governed by two initial-value differential equations
involving the rates of the attachment of ions and electrons to the dust grain.
Grain charging in a plasma containing electrons, protons and alpha particles
with Maxwellian distributions is considered as an example problem. The Gaussian
solution is in very good agreement with the master equation solution
numerically obtained for this problem.
