It is a known fact that in electron cyclotron resonance ion sources, plasma impurities play a role in the formation of the ion charge state distribution (CSD). Writing the balance equations for the ion densities in a matrix form allows us to calculate CSD easily for plasmas containing an arbitrary number of elements, taking into account electron ionization, radiative recombination, charge exchange between ions, and ion flowing out of the magnetic trap. Moreover, by defining two global quantities—S0andSc—representative of charge exchange, the stationary case can be reduced to the resolution of only one nonlinear equation forS0andSc.Therefore plasma equilibria even with several species of impurity ions (carbon, oxygen, hydrogen, etc.) can be easily described and solved in this model. The application to the special case of no ion flow is discussed, to study a case similar to thermodynamic equilibrium. An additional factorexp{&mgr;˜ i4/3},whereiis the charge state, is shown to be necessary to fit the CSD. The relationship between the ionization temperature as it appears from the CSD and the electron temperature is given. ©1998 American Institute of Physics.