Models of many-element electron cyclotron resonance plasmas

Abstract

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—S0 and Sc—representative of charge exchange, the stationary case can be reduced to the resolution of only one nonlinear equation for S0 and Sc. 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 factor exp{μ̃ i4/3}, where i is 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.