Population probabilities of the excited levels of ions in a steady-state plasma. I. Basic equations and results

In this work an explicit formula is obtained for the population probabilities of the excited levels of the various charge states in an optically thin plasma. The plasma is assumed to be in a complete steady state, i.e., time independent and homogeneous. First, a recursive expression is obtained for the partial densities of the various charge states in the plasma. This expression is used to get an implicit algebraic expression for the population probabilities of the excited states, which is finally solved for low electron densities to yield an explicit, and simple, expression for the population probabilities. Simplified formulas for H-like ions and a few numerical examples are also presented.