From an analytical model for the population of high-lying excited levels in ionizing plasmas it appears that the distribution is a superposition of the equilibrium (Saha) value and an overpopulation. This overpopulation takes the form of a Maxwell distribution for free electrons. Experiments for He II, Na I and Ar I confirm the general validity of the model.
Mullen, van der, J. J. A. M., Sijde, van der, B., & Schram, D. C. (1983). An analytical excitation model for an ionizing plasma. Physics Letters A, 96(5), 239-242. https://doi.org/10.1016/0375-9601(83)90342-0