Collisional radiative (CR) models based on ab initio atomic structure calculation have been utilized over 20 years to analyze many-electron atomic and ionic spectra. Although the population distribution of the excited states in plasmas and their emission spectra are computed using CR models, systematic and analytical understanding of the population kinetics is still lacking. In this work, we present a reduced model of the population dynamics in many-electron atomic ions, in which we approximate the dense energy structure of complex many-electron atoms by a continuum, a continuous CR model (CCRM). Using this simplification, we show an analytical population distribution of many-electron atoms in plasmas and its electron-density and temperature dependence. In particular, the CCRM shows that the population distribution of highly excited states of many-electron atoms in plasmas resembles a Boltzmann distribution but with an effective excitation temperature. We also show the existence of three typical electron-density regions and two electron-temperature regions where the parameter dependence of the excitation temperature is different. Analytical representations of the effective excitation temperature and the boundaries of these phases are also presented.
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