  Collisional--radiative (CR) models based on \textit{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 the CR models,
systematic and analytical understanding of the population kinetics are 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.
