Collisional ionization equilibrium ($n_i{C}_i(T)=n_{i+1}{\alpha }_{i+1}(T)$)

In collisional ionization equilibrium, collision-driven ionization and recombination balance for the populated ion stages, determining their relative abundances at a given temperature. The resulting cooling curve includes the loss of line-emitting bound states as temperature increases. Rapidly cooling gas or external photoionization can invalidate this equilibrium assumption.

The coronal approximation treats an optically thin, low-density plasma with electron-impact ionization balanced by radiative and dielectronic recombination. Excited-level populations are determined mainly by collisional excitation and radiative decay, not by a Boltzmann distribution over levels. Ion fractions can depend primarily on electron temperature while metastable populations retain density dependence; this distinction enables density diagnostics.