A multistage ionization-recombination model is proposed to describe the formation and loss of atomic ions in low-energy cesium plasmas. Solutions of the ambipolar diffusion equation are investigated with due consideration given to these processes. The solutions indicate the existence of a state of quasi-equilibrium throughout most of a low-energy plasma in which the electron temperature is more than several hundred degrees above a critical ignition temperature. The assumption of quasi-equilibrium in the interelectrode plasma of a thermionic converter operating in the collisional ignited mode is shown to result in a plasma model which correlates a wide variety of experimental data. Included in the successful correlations are electron random current density and temperature profiles as well as output-current characteristics. The experimentally observed state of quasi-equilibrium in thermionic converter plasmas is found to be near the Saha-equilibrium limit. It is therefore concluded that the multistage ionization-recombination processes in these plasmas involve numerous excited states.