Behavior of relaxation plasmas near emitting electrodes

The transport of charged particles in a thermionic plasma near an emitting electrode is studied in two regions: a collisionles sheath region and a non-LTE ionization region. The division of these two regions is shown to be closely related to the magnitude of two quantities, the Debye length L_D and the relaxation length R, which gives the characteristic distance an ion diffuses before the rate of recombination becomes important. The spatial profiles of the electron density and potential are determined analytically and the potential drop and the electron density in the sheath are determined by properly joining the solutions in the ionization and sheath regions. It is found that by taking the ion and electrical emissions from the emitted into consideration the well-known Bohm's criterion is not a necessary condition to ensure a stable matching of the solutions from these two regions. The significance of the present theoretical model as applied to thermionic convertors is discussed.