A steady-state kinetic treatment of the number density of excited atoms in a helium dlscharge has shown these populations to be consistent wlth electron impact excitation. This study was initiated since it has been well establlshed that the electrons are the activating species In discharges. The calculated number densitles of exclted atoms were obtained by conslderation of the processes which cause excltatlon and deactivation. The processes whlch produce the population of a particular state are the followlng: electron Impact and radlative cascading from higher levels. The processes which reduce the population of a particular state are radiative and nonradiative deactivation. The results of this klnetlc treatment compare remarkably well wlth experlmental number densities obtained from emission studies.In a number of recent studies of light emission from electrical discharges, it has been reported that the population densities n, of the emitting states depend exponentially on the energy level of the state, i.e., n, CE e-PtJ where 6 is the slope of a plot of In n, us. e, . A consequence of this rather familiar dependence has been to identify this slope p with (kT)-', where k is Boltzmann's constant, and T is the excitation temperature (1-11). While it may be useful to characterize the excited state population densities of electrical discharges in this way, the attendant implication that the species present are in thermal equilibrium can be misleading.The process of excitation in electrical discharges is definitely not the result of collisions between particles in thermal equilibrium. Rather, excitation in such systems is brought about principally by the impact of energetic electrons on the gas atoms or molecules (12). The population densities of atoms in the various electronic states are then determined by a dynamic balance between formation via electron impact and decay via emission of radiation and nonradiative decay processes. In this paper, we treat this balance for reduced pressure microwave-induced discharges in helium by the method of steady-state kinetics.
(4)in which the subscript i denotes optically accessible states of lower energy than j and the subscript k denotes optically accessible states of higher energy than j, kj is the rate constant (cm3/s) for excitation of the j t h state, A;i and Ak, are transition probabilities (s-l) for the emission processes j -i and k -j, respectively, and kA is the rate constant (cm3/s) for associative ionization. At the pressure of interest, it is easily shown that an emitting state will decay by Reaction 3 or 4 before it reaches a wall.On the basis of this mechanistic scheme, the change in number density of the j t h state with respect to time is:where ne is the density (~m -~) of electrons and n is the density (cm-3) of ground state helium atoms. The rate of population of the j t h state by radiative decay from higher states, Le., Reaction 3, is most probably only a few percent (23) of the rate of electron-impact excitation, Reaction 1. Therefore, as a reasonable appro...