Energy Distribution of Electrons in a Cesium Thermionic Discharge

Abstract

The electron energy distribution is obtained for a cesium plasma in a thin region close to the emitter of an ignited-mode thermionic converter. Assuming that the steady-state plasma is spatially uniform, the Boltzmann equation with only the electric field and the collision terms is solved by the use of WKBJ method. The collision terms include the elastic, inelastic and electron-electron Coulomb interactions. A parameter p which is proportional to the ratio of the degree of ionization and the electric field, is used to characterize the effect of the electron-electron interaction on the energy distribution. The stability of the present solution depends on the position of a singular point, a so-called turning point in the wave equation. The present method gives a stable solution when p≥3. When p<3, the ``turning point'' moves inside the inelastic region, and the equation has multivalued solutions. Thus the present method cannot be applied to those cases with very large induced electric field and small degree of ionization. The solution is examined in various values of p, and the effect of nonequilibrium ionization in the energy distribution function is discussed.