An analytical model of thermionic discharges

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Abstract
An analytical model is developed to describe a thermionic plasma discharge. With three easily interpreted algebraic equations, the behavior of the temperature, electron density, and arc drop are determined. Excellent agreement with experiment is found. The model considers a transverse discharge between two electrodes, one of which emits electrons thermionically. Transport of electrons and ions by electric field and density gradient is included. Ions are assumed to be created by volume ionization and are destroyed by recombination either on the walls or by three-body collision in the volume. Conservation of energy for the electrons requires that ohmic heating balance energy losses by collisions and by heat transfer to the walls. Thermionic discharges are also known as low-voltage arcs and occur in some types of thermionic energy converters. The role of the double-valued sheath and Schottky effects is discussed. A possible cause for discharge constriction is mentioned. Also, a ‘‘plasma ideal’’ thermionic discharge is defined and compared with the well-known ‘‘vacuum ideal’’ thermionic diode.