A reformulation of thermionic theory for vacuum diodes

Methods for predicting thermionic diode current–voltage characteristics have been in wide use for decades; however, serious limitations have been identified in the conventional formulations of thermionic theory. A reformulation of thermionic theory for vacuum diodes has been developed to improve predictive accuracy, to broaden the scope of application, and to establish a more consistent approach. Electron reflection effects and temperature dependent work functions are shown to be important considerations for thermionic diodes; consequently, the revised formulation focuses on proper treatment of these considerations. Revised equations are derived for predicting current densities, space charge, and electron cooling. In addition, equations are developed that provide energy–angle dependent current density spectra used to compute average transmission coefficients. An approach for computing space charge reflection parameters is also provided. Methods are given that permit application of the revised approach to inhomogeneous (patchy) electrode surfaces. A preliminary comparison shows that the predicted current–voltage characteristics using the revised formulations are in good agreement with test results for a prototype microminiature thermionic converter; whereas, more conventional formulations do not provide accurate predictions. Several new parameters are recommended to take advantage of the more precise methodology provided by the reformulation.