Unification of the breakdown criterion for thermal field emission-driven microdischarges

Determining the characteristics of thermal field emission-induced breakdown is essential for various electron emission devices, such as thermionic energy converters. In previous studies, several mathematical models were developed to determine the breakdown voltages driven by field emission under different conditions; however, complicated computations were required to solve the numerical equations. There is still no consensus on the breakdown criterion when the thermal field emission comes into play. In this work, a unified breakdown criterion for the thermal field emission-induced microdischarge is proposed based on the definition of the thermal field emission coefficient γTFE (combined with the thermionic emission coefficient γTE and field emission coefficient γFE) from the emission current. The breakdown voltages scaling with the cathode temperature and gap distance are quantified. Distinct regimes corresponding to different electron emissions and their transitions are examined with the cathode temperature and gap distance tuned across a range of values. The results from this study provide an evaluation of thermal field emission-induced breakdowns and the dominant electron emission mechanisms in distinct regimes can be straightforwardly determined from the present model.