Thermo-field emission: A comparative study

Thermo-field emission current densities calculated by the commonly used Richardson-Dushman equation corrected for the Schottky effect are compared with those calculated using the more accurate treatment of Murphy and Good for a wide range of temperatures (1000-5000 K), electric field strengths (10(7)-10(10) V m(-1)) and work functions (25 eV) encountered in numerical modelling of the thermal arc-cathode interactions. Results show that the emission current densities predicted by the Richardson-Dushman equation are always lower than those predicted by the more accurate treatment. The disagreement between the two predictions is in the range 20-30% for the conditions encountered in numerical modelling of the attachment of a thermal are to a hot tungsten cathode whereas it is much larger when a cold copper cathode is considered (>175%). It is suggested that the more accurate treatment of Murphy and Good should be used in order to increase the accuracy of prediction of the numerical models.