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 ( ) and work functions (2 - 5 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 arc 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.
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Coulombe et al. (1997) studied this question.
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