Temperature variation of a thermionic cathode during electron emission

It is necessary to know the actual temperature of a thermionic cathode that works as the electron source in a microwave tube. It has been found that the temperature of the cathode drops markedly during the thermionic emission. For example, the temperature could fall by about 30°C under a current density of 2.92 A/cm2. Using the molecular thermodynamics, the dependence of the cathode temperature on the emission current density has been obtained. It has been theoretically pointed out that several factors, such as heating model and temperature coefficient of resistance of heater, can influence the cathode temperature. These theoretical conclusions were supported by the experimental results.