Thermal analysis of a cathode: temperature distribution and warm-up time

Abstract

This paper gives a theoretical estimate of the cathode temperature distribution at the surface and the warm-up time. Several cases of practical interest have been studied from the thermodynamic considerations using the software specially developed for this application. The software is in two parts, viz., the steady-state analysis which gives the cathode surface temperatures and the transient analysis which yields the warm-up time. Temperature-dependent thermal conductivity, specific heat, density, and emissivity have been used in the transient analysis which improves the accuracy. Scaling laws for the determination of cathode surface temperature have been devised to cater for various sizes of cathodes used in industry. Not reported so far, our results show that a pancake-heater configuration has a better thermal response but a non-uniform cathode surface temperature profile whereas the conventional helical-heater configuration has a relatively poor thermal response but a more uniform temperature profile on the cathode. This aspect gets amplified and is very revealing at larger cathode dimensions. © 1990.