Nottingham Heating, Inversion Temperature and Joule Heating

Abstract

Long-term research has been done on the unstable behaviors and electron emission from microprotrusions, but the whole reason is still not clear. It is difficult to study instabilities experimentally since vacuum breakdown can happen. In this model, we show the factors that lead to thermal instability during field emission. After the Nottingham flux inversion, we see a considerable rise in temperature above a threshold electric field, followed by a thermal runaway. Cathode spots experience unexpected thermal defects and breakdowns, which is a phenomenon known as the Nottingham Inversion Instability. Although the idea of micro protrusions is frequently used in modeling studies, this study concentrates on the thermal effects during field emission from a planar cathode without taking the existence of such protrusions into account. The study reveals how Nottingham's heating effect changes from heating to cooling. In our study, we have investigated the interaction between Nottingham, Joule heating, and effective work function. The results also imply that faster reaching critical temperature is associated with larger maximum beta values. These discoveries have significance for the design and improvement of high-voltage systems and help to understand vacuum breakdown. The possibility of cathode spot ignition and subsequent vacuum breakdown is predicted by our model, which would make it possible to create a self-consistent model for that.