Characteristics of Field Emission Phenomena of Single Micro-protrusion on Vacuum Gap Cathode Based on Fractal Theory

It is well known that a seemingly smooth electrode surface is anything but smooth when observed at a microscopic level. In fact, there are a great amount of micro-protrusions on the electrode surface in vacuum gap, which will enhance the local electrical field on the tip dramatically. However, the classical Fowler-Nordheim equation for the planar surfaces is still being used to analyze the field emission phenomenon despite of the micro-protrusions' existence. The objective of this paper is to investigate the characteristics of the field emission phenomena on the tip of a single micro-protrusion based on the fractal theory. In addition, the thermal instability of a single micro-protrusion will be taken into account, which is caused by the thermal effect of the field emission current and the heat conduction inside the micro-protrusion. The research of this paper will look deep into the mechanism of the formation of metal vapor in the vacuum gap that will do great harm to the vacuum insulation characteristics.