Study of electron emission characteristics based on fractal micro-protrusions on electrode surface

Abstract

It is widely known that electron emission is one of key initiation factors of vacuum breakdown. The electron emission can be influenced by many factors, such as the geometry of the emitter, the material properties of the emitter, the electric field distribution of the emitter, and so on. The purpose of this paper is to investigate the electron emission characteristics of tungsten, chromium and aluminum micro-protrusions under different electric fields by fractal theory modeling. Firstly, the micro- protrusions on the electrode surface are modeled based on Weirstrass-Mandelbrot (W-M) fractal function. Then, the amended thermal-field emission equations are used to calculate the emission current density. Finally, considering the Nottingham effect and resistance heating, the variation of temperature distribution and the electron emission current density under different given electric fields are calculated iteratively. The results of this paper may provide some useful information to study the electron emission characteristics and clarify the mechanism of cathode-initiated vacuum breakdown.