Research on the influence of cathode surface topography on spark discharge

Abstract

To obtain the relation between spark discharges and the topography of electrode surfaces, some models, such as a micro-initial model of cone and spherical head cylinder, generated from the scanning of a scanning electron microscope are introduced. Based on the principles of energy conservation and thermal equilibrium, the second-order non-homogeneous differential equation is established. The relationships between the temperature of the cathode surface and the distance from the top of micro-protrusions, the cone angle, and the radius of the ball head are derived from a set of second-order non-homogeneous differential equations. When introduced electron emission theory, the main emission type at the initial stage of the discharge is electron field emission. As the discharge progresses, the Joule heat generated by the emission current will cause thermionic emission. During this progress, the emission current density gradually increases. When the temperature of the cathode surface reaches the melting point of the cathode metal, the current density will increase sharply. Observed from the discharge, the temperature of the cathode surface is inversely proportional to the cone angle and the radius of the ball head maintains a gradually decreasing slope. It is proportional to micro-protrusions maintaining a gradually increasing slope. When the cone angle is less than 12° and the radius of the ball head is less than 0.04 µm, the temperature of the cathode surface changes more dramatically. Through this study, a further understanding of factors that affect the density of cathode current emission can be obtained, which is of great significance to improve the capacity of cathode emission.