Temperature Distribution of Cathode Micro-protrusion Based on Smoothed Particle Hydrodynamics Method

In this paper, Smoothed Particle Hydrodynamics (SPH) method is introduced into the study of the temperature characteristics of the cathode micro-protrusion with considering the resistive heating caused by field emission current. Firstly, the partial differential equations for hydrodynamics with material strength are established. Then, the kernel approximation is used to approximate the field function in the partial differential equations, and the particle approximation is used to discretize the kernel approximation equations in order to obtain a series of SPH governing equations. At the same time, the heat conduction equation with considering Joule heat is introduced into the SPH governing equations. Based on the source code of SPH, the mathematical model of cathode micro-protrusion is established. The SPH equations are solved by using the explicit integration method. The temperature distributions of cathode micro-protrusion with different field emission current Joule heat are simulated. The results can provide theoretical guidance for the quantitative study of the physical mechanism of vacuum breakdown induced by field emission.