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The study of dynamic temperature characteristics of cathode microprotrusion under electron emission would be essential to the development of high-voltage vacuum systems. Owing to the multiscale and multiphysics characteristics of the microprotrusions under the electron emission, smoothed particle hydrodynamics (SPH) method has become one of the feasible methods. In this article, the SPH method is introduced to study the dynamic temperature characteristics of a micrometer scale microprotrusion under the electron emission. First, the constitutive model and the equation of state with the material strength and the coupling effect of the heat conduction, Joule heating, Nottingham effect, and electron emission have been introduced into the SPH method. Then, an SPH model of the microprotrusion under the electron emission with considering the temperature correction is established by combining the SPH method and thermal-field emission heating model. Compared with the finite element method (FEM) and theoretical calculation, the SPH model of the microprotrusion under the electron emission is verified. Based on the SPH model of the microprotrusion, the dynamic temperature characteristics under the different conditions are quantitatively obtained and analyzed. The results of this article may provide some useful references for the vacuum insulation design and the insulation state evaluation of the high-voltage vacuum system.

Microprotrusions under high electric fields are considered to be sources of metal vapor and microplasma on metal electrode surfaces and may even initiate vacuum breakdown in vacuum gaps. The mechanism of the phenomena has been studied for a long time. However, the dynamic evolution processes of microprotrusions under high electric fields considering the influence of the material properties are still not clear. The objective of this article is to study the dynamic evolution processes of the nanoscale microprotrusions on Cu and Cr electrode surfaces under high electric fields based on atomistic modeling. With considering the electron emission heating, surface charge, Coulomb, and electric field forces, a 3-D numerical model is established by coupling molecular dynamics (MD) and finite difference method (FDM), for simulating the dynamic evolution processes of the microprotrusions under high electric field. Furthermore, the influence of material properties on the dynamic evolution processes is discussed and compared between Cu and Cr. The simulation results show that the heating effect of the electron emission induced by an intense electric field could lead the microprotrusions to localized melting and subsequent elongation and may finally generate metal vapor in the vacuum gap. In addition, the material properties have a significant influence on the field-induced dynamic evolution processes of microprotrusions.

It is well known that electron emission is one of the key factors to cause electrical breakdown in vacuum gaps. In previous studies, it tended to use simplified numerical models with uniform electric field on emission region to investigate the electron emission characteristics at the cathode micro-protrusion and the influence of the materials of the micro-protrusions. The objective of this article is to introduce an improved numerical model of a nanoscale micro-protrusion with nonuniform electrical field on the emission region, which could be used for micro-protrusions with various irregular geometries. The improved numerical model is used in this article to study the dynamic characteristics of the electron emission of Cu and Cr micro-protrusions under different macroscopic electric fields. First, the electric field distribution is obtained by solving Laplace equation based on finite difference method (FDM). Then, the emission current and Nottingham effect are obtained by calculating the general thermal-field (GTF) equations based on the electric field distribution. Finally, the dynamic characteristics of the electron emission current and temperature distribution are iteratively calculated considering the Joule heating and Nottingham effect. The calculation results of the improved numerical model are compared with those of the previous simplified numerical model. The results show that for Cu and Cr micro-protrusions, the Joule heating, and Nottingham effect would play different roles in the emission process. In general, it is more likely for the Cr micro-protrusions to evaporate than the Cu micro-protrusions. The results of this article may provide some useful information to further understand the vacuum breakdown initiated by electron emission.