Electron emission characteristics of cathode micro-protrusion and the comparison with the MG theory analysis

Abstract Electron emission from micro-protrusions on the surface of metal electrodes is crucial for vacuum breakdown. The emission characteristics of cathode micro-protrusions and the impact of the space charge effect are investigated in this study, with a comparison to the Murphy–Good (MG) theory analysis. Precise calculations of the emission current density and the Nottingham effect are achieved. A thermal-field emission model for copper micro-protrusion is established to analyze emission characteristics and clarify the mismatches between the results of simulations and MG theory. The results indicate that, for copper micro-protrusions, before breakdown, the emission current is primarily field emission, with thermal emission constituting only 7% of the total. The Nottingham effect results in consistent heating during this phase. The field enhancement factor obtained through the MG theory ( γ MG ) is slightly smaller than that derived from the geometric model ( γ geom ). This is because γ geom reflects the characteristics of the apex of the protrusion, while γ MG reflects the characteristics of the entire electron emission region. The space charge effect bends the MG plot curve and decreases its slope, making it impossible to analyze the emission current using MG theory at this point, which is consistent with the theoretical derivations recorded in the current literature.