Formation of field-induced breakdown precursors on metallic electrode surfaces

Understanding the underlying factors responsible for higher-than-anticipated local field enhancements that trigger vacuum breakdown on pristine metal surfaces is crucial for the development of devices capable of withstanding intense operational fields. In this study, we investigate the behavior of nominally flat copper electrode surfaces exposed to electric fields of hundreds of MV/m. Our novel approach considers curvature-driven diffusion processes to elucidate the formation of sharp breakdown precursors. To do so, we develop a mesoscale finite element model that accounts for driving forces arising from both electrostatic and surface-tension-induced contributions to the free energy. Our findings reveal a dual influence: surface tension tends to mitigate local curvature, while the electric field drives mass transport toward regions of high local field density. This phenomenon triggers the growth of sharper protrusions, ultimately leading to a rapid enhancement of local fields and, consequently, system instability. Furthermore, we delineate supercritical and subcritical regimes across a range of initial surface roughness. Our numerical results align closely with experimentally reported data, predicting critical precursor formation fields in the range of 200 MV/m to 500 MV/m.