Features of the development of electrohydrodynamic instability of the molten metal boundary in a strong electric field

The dynamics of the instability development of the free boundary of liquid metal (molten copper) in a strong electric field of about 10$^8$ V/cm has been studied. Under such local fields, natural submicron-scale protrusions on the cathode surface melt due to the flow of field emission current through them. Electrohydrodynamic instability of the melt boundary leads to a sharpening of the boundary, which provides a local increase in the electric field and, as a consequence, accelerates the processes of vacuum breakdown. It has been demonstrated that the feature of electrohydrodynamic instability under the considered conditions is the need to take into account viscous effects. A relatively simple nonlinear model is proposed to describe them.