Numerical simulation of vacuum prebreakdown phenomena in a cathode microprotrusion at subnanosecond pulse durations

A two-dimensional, two-temperature model has been developed to describe the prebreakdown phenomena in a cathode microprotrusion at nanosecond durations of the applied voltage pulse. The simulation procedure includes a particle-in-cell (PIC) simulation to calculate the self-consistent electric field at the cathode and the field-emission characteristics of the cathode. A numerical simulation performed for a copper cathode for voltage pulses with ~10¹⁵ V/s rise rates has demonstrated that (i) the screening of the external field by the space charge of emitted electrons has the result that the electric field strength levels off approaching to that at the microprotrusion tip, and this gives rise to a region inside the microprotrusion where the current density is about twice the maximum field emission current density at the tip; (ii) the electron temperature can be greater than the lattice temperature by 0.5-1 eV at the onset of the explosive metal-plasma phase transition; (iii) with a 5-mum characteristic height of microprotrusions on a point cathode whose radius of curvature is 50 mum the field emission-to-explosive emission transition can occur within (1.2)ldr10^-10 s only for microprotrusions with a tip radius no more than 0.1 mum.