PIC simulation of the electric field at a cathode with a surface microprotrusion under intense field emission

The effect of the space charge of the emitted electrons on the strength of the self-consistent electric field at the surface of a pointed microprotrusion on a metal cathode has been investigated for the first time in the framework of a two-dimensional axisymmetric statement of the problem. Based on the method of large particles in cells (PIC), a model has been developed and self-consistent calculations of the electric field and of the field emission characteristics of a metal cathode taking into account the space charge have been performed. It has been shown that for a pulse peak voltage of ~250-300 kV and a microprotrusion radius of ~10^-5 cm the current density in the microprotrusion can reach ~10¹⁰ A/cm², which suffices for the field-to-explosive emission transition within 10^-10 s.