Mathematical simulation of a diode system with a field-emission matrix cathode

A mathematical model of a diode system based on a matrix field-emission cathode with an edge structure of vertical-type emitters is constructed. We calculate the macroscale electrostatic field distribution for the planar and spherical configurations of the anode. In the microscale, the field distribution at the emitter edge is determined for various versions of the arrangement of the matrix cathode relative to the edge.