Self-Consistent Simulations of the Electric Field at the Cathode Surface

The paper studies the effects of the space charge of emitted electrons on the electric field at the cathode surface in a planar vacuum diode with a field emission cathode. To analyze the phenomenon, Poisson's equation was solved numerically for different parameters of applied electric field and field enhancement factor in a finite-difference time-domain particle in cell simulation. The time-dependence of the electric field at the cathode surface for different cases has been compared with each other. It has been shown that the self-consistent electric field at the cathode surface oscillates at the local plasma frequency associated with the applied electric field and finally yields a steady state, and the electric field completely determines the extracted field emission current density.