On the screening of the electric field at the cathode surface by an electron space charge at intense field emission

The paper considers the effect of the space charge of emitted electrons on the electric field at the tip of a field emitter. To analyze this phenomenon, the Poisson equation was solved numerically for a spherical vacuum diode with a field emission cathode. The dependence of the actual electric field on the geometric electric field has been compared with the known approximate dependencies. Strong screening of the electric field at the cathode by the space charge of emitted electrons at fields over 5×10⁷ V/cm is noted. Based on the obtained dependencies of the actual field on the geometric one and using the SuperSAM code, the field emission occurring in a Muller projector has been simulated. It has been shown that the “ring effect” appearing in field emission patterns can well be explained by the field emission from the peripheral regions of the field emitter. The current density distributions over the surface and in the bulk of the emitter have been analyzed