With a large-area field electron emitter (LAFE), it is desirable to choose the spacings of individual emitters in such a way that the LAFE-average emission current density and total current are maximised, when the effects of electrostatic depolarization (mutual screening) are taken into account. This paper uses simulations based on a finite element method to investigate how to do this for a LAFE with randomly distributed emitters. The approach is based on finding the apex field enhancement factor and the specific emission current for an emitter, as a function of the average nearest neighbor spacing between emitters. Using electrostatic simulations based on the finite element method, the influence of neighboring emitters on a reference emitter being placed at the LAFE centre is investigated. Arrays with 25 ideal (identical) conical emitters with rounded tops are studied for different emitter densities and applied macroscopic fields. A theoretical average spacing is derived from the Poisson Point Process Theory. An optimum average spacing, and hence optimum emitter density, can be predicted for each macroscopic field.INDEX TERMS Field electron emission, large area field emitters, micro-nano-integration, modelling, simulation.