Modelling field emitter arrays using line charge distributions

Abstract

Field emitter arrays are high-brightness electron sources with important current and future applications in vacuum electronics, particle accelerators, and directed energy. The current produced by individual emitters in these arrays is controlled by the total electric field on their surfaces, which depends on the background field, the space charge field from previously-emitted electrons, and field enhancements due to geometric features at the macro-, meso-, and micro-scales. To facilitate the study of shielding and space charge effects in these arrays, we have developed a mathematical model using tapered line charges to generate equipotential surfaces which approximate the geometry of high aspect ratio field emitters. This model provides an analytic approach for studying contributions to array performance due to macro-scale and meso-scale features such as array geometry, emitter height, and emitter tip radius. Here we present this model and use it to assess the impact of these parameters on the field enhancement factor of individual field emitters and emitters in 1D and 2D arrays.