5.1: Space charge, emittance, trajectories and the modeling of field emitter arrays

A recently developed analytical model for current from a protrusion coupled with the point charge model of an emitter makes models of emittance and space charge from a single tip (the “unit cell”) treatable. Likewise, 1D space charge models connect field-dependent current density to charge between the anode and a flat cathode plane (the “macro region”). The connection between the unit cell and macro region models is explored and developed with regard to the trajectories, their weights, and their location on the unit cell / macro region boundary. The development is with an eye towards the needs of particle-in-cell beam simulation codes, as well as for the evaluation of intrinsic (cathode) emittance.