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

摘要

An accurate methodology for the evaluation of space charge effects, tip and array emittance, and the distribution of electron position and velocity components (trajectories) near a conical field emission tip is made possible by a point charge model (PCM) describing a single conical emitter (the “unit cell”). The elements of the point charge model are intentionally constructed to make use of self-similarity, and thus provide good analytical and intuitive models of behavior in addition to being numerically tractable. Methods for calculation of potentials, fields, field enhancement factors, tip currents, and trajectories are given in a systematic fashion as well as scaling behavior deduced from their asymptotic forms. The connection between the unit cell (PCM realm) and macroscopic region (realm of particle-in-cell codes) is discussed.