Application of reciprocity to the design of electron guns
We develop a sensitivity function for the design of electron guns, based on a form of reciprocity implicit in Hamilton's equations of motion. The sensitivity function allows for the determination of the effect of small, arbitrary changes in electrode potentials, electrode positions, and magnet locations on specific beam quality figures of merit with a single, time-reversed run of a beam optics code. The sensitivity function can thus be used to predict the sensitivity of a design to manufacturing errors, or it can be used in an optimization cycle of a gun's design.