Adjoint Approach to Beam Optics Sensitivity Based on Hamiltonian Particle Dynamics

We develop a sensitivity function for the design of electron optics using an adjoint approach based on a form of reciprocity implicit in Hamilton's equations of motion. The sensitivity function, which is computed with a small number of time-reversed runs of a beam optics code, allows for the determination of the effects on specific beam quality figures of merit of small, but arbitrary changes in electrode potentials, positions, and shapes and in magnet strengths and locations. The sensitivity function can thus be used in an optimization cycle of a focusing system's design and/or to predict the sensitivity of a particular design to manufacturing, assembly, and alignment errors.