Adjoint Approach to Beam Optics Sensitivity Based on Hamiltonian Particle Dynamics

TL;DR

This paper introduces an adjoint sensitivity approach based on Hamiltonian dynamics for beam optics, enabling efficient evaluation of how small design changes affect beam quality, useful for optimization and error analysis.

Contribution

It presents a novel adjoint method leveraging Hamiltonian reciprocity to compute beam optics sensitivities with minimal computational effort.

Findings

Sensitivity functions can be computed with few time-reversed runs.

The method allows for efficient optimization of beam focusing systems.

It enables prediction of sensitivity to manufacturing and alignment errors.

Abstract

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.