A Hamiltonian Mechanics Framework for Charge Particle Optics in Straight and Curved Systems

TL;DR

This paper introduces a Hamiltonian mechanics-based framework for analyzing charged particle optics, enabling accurate computation of optical properties and aberrations in systems with straight and curved axes.

Contribution

It provides a complete, perturbative Hamiltonian approach that simplifies the calculation of optical properties and preserves symplectic structure for charged particle systems.

Findings

Framework allows straightforward computation of optical properties.

Preserves symplectic phase space structure in numerical schemes.

Enables analytic and numerical analysis of aberrations.

Abstract

Charged particle optics, the description of particle trajectories in the vicinity of some optical axis, describe the imaging properties of particle optics devices. Here, we present a complete and compact description of charged particle optics employing perturbative expansion of Hamiltonian mechanics. The derived framework allows the straightforward computation of transversal and longitudinal (chromatic) properties of static and dynamic optical devices with straight and curved optical axes. It furthermore gives rise to geometric integration schemes preserving the symplectic phase space structure and pertaining Lagrange invariants, which may be employed to derive analytic approximations of aberration coefficients and efficient numerical trajectory solvers.