Simulation methods for multipole imaging systems and aberration correctors

Two different methods have been derived and implemented for simulation of multipole imaging systems and aberration correctors. The first method uses an aberration theory for combinations of multipole lenses and deflectors, including primary and secondary aberrations up to the fifth order. A damped least-squares algorithm is used to minimise the dynamically correctable aberrations. This yields the appropriate signals for the dynamic correction elements, e.g. stigmators and dynamic focus lenses. The second method uses a direct ray-tracing approach. The numerically computed multipole lens and deflection fields are fitted with analytic functions through which trajectories are directly traced with a high degree of self-consistency. By computing the paths of many particles simultaneously, the combined effects of aberrations and discrete Coulomb interactions are accurately simulated. Furthermore, the effects of electrical and mechanical asymmetries on the multipole elements can readily be simulated with this approach.