Design of electrostatic lenses through genetic algorithm and particle swarm optimisation methods integrated with differential algebra

Genetic algorithm (GA) and particle swarm optimisation (PSO) techniques have been integrated with the differential algebra (DA) method in charged particle optics to optimise an Einzel lens. The DA method is a robust and efficient tool for the calculation of aberration coefficients of electrostatic lenses, which makes use of nonstandard analysis for ray tracing a particle as it is subjected to the field generated by a lens. In this study, initial populations of lenses with random geometrical configurations are generated. These initial populations are then subjected to GA and PSO algorithms to alter the geometry of each lens for a set number of iterations. The lens performance is evaluated by calculating the spot size using the aberrations coefficients up to third-order generated by the DA method. Moreover, a focusing column comprising two lenses and a Wien filter was optimised using GA method.