The CPO programs and the BEM for charged particle optics

The Boundary Element Method for solving the Laplace and Poisson equations for electrostatic systems will be outlined, with the emphasis on 3D systems and the commercial CPO programs. Some applications to charged particle optics will be described. Since the BEM is a charge-based method it is ideally suited for systems that include space-charge and/or cathodes. It is also exceptionally accurate and can deal easily with electrodes of very different sizes. Several ‘benchmark tests will be presented, in which systems with known analytic solutions are used to illustrate the accuracy and versatility of the programs.