Jung, Paul Matthew2020-08-282020-08-2820202020-08-27http://hdl.handle.net/1828/12036A particle accelerator simulation which straddles the gap between multi-particle and moment codes is derived. The hybrid approach represents the beam using macro-particles which contain discrete longitudinal coordinates and transverse second moments. The discretization scheme for the macro-particles is derived using variational principles, as a natural extension of well known variational approaches. This variational discretization allows for exact transverse emittance conservation. The electrostatic self-potential is discrete in the longitudinal direction and solved semi-analytically in the transverse direction using integrated Green’s functions. The algorithm is implemented and tested against both a moment and multi-particle code.enAvailable to the World Wide WebParticle AcceleratorSimulationvariational principlesThesis