Hybrid macroparticle algorithm for modeling space charge

Abstract

A space charge algorithm is constructed that is a hybrid between envelope and multiparticle models. The transverse dynamics is simplified by tracking the transverse envelope of each macroparticle. The equations of motion are derived from the Hamiltonian-fluid formulation of the Vlasov Poisson system. A novel electrostatic self-field solver is derived that solves directly for the self-consistent on-axis potential and linear defocusing force, including longitudinal and beam pipe boundary conditions. The implementation of the algorithm, hyper3d, is presented. It is tested against the particle-in-cell code warp, using various configurations of a periodic focusing structure with rf cavities. The required number of macroparticles is reduced substantially compared to standard particle-tracking codes. This model is well adapted to cases where the transverse dynamics is linear and where the details of the longitudinal dynamics are the principal point of interest; an example is where a dc beam is converted to a bunched beam.