A particle-in-cell model of beam dynamics in a dielectric wall accelerator
Dielectric wall accelerator (DWA) technology has been proposed as a compact, cost-effective alternative to rf accelerators for proton therapy, but its beam dynamics and practical feasibility remain relatively unexplored. In this work, we derive a three-dimensional, time-dependent axisymmetric electromagnetic field model from a prescribed on-wall excitation and implement it as stacked external field elements in the particle-in-cell code Warp. In the absence of experimental DWA beam-transport data, the implementation is cross-checked against a previously developed linear optics model in TRANSOPTR using deliberately idealized beam conditions. Strong agreement is observed between the two models in this regime. The models are then compared for larger transverse and longitudinal emittances, bunch charges up to 1x10^8e, and beam parameters representative of a low-energy proton source. The PIC simulations remain consistent with the linear predictions over much of the investigated range, while also identifying wall interactions, longitudinal phase-space distortions, and space-charge induced aberrations. The PIC model represents an intermediate step between linear optics and combined, geometry-specific electromagnetic and particle-transport simulations. It resolves particle-level transport and beam self-fields while retaining an analytical field description that can be varied without committing to a particular DWA structure. More detailed effects may be introduced through externally generated field data or empirical corrections, including models of cell-to-cell coupling, providing a practical basis for increasingly realistic DWA field and beamline studies.