Parallel 3D Poisson solver for a charged beam in a conducting pipe

In this paper, we present a parallel three-dimensional Poisson solver for the electrostatic potential of a charged beam in a round or rectangular conducting pipe with open-end boundary conditions. This solver uses an eigenfunction expansion in the transverse direction and a finite difference method in the longitudinal direction. The computational domain in the longitudinal direction contains only the beam since only the potential inside the beam will be calculated. The potential on both ends of the beam is matched into the source-free region for each eigenmode. This method avoids the use of a large computational domain outside the beam to implement the open boundary condition. This saves unnecessary computational time and memory storage that would be required if a large computational domain was used to simulate the open boundary. Parallel implementation using a two-dimensional domain decomposition approach and a message passing paradigm shows good scalability on both distributed memory machines and distributed shared-memory machines. This solver has important applications in accelerator physics studies that involve modeling high-intensity beam dynamics. As a specific example, we present results from large-scale simulations of beam halo formation in a linear accelerator.