A Fast 3D Poisson Solver with Longitudinal Periodic and Transverse Open Boundary Conditions for Space-Charge Simulations

摘要

A three-dimensional (3D) Poisson solver with longitudinal periodic andtransverse open boundary conditions can have important applications in beamphysics of particle accelerators. In this paper, we present a fast efficientmethod to solve the Poisson equation using a spectral finite-difference method.This method uses a computational domain that contains the charged particle beamonly and has a computational complexity of $O(N_u(logN_{mode}))$, where $N_u$is the total number of unknowns and $N_{mode}$ is the maximum number oflongitudinal or azimuthal modes. This saves both the computational time and thememory usage by using an artificial boundary condition in a large extendedcomputational domain.