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

TL;DR

This paper introduces a fast spectral finite-difference method for solving 3D Poisson equations with specific boundary conditions, optimizing computational efficiency for space-charge simulations in accelerator physics.

Contribution

The paper presents a novel spectral finite-difference approach that significantly reduces computational complexity and memory usage for 3D Poisson problems with mixed boundary conditions.

Findings

Achieves $O(N_u \, log N_{mode})$ computational complexity.

Reduces computational time and memory compared to traditional methods.

Effective for beam physics simulations in particle accelerators.

Abstract

A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only 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 of longitudinal or azimuthal modes. This saves both the computational time and the memory usage by using an artificial boundary condition in a large extended computational domain.