Paper Info
Title
Three-dimensional Poisson solver for a charged beam with large aspect ratio in a conducting pipe
Abstract
In this paper, we present a three-dimensional Poisson equation solver for the electrostatic potential of a charged beam with large longitudinal to transverse aspect ratio in a straight and a bent conducting pipe with open-end boundary conditions. In this solver, we have used a Hermite–Gaussian series to represent the longitudinal spatial dependence of the charge density and the electric potential. Using the Hermite–Gaussian approximation, the original three-dimensional Poisson equation has been reduced into a group of coupled two-dimensional partial differential equations with the coupling strength proportional to the inverse square of the longitudinal-to-transverse aspect ratio. For a large aspect ratio, the coupling is weak. These two-dimensional partial differential equations can be solved independently using an iterative approach. The iterations converge quickly due to the large aspect ratio of the beam. For a transverse round conducting pipe, the two-dimensional Poisson equation is solved using a Bessel function approximation and a Fourier function approximation. The three-dimensional Poisson solver can have important applications in the study of the space-charge effects in the high intensity proton storage ring accelerator or induction linear accelerator for heavy ion fusion where the ratio of bunch length to the transverse size is large.
Year
DOI
Venue
2004
10.1016/j.cpc.2004.03.002
Computer Physics Communications
Keywords
DocType
Volume
52.65.Rr,52.75.Di
Journal
160
Issue
ISSN
Citations 
2
0010-4655
5
PageRank 
References 
Authors
0.88
0
2
Name
Order
Citations
PageRank
Ji Qiang17910.07
Robert L. Gluckstern250.88