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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 ration 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 ration of bunch length to the transverse size is large.

Authors:
;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Director. Office of Science. Office of High Energy and Nuclear Physics. Division of High Energy Physics, Office of Advanced Scientific Computing Research, Scientific Discovery through Advanced Computing Project (US)
OSTI Identifier:
837240
Report Number(s):
LBNL-54282
R&D Project: 453401; TRN: US0500936
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Journal Article
Resource Relation:
Journal Name: Computer Physics Communications; Journal Volume: 160; Journal Issue: 2; Other Information: Submitted to Computer Physics Communications: Volume 160, No.2; Journal Publication Date: 07/01/2004; PBD: 8 Jan 2004
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ACCELERATORS; ASPECT RATIO; BESSEL FUNCTIONS; BOUNDARY CONDITIONS; CHARGE DENSITY; ELECTRIC POTENTIAL; ELECTROSTATICS; HEAVY IONS; INDUCTION; LINEAR ACCELERATORS; PARTIAL DIFFERENTIAL EQUATIONS; POISSON EQUATION; PROTONS; SPACE CHARGE; SPACE DEPENDENCE; STORAGE RINGS; POISSON SOLVER HERMITE-GAUSSIAN APPROXIMATION LARGE ASPECT RATIO OPEN BOUNDARY CONDITIONS

Citation Formats

Qiang, Ji, and Gluckstern, Robert L. Three-dimensional poisson solver for a charged beam with large aspect ratio in a conducting pipe. United States: N. p., 2004. Web. doi:10.1016/j.cpc.2004.03.002.
Qiang, Ji, & Gluckstern, Robert L. Three-dimensional poisson solver for a charged beam with large aspect ratio in a conducting pipe. United States. doi:10.1016/j.cpc.2004.03.002.
Qiang, Ji, and Gluckstern, Robert L. Thu . "Three-dimensional poisson solver for a charged beam with large aspect ratio in a conducting pipe". United States. doi:10.1016/j.cpc.2004.03.002. https://www.osti.gov/servlets/purl/837240.
@article{osti_837240,
title = {Three-dimensional poisson solver for a charged beam with large aspect ratio in a conducting pipe},
author = {Qiang, Ji and Gluckstern, Robert L.},
abstractNote = {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 ration 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 ration of bunch length to the transverse size is large.},
doi = {10.1016/j.cpc.2004.03.002},
journal = {Computer Physics Communications},
number = 2,
volume = 160,
place = {United States},
year = {Thu Jan 08 00:00:00 EST 2004},
month = {Thu Jan 08 00:00:00 EST 2004}
}