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Title: Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

Abstract

Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log (N)), where N is the number of grid points. The cost of the 3D spectral solver scales as O(N>nN), where Nn is the maximum longitudinal mode number. Lastly, we compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.

Authors:
 [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1576496
Alternate Identifier(s):
OSTI ID: 1358994
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 203; Journal Issue: C; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Poisson equation; Spectral method; Green function

Citation Formats

Qiang, Ji. Efficient three-dimensional Poisson solvers in open rectangular conducting pipe. United States: N. p., 2016. Web. doi:10.1016/j.cpc.2016.02.012.
Qiang, Ji. Efficient three-dimensional Poisson solvers in open rectangular conducting pipe. United States. doi:10.1016/j.cpc.2016.02.012.
Qiang, Ji. Fri . "Efficient three-dimensional Poisson solvers in open rectangular conducting pipe". United States. doi:10.1016/j.cpc.2016.02.012. https://www.osti.gov/servlets/purl/1576496.
@article{osti_1576496,
title = {Efficient three-dimensional Poisson solvers in open rectangular conducting pipe},
author = {Qiang, Ji},
abstractNote = {Three-dimensional (3D) Poisson solver plays an important role in the study of space-charge effects on charged particle beam dynamics in particle accelerators. In this paper, we propose three new 3D Poisson solvers for a charged particle beam in an open rectangular conducting pipe. These three solvers include a spectral integrated Green function (IGF) solver, a 3D spectral solver, and a 3D integrated Green function solver. These solvers effectively handle the longitudinal open boundary condition using a finite computational domain that contains the beam itself. This saves the computational cost of using an extra larger longitudinal domain in order to set up an appropriate finite boundary condition. Using an integrated Green function also avoids the need to resolve rapid variation of the Green function inside the beam. The numerical operational cost of the spectral IGF solver and the 3D IGF solver scales as O(N log (N)), where N is the number of grid points. The cost of the 3D spectral solver scales as O(N>nN), where Nn is the maximum longitudinal mode number. Lastly, we compare these three solvers using several numerical examples and discuss the advantageous regime of each solver in the physical application.},
doi = {10.1016/j.cpc.2016.02.012},
journal = {Computer Physics Communications},
number = C,
volume = 203,
place = {United States},
year = {2016},
month = {2}
}

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