Efficient three-dimensional Poisson solvers in open rectangular conducting pipe

Journal Article · 26 February 2016 · Computer Physics Communications

DOI: https://doi.org/10.1016/j.cpc.2016.02.012 · OSTI ID:1576496

Qiang, Ji ^[1]

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1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

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 N_n 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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1576496
• Alternate ID(s): OSTI ID: 1358994
• Journal Information: Computer Physics Communications, Vol. 203, Issue C; ISSN 0010-4655
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English