The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.
References
[1]
Qiang, J., Lidia, S., Ryne, R.D. and Limborg-Deprey, C. (2006) Three-Dimensional Quasistatic Model for High Brightness Beam Dynamics Simulation. Physical Review Special Topics—Accelerators and Beams, 9, Article 044204. https://doi.org/10.1103/physrevstab.9.044204
[2]
Qiang, J., Ryne, R.D., Venturini, M., Zholents, A.A. and Pogorelov, I.V. (2009) High Resolution Simulation of Beam Dynamics in Electron Linacs for X-Ray Free Electron Lasers. Physical Review Special Topics—Accelerators and Beams, 12, Article 100702. https://doi.org/10.1103/physrevstab.12.100702
[3]
Floettmann, K. (2017) ASTRA: A Space-Charge TRacking Algorithm. https://www.desy.de/~mpyflo/Astra_manual/Astra-Manual_V3.2.pdf
[4]
Adelmann, A., et al. (2018) The OPAL (Object Oriented Parallel Accelerator Library) Framework. Paul Scherrer Institut PSI-PR-08-02. https://gitlab.psi.ch/OPAL/src/wikis/home
[5]
Tomin, S., et al. (2017) OCELOT as a Framework for Beam Dynamics Simulations of X-Ray Sources. Proceedings of the 8th International Particle Accelerator Conference, Copenhagen, 14-19 May 2017, 2642.
[6]
Mayes, C.E., Ryne, R.D. and Sagan, D.C. (2018) 3D Space Charge in BMAD. Proceedings of the 9th International Particle Accelerator Conference, Vancouver, 29 April-4 May 2018, 3428.
[7]
Oeftiger, A. and Hegglin, S. (2016) Space Charge Modules for PyHEADTAIL. Proceedingsof HB 2016, Malmo, 3-8 July 2016, 124.
[8]
Latina, A. (2020) RF-Track Reference Manual. Tech. https://zenodo.org/record/3887085
[9]
Iadarola, G., et al. (2023) Xsuite: An Integrated Beam Physics Simulation Framework. Proceedingsof HB 2023, Geneva, 9-13 October 2023, 73.
[10]
Fedeli, L., Huebl, A., Boillod-Cerneux, F., Clark, T., Gott, K., Hillairet, C., et al. (2022) Pushing the Frontier in the Design of Laser-Based Electron Accelerators with Groundbreaking Mesh-Refined Particle-in-Cell Simulations on Exascale-Class Supercomputers. SC22: International Conference for High Performance Computing, Networking, Storage and Analysis, Dallas, 13-18 November 2022, 1-12. https://doi.org/10.1109/sc41404.2022.00008
[11]
Huebl, A., Lehe, R., Mitchell, C.E., Qiang, J., Ryne, R.D., Sandberg, R.T. and Vay, J. (2022) Next Generation Computational Tools for the Modeling and Design of Particle Accelerators at Exascale. Proceedings of 2022 North American Particle Accelerator Conference, Albuquerque, 7-12 August 2022, 302-306.
[12]
Qiang, J., Lidia, S., Ryne, R.D. and Limborg-Deprey, C. (2007) Erratum: Three-Dimensional Quasistatic Model for High Brightness Beam Dynamics Simulation. Physical Review Special Topics—Accelerators and Beams, 10, Article 129901. https://doi.org/10.1103/physrevstab.10.129901
[13]
Hockney, R. and Eastwood, J. (1988) Computer Simulation Using Particles. Taylor & Francis. https://doi.org/10.1201/9781439822050
[14]
Stupakov, G. and Penn, G. (2018) Classical Mechanics and Electromagnetism in Accelerator Physics. Springer.
