- Editors' Suggestion
- Open Access
Extracting symplectic maps for space-charge dominated beams
Phys. Rev. Accel. Beams 28, 104602 – Published 14 October, 2025
DOI: https://doi.org/10.1103/jykb-d8f1
Abstract
Symplecticity of transfer maps is important for reliable evaluation of space-charge dominated beams in accelerators. Unfortunately, most simulation codes that include collective effects, such as space charge, do not use canonical phase-space variables and therefore are not symplectic in the presence of electromagnetic fields. In this paper, we present a numerical method to extract local linear symplectic transfer maps using particle tracking simulation code impact-t for space-charge dominated beams. We demonstrate this method for the photoinjector (113 MHz SRF gun) section of the Coherent electron Cooling (CeC) Proof of Principle (POP) experiment.
Physics Subject Headings (PhySH)
Article Text
References (30)
- A. A. Vlasov, The vibrational properties of an electron gas, Sov. Phys. Usp. 10, 721 (1968).
- V. N. Litvinenko, Y. Jing, D. Kayran, P. Inacker, J. Ma, T. Miller, I. Petrushina, I. Pinayev, K. Shih, G. Wang, and Y. H. Wu, Plasma-cascade instability, Phys. Rev. Accel. Beams 24, 014402 (2021).
- V. N. Litvinenko, Y. Jing, J. Ma, I. Petrushina, K. Shih, and G. Wang, 3D theory of microscopic instabilities driven by space-charge forces, Phys. Rev. Accel. Beams 26, 054402 (2023).
- J. Qiang, S. Lidia, R. Ryne, and C. Limborg, A 3D parallel beam dynamics code for modeling high brightness beams in photoinjectors, in Proceedings of the 2005 Particle Accelerator Conference, Knoxville, TN (2005), pp. 3316–3318, 10.1109/PAC.2005.1591453.
- A. Friedman, D. P. Grote, and I. Haber, Three—dimensional particle simulation of heavy–ion fusion beams, Phys. Fluids B 4, 2203 (1992).
- K. Floettmann, ASTRA, a space charge tracking algorithm (2000), https://www.desy.de/~mpyflo/Astra_manual/Astra-Manual_V3.2.pdf.
- L. Young and J. Billen, The particle tracking code Parmela, in Proceedings of the 2003 Particle Accelerator Conference, Portland, OR (JACoW, Geneva, Switzerland, 2003), Vol. 5, pp. 3521–3523, 10.1109/PAC.2003.1289968.
- J. Qiang, Symplectic multiparticle tracking model for self-consistent space-charge simulation, Phys. Rev. Accel. Beams 20, 014203 (2017).
- J. Qiang, Symplectic particle-in-cell model for space-charge beam dynamics simulation, Phys. Rev. Accel. Beams 21, 054201 (2018).
- G. Iadarola, A. Abramov, P. Belanger, X. Buffat, R. D. Maria, D. Demetriadou, L. Deniau, D. D. Croce, P. Hermes, P. Kicsiny, P. Kruyt, A. Latina, L. Mether, P. Niedermayer, K. Paraschou, T. Pieloni, M. Seidel, G. Sterbini, F. V. der Veken, L. van Riesen-Haupt, and S. Åopaciuk, Xsuite: An integrated beam physics simulation framework, in Proceedings of the 68th Advance Beam Dynamics Workshop High-Intensity High-Brightness Hadron Beams (HB’23) (JACoW, Geneva, Switzerland, 2024), pp. 73–80, 10.18429/JACoW-HB2023-TUA2I1.
- D. Sagan, Bmad: A relativistic charged particle simulation library, Nucl. Instrum. Methods Phys. Res., Sect. A 558, 356 (2006).
- L. Jian-Qin, Numerical simulation for space charge dominated beam transport, Chin. Phys. B 19, 032901 (2010).
For bmad, see [11]. For impact-z, it was directly communicated by J. Qiang (impact-z author) that symplectic tracking for injectors with low energy electrons at the photocathode (0.5 eV KE electrons at cathode for CeC photo-injector), is not yet available for public use.
- B. Erdelyi, E. Nissen, and S. Manikonda, A differential algebraic method for the solution of the Poisson equation for charged particle beams, Commun. Comput. Phys. 17, 47 (2015).
- V. Litvinenko, Z. Altinbas, J. Brutus, A. D. Lieto, D. Gassner et al., Coherent electron cooling experiment at RHIC: Status and plans, in Proceedings of the COOL’19, 12th Workshop on Beam Cooling and Related Topics, Novosibirsk, Russia (JACoW, Geneva, Switzerland, 2019), pp. 35–40, 10.18429/JACoW-COOL2019-TUZ01.
- I. Pinayev et al., High charge high current beam from BNL 113 MHz SRF gun, in Proceedings of the ERL’19 (JACoW, Geneva, Switzerland, 2019), pp. 145–149, 10.18429/JACoW-ERL2019-THCOYBS02.
For codes using coordinates along the reference trajectory, , one would need to know transverse components of the vector potential and scalar potential at initial and final azimuth to extract symplectic transfer map for (x,y, -ct, Px,Py, H/c). While technically it is different for the above description, the idea of the method is the same.
- A. J. Dragt, Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics (University of Maryland, College Park, MD, 1997), https://www.physics.umd.edu/dsat/docs/Book19Nov2020.pdf.
Or in the case of tracking codes using as the independent variable, one would require information about the transverse components of the vector potential and about the scalar potential. Note that information about magnetic and electric field is generally insufficient, because 6 parameters (, ) are insufficient to fully determine the 9 parameters of matrix , or its equivalent in -based codes.
- K. Shih, Intelligent control of instabilities in space-charge dominated beams, Ph.D. thesis, SUNY Stony Brook, New York, 2023, https://www.proquest.com/openview/1c9f58c93ce4ea75eefa2f1b9f6bb123/1?pq-origsite=gscholar&cbl=18750&diss=y.
- I. Petrushina. The chilling recount of an unexpected discovery: First observations of the plasma-cascade instability in the coherent electron cooling experiment, Ph.D. thesis, SUNY Stony Brook, New York, 2019, https://ui.adsabs.harvard.edu/abs/2019PhDT........96P.
- P. L. Morton, Particle dynamics in linear accelerators, Ph.D. thesis, The Ohio State University, Ohio, 1963, http://rave.ohiolink.edu/etdc/view?acc_num=osu1486560879965688.
- J. Qiang, IMPACT-T user document Version 2.2, 2022, Lawrence Berkeley National Laboratory, California, https://github.com/impact-lbl/IMPACT-T/blob/master/doc/ImpactTv2.pdf.
- R. Li, T. Sen, and J.-F. Ostiguy, Modeling transverse space charge effects in IOTA with pyORBIT (2021).
- H. P. Li, M. J. Easton, Y. R. Lu, Z. Wang, and J. Qiang, Development and benchmarking of the IMPACT-T code, in Proceedings of the International Particle Accelerator Conference (IPAC’18), Vancouver, BC, Canada (JACoW, Geneva, Switzerland, 2018), pp. 3408–3410, 10.18429/JACoW-IPAC2018-THPAK076.
- L. M. Healy. Lie-algebraic methods for treating lattice parameter errors in particle accelerators, Ph.D. thesis, Univ. of Maryland, College Park, MD, 1985, https://www.osti.gov/biblio/6796986.
- W. W. MacKay, Comment on healy’s symplectification algorithm, in Proceedings of the European Particle Accelerator Conference (EPAC’06), Edinburgh, Scotland (JACoW, Geneva, Switzerland, 2006), pp. 2281–2283, https://proceedings.jacow.org/e06/PAPERS/WEPCH152.pdf.
- L. E. Cook, J. E. Runeson, J. O. Richardson, and T. J. H. Hele, Which algorithm best propagates the Meyer–Miller–Stock–Thoss mapping Hamiltonian for non-adiabatic dynamics?, J. Chem, Theory Comput. 19, 6109 (2023).
- A. N. Ivanov, S. N. Andrianov, N. V. Kulabukhova, R. Maier, Y. Senichev, and D. Zyuzin, Testing of symplectic integrator of spin-orbit motion based on matrix formalism, in Proceedings of the International Particle Accelerator Conference (IPAC’13), Shanghai, China (JACoW, Geneva, Switzerland, 2013), pp. 2582–2584, https://jacow.org/IPAC2013/papers/WEPEA037.pdf.
- N. Bachhawat, Dataset for “Extracting symplectic maps for space charge dominated beams”, Zenodo (2025), 10.5281/zenodo.17160199.