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Two-and-a-half dimensional symplectic space-charge solver

Ji Qiang*

  • *Contact author: jqiang@lbl.gov
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Phys. Rev. Accel. Beams 28, 114602 – Published 17 November, 2025

DOI: https://doi.org/10.1103/npx1-nclt

Abstract

The nonlinear space-charge effect plays a significant role in high-intensity accelerators and has been extensively studied using multiparticle tracking methods. In this paper, we present a novel 2.5-dimensional symplectic space-charge solver specifically designed for long beam bunches. We begin by detailing its application to a transverse Gaussian density distribution under open boundary conditions in a straight system, where a semianalytical expression is derived. We then demonstrate the solver’s adaptation to arbitrary distributions in open space, as well as within rectangular and round conducting pipes. Finally, we discuss the extension of this solver to circular accelerator systems. This study shows that the fast 2.5-dimensional solver can be a good approximation to the fully three-dimensional solver for long bunches in large circular accelerators.

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Phys. Rev. Accel. Beams 28, 114602– Published 17 November, 2025
  • Received 22 July 2025
  • Accepted 14 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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