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Space charge modeling method in 2.5D for scaling fixed-field alternating-gradient accelerators

Kai Zhou1,2, Ming-Yang Huang1,2,3,*, Xiao Li1,2,3,†, Bin Wu1,2, Hanyang Liu1,2, Shouyan Xu1,2, and Sheng Wang1,2,3

  • *Contact author: huangmy@ihep.ac.cn
  • †Contact author: lixiao@ihep.ac.cn
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Phys. Rev. Accel. Beams 29, 113301 – Published 5 November, 2026

DOI: https://doi.org/10.1103/q1xb-z29j

Abstract

Scaling fixed-field alternating-gradient accelerators (scaling FFAs) are promising candidates for high-intensity proton drivers, for which space charge effects are a key limitation of beam performance. For long bunches in circular accelerators, 2.5D space charge methods provide an efficient alternative to full 3D PIC methods by exploiting the large longitudinal-to-transverse aspect ratio of the bunch. In scaling FFAs, however, the reference closed orbit varies with particle energy, and the transverse and longitudinal directions are not directly available in cylindrical coordinates. Therefore, the longitudinal slicing and transverse planes required by a 2.5D model must be reconstructed dynamically, rather than defined from a single fixed reference orbit, which poses a central challenge for efficient 2.5D modeling in high-intensity scaling FFAs. This paper presents a new 2.5D space charge modeling method for high-intensity scaling FFAs and its implementation in the PyFFA code. The central idea is to replace the fixed reference orbit used in conventional 2.5D models with a dynamically reconstructed local reference frame based on a precomputed family of energy-dependent closed orbits. During tracking, this frame is updated according to the instantaneous particle state, enabling transverse Poisson equations to be solved consistently in this dynamic local coordinate system. The resulting space charge field is then transformed back to global cylindrical coordinates and applied in the tracking equations. Benchmarks of space charge fields, tune shifts, rms envelope evolution, and longitudinal phase-space evolution show good agreement with analytical results, validating the field calculation and its coupling to beam dynamics for long, arc-shaped bunches in scaling FFAs. The implemented model enables efficient studies of space charge effects on beam dynamics in high-intensity scaling FFAs.

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Phys. Rev. Accel. Beams 29, 113301– Published 5 November, 2026
  • Received 10 June 2026
  • Accepted 23 October 2026
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