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Nonlinear dynamics optimization based on minimizing resonance driving terms along a storage ring

Bingfeng Wei, Zhenghe Bai*, and Guangyao Feng

Pascale Brunelle, Alexandre Loulergue, and Laurent S. Nadolski†

  • *Contact author: baizhe@ustc.edu.cn
  • †Contact author: laurent.nadolski@synchrotron-soleil.fr
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Phys. Rev. Accel. Beams 29, 083404 – Published 28 August, 2026

DOI: https://doi.org/10.1103/hlyb-qqx6

Abstract

The optimization of nonlinear dynamics for a storage ring lattice aims to achieve large dynamic aperture (DA) and momentum aperture (MA), which are critical for beam injection and lifetime. One of the main factors affecting MA is off-momentum DA. In our previous work, it was demonstrated that reducing on- and off-momentum resonance driving terms (RDTs) along the ring is very effective in enlarging on- and off-momentum DAs. In this paper, the previous effectiveness analysis is formulated into a practical nonlinear optimization method, in which the on- and off-momentum ring-averaged RDTs are minimized simultaneously while constraints on tune shifts and the working point are imposed. Off-momentum ring-averaged RDTs are evaluated over a range of momentum deviations to optimize MA more effectively. The dependence of the ring-averaged RDT and DA on tune is also analyzed, showing that reducing the ring-averaged RDT can help guide the working point away from structural resonance lines and control tune shifts with momentum to avoid dangerous resonance lines. Applied to the SOLEIL storage ring, this efficient ring-averaged RDT optimization enables a rapid iterative workflow of optimization, analysis, and refinement, providing physical insight into the lattice and leading to improved nonlinear solutions. One optimized solution achieves a DA comparable to that of the reference solution obtained from tracking-based optimization while improving the beam lifetime, as validated experimentally on the SOLEIL storage ring.

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Phys. Rev. Accel. Beams 29, 083404– Published 28 August, 2026
  • Received 19 January 2026
  • Accepted 11 August 2026
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