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Convexity of the longitudinal variation of third-order resonance driving terms and its application in dynamic aperture optimization

Wanbin Li, Zihan Wang, Yuejing Huang, Bingfeng Wei*, and Zhenghe Bai†

  • *Contact author: weibf@ustc.edu.cn
  • †Contact author: baizhe@ustc.edu.cn
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Phys. Rev. Accel. Beams 29, 083401 – Published 7 August, 2026

DOI: https://doi.org/10.1103/8w2l-psz3

Abstract

The optimization of the dynamic aperture (DA) of a storage ring is typically a nonconvex problem with multiple local optima. Recent studies showed that reducing the variation of resonance driving terms (RDTs) along the longitudinal position improves DA very effectively, as the reduction in the longitudinal variation of lower-order RDTs suppresses higher-order nonlinear terms. Therefore, minimizing the longitudinal variation of third-order RDTs is crucial for DA optimization. In this paper, we prove that the longitudinal variation of third-order RDTs, quantified using their rms value f3,rms at sextupole locations, is a special convex function. In the space of sextupole strengths, the isosurfaces of f3,rms are a series of concentric and coaxial ellipsoidal surfaces, with the central position possessing minimum f3,rms. The scanning results of a storage ring lattice show a strong consistency between the distributions of f3,rms and DA, indicating that the optimization of DA can be regarded as a roughly approximate convex optimization problem. Based on this, a fast DA optimization method based on particle tracking is developed, where a high-quality initial population for an intelligent algorithm is generated with a Gaussian distribution based on the geometric structure of f3,rms.

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Phys. Rev. Accel. Beams 29, 083401– Published 7 August, 2026
  • Received 15 January 2026
  • Accepted 14 July 2026
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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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