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  • Open Access

Construction of approximate invariants for nonintegrable Hamiltonian systems

Yongjun Li1,*, Derong Xu1, and Yue Hao2

  • *Contact author: yli@bnl.gov
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Phys. Rev. Accel. Beams 28, 074001 – Published 28 July, 2025

DOI: https://doi.org/10.1103/m349-wmnr

Abstract

We present a method to construct high-order polynomial approximate invariants (AI) for nonintegrable Hamiltonian dynamical systems and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps expressed as square matrices, AIs can be constructed order by order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

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Phys. Rev. Accel. Beams 28, 074001– Published 28 July, 2025
  • Received 21 January 2025
  • Accepted 2 July 2025
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