Construction of approximate invariants for nonintegrable Hamiltonian systems
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-07-01
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| Series: | Physical Review Accelerators and Beams |
| Online Access: | http://doi.org/10.1103/m349-wmnr |
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| _version_ | 1849701141251620864 |
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| author | Yongjun Li Derong Xu Yue Hao |
| author_facet | Yongjun Li Derong Xu Yue Hao |
| author_sort | Yongjun Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-59b0b46f5bf640e0bb322e28ec5ab6bb |
| institution | DOAJ |
| issn | 2469-9888 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Accelerators and Beams |
| spelling | doaj-art-59b0b46f5bf640e0bb322e28ec5ab6bb2025-08-20T03:18:02ZengAmerican Physical SocietyPhysical Review Accelerators and Beams2469-98882025-07-0128707400110.1103/m349-wmnrConstruction of approximate invariants for nonintegrable Hamiltonian systemsYongjun LiDerong XuYue HaoWe 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.http://doi.org/10.1103/m349-wmnr |
| spellingShingle | Yongjun Li Derong Xu Yue Hao Construction of approximate invariants for nonintegrable Hamiltonian systems Physical Review Accelerators and Beams |
| title | Construction of approximate invariants for nonintegrable Hamiltonian systems |
| title_full | Construction of approximate invariants for nonintegrable Hamiltonian systems |
| title_fullStr | Construction of approximate invariants for nonintegrable Hamiltonian systems |
| title_full_unstemmed | Construction of approximate invariants for nonintegrable Hamiltonian systems |
| title_short | Construction of approximate invariants for nonintegrable Hamiltonian systems |
| title_sort | construction of approximate invariants for nonintegrable hamiltonian systems |
| url | http://doi.org/10.1103/m349-wmnr |
| work_keys_str_mv | AT yongjunli constructionofapproximateinvariantsfornonintegrablehamiltoniansystems AT derongxu constructionofapproximateinvariantsfornonintegrablehamiltoniansystems AT yuehao constructionofapproximateinvariantsfornonintegrablehamiltoniansystems |