Square matrix-based six-dimensional convergence map for nonlinear beam dynamics analysis
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912824097243136 |
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| author | Wan, Jinyu Hao, Yue |
| author_facet | Wan, Jinyu Hao, Yue |
| contents | The square matrix-based convergence map (CM) method has proven effective in characterizing nonlinear dynamics in several 4-D dynamical systems. However, when time-dependent perturbations, such as crabbing kicks in colliders, are present, a comprehensive 6-D analysis becomes essential to accurately capture the coupling between transverse and longitudinal motions. In this work, we extend the CM method to the full 6-D phase space by employing an eigen-decomposition-based formulation of the square matrix combined with iterative procedures. The proposed 6-D CM approach is first validated using a simplified crabbing map. We demonstrate that the 6-D CM preserves computational efficiency by using only one-turn map, while successfully resolving high-order resonance structures that remain unresolved by conventional frequency map analysis (FMA). This method is subsequently applied to the dynamic aperture (DA) study of the future Electron-Ion Collider (EIC). The results obtained from the CM analysis exhibit close agreement with those derived from FMA, demonstrating its potential as a powerful tool for nonlinear beam dynamics analysis and DA evaluation, as well as for broader applications in other nonlinear dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09574 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Square matrix-based six-dimensional convergence map for nonlinear beam dynamics analysis Wan, Jinyu Hao, Yue Accelerator Physics The square matrix-based convergence map (CM) method has proven effective in characterizing nonlinear dynamics in several 4-D dynamical systems. However, when time-dependent perturbations, such as crabbing kicks in colliders, are present, a comprehensive 6-D analysis becomes essential to accurately capture the coupling between transverse and longitudinal motions. In this work, we extend the CM method to the full 6-D phase space by employing an eigen-decomposition-based formulation of the square matrix combined with iterative procedures. The proposed 6-D CM approach is first validated using a simplified crabbing map. We demonstrate that the 6-D CM preserves computational efficiency by using only one-turn map, while successfully resolving high-order resonance structures that remain unresolved by conventional frequency map analysis (FMA). This method is subsequently applied to the dynamic aperture (DA) study of the future Electron-Ion Collider (EIC). The results obtained from the CM analysis exhibit close agreement with those derived from FMA, demonstrating its potential as a powerful tool for nonlinear beam dynamics analysis and DA evaluation, as well as for broader applications in other nonlinear dynamical systems. |
| title | Square matrix-based six-dimensional convergence map for nonlinear beam dynamics analysis |
| topic | Accelerator Physics |
| url | https://arxiv.org/abs/2601.09574 |