dorsal/arxiv
View SchemaSquare matrix-based six-dimensional convergence map for nonlinear beam dynamics analysis
| Authors | Jinyu Wan, Yue Hao |
|---|---|
| Categories | |
| ArXiv ID | 2601.09574vv1 |
| URL | https://arxiv.org/abs/2601.09574 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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.
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"abstract": "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.",
"arxiv_id": "2601.09574",
"authors": [
"Jinyu Wan",
"Yue Hao"
],
"categories": [
"physics.acc-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Square matrix-based six-dimensional convergence map for nonlinear beam dynamics analysis",
"url": "https://arxiv.org/abs/2601.09574",
"version": "v1"
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