dorsal/arxiv
View SchemaApplication of the SALI chaos detection method to accelerator mappings
| Authors | T. Bountis, Ch. Skokos |
|---|---|
| Categories | |
| ArXiv ID | physics/0512115 |
| URL | https://arxiv.org/abs/physics/0512115 |
| DOI | 10.1016/j.nima.2006.01.009 |
| Journal | Nucl.Instrum.Meth.A561:173-179,2006 |
Abstract
We apply the Smaller ALignment Index (SALI) method to a 4--dimensional mapping of accelerator dynamics in order to distinguish rapidly, reliably and accurately between ordered and chaotic motion. The main advantage of this index is that it tends {\it exponentially} to zero in the case of chaotic orbits, while it fluctuates around non--zero values in the case of quasiperiodic trajectories. Thus, it avoids the notorious ambiguities concerning the eventual convergence of (maximum) Lyapunov exponents to (positive) non-zero values. Exploiting the different behavior of SALI in these two cases we produce phase space `charts' where regions of chaos and order are clearly identified. Evaluating the percentage of chaotic and escaping orbits as a function of the distance from the origin we are able to estimate rapidly and accurately the boundaries of the {\it dynamical aperture} of a proton beam, passing repeatedly through an array of magnetic focusing elements.
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"abstract": "We apply the Smaller ALignment Index (SALI) method to a 4--dimensional\nmapping of accelerator dynamics in order to distinguish rapidly, reliably and\naccurately between ordered and chaotic motion. The main advantage of this index\nis that it tends {\\it exponentially} to zero in the case of chaotic orbits,\nwhile it fluctuates around non--zero values in the case of quasiperiodic\ntrajectories. Thus, it avoids the notorious ambiguities concerning the eventual\nconvergence of (maximum) Lyapunov exponents to (positive) non-zero values.\nExploiting the different behavior of SALI in these two cases we produce phase\nspace `charts\u0027 where regions of chaos and order are clearly identified.\nEvaluating the percentage of chaotic and escaping orbits as a function of the\ndistance from the origin we are able to estimate rapidly and accurately the\nboundaries of the {\\it dynamical aperture} of a proton beam, passing repeatedly\nthrough an array of magnetic focusing elements.",
"arxiv_id": "physics/0512115",
"authors": [
"T. Bountis",
"Ch. Skokos"
],
"categories": [
"physics.acc-ph",
"astro-ph",
"nlin.CD"
],
"doi": "10.1016/j.nima.2006.01.009",
"journal_ref": "Nucl.Instrum.Meth.A561:173-179,2006",
"title": "Application of the SALI chaos detection method to accelerator mappings",
"url": "https://arxiv.org/abs/physics/0512115"
},
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