Application of the SALI chaos detection method to accelerator mappings

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dc.creatorBountis, T.
dc.creatorSkokos, Ch.
dc.date2005-12-13
dc.date.accessioned2026-07-07T10:47:02Z
dc.date.available2026-07-07T10:47:02Z
dc.descriptionWe 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.
dc.description7 pages, 6 figures, to appear in 'Nuclear Instruments and Methods in Physics Research - Section A'
dc.identifierhttps://arxiv.org/abs/physics/0512115
dc.identifierhttp://arxiv.org/abs/physics/0512115
dc.identifierNucl.Instrum.Meth.A561:173-179,2006
dc.identifierdoi:10.1016/j.nima.2006.01.009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183433
dc.subjectAccelerator Physics
dc.subjectAstrophysics
dc.subjectChaotic Dynamics
dc.titleApplication of the SALI chaos detection method to accelerator mappings
dc.typetext

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