2005/12/13 by Tassos Bountis, T. Bountis, Ch. Skokos · 1 citation
Mathematics · Physics and Astronomy · #Artificial intelligence #CHAOS (operating system) #Chaotic #Computer science #Convergence (economics) #Function (biology) #Lyapunov exponent #Lyapunov function #Magnetic confinement fusion research #Mathematical analysis #Mathematics #Nonlinear system #Phase space #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quasiperiodic function #Scientific Research and Discoveries #Standard map #Statistical physics #Zero (linguistics) #astro-ph #nlin.CD #physics.acc-ph
paper · pdf · doi:10.1016/j.nima.2006.01.009
published as Nucl.Instrum.Meth.A561:173-179,2006 · 7 pages, 6 figures, to appear in 'Nuclear Instruments and Methods in Physics Research - Section A'
arxiv created 2005/12/13 · openalex publication_date 2006/01/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.