TY - JOUR
T1 - Application of the SALI chaos detection method to accelerator mappings
AU - Bountis, T.
AU - Skokos, Ch
N1 - Funding Information:
Ch. Skokos was partially supported by the Research Committee of the Academy of Athens and the EMPEIRIKEION Foundation. T. Bountis acknowledges the partial support of the European Social Fund (ESF), Operational Program for Educational and Vocational Training II (EPEAEK II) of the Greek Ministry of Education and particularly the Programs “HERAKLEITOS” and “PYTHAGORAS II”.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2006/6/1
Y1 - 2006/6/1
N2 - We apply the Smaller ALignment Index (SALI) method to a four-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 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 dynamical aperture of a proton beam, passing repeatedly through an array of magnetic focusing elements.
AB - We apply the Smaller ALignment Index (SALI) method to a four-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 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 dynamical aperture of a proton beam, passing repeatedly through an array of magnetic focusing elements.
KW - Accelerator mappings
KW - Dynamical aperture
KW - SALI method
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U2 - 10.1016/j.nima.2006.01.009
DO - 10.1016/j.nima.2006.01.009
M3 - Article
AN - SCOPUS:33646685229
VL - 561
SP - 173
EP - 179
JO - Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
JF - Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
SN - 0168-9002
IS - 2
ER -