Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 173-179 |
| Number of pages | 7 |
| Journal | Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment |
| Volume | 561 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 1 2006 |
| Externally published | Yes |
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Keywords
- Accelerator mappings
- Dynamical aperture
- SALI method
ASJC Scopus subject areas
- Instrumentation
- Nuclear and High Energy Physics
Cite this
Application of the SALI chaos detection method to accelerator mappings. / Bountis, T.; Skokos, Ch.
In: Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 561, No. 2, 01.06.2006, p. 173-179.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Application of the SALI chaos detection method to accelerator mappings
AU - Bountis, T.
AU - Skokos, Ch
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
UR - http://www.scopus.com/inward/record.url?scp=33646685229&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33646685229&partnerID=8YFLogxK
U2 - 10.1016/j.nima.2006.01.009
DO - 10.1016/j.nima.2006.01.009
M3 - Article
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 -