THEME SECTION: Nonlinear Dynamics and Complexity: Theory, Methods and Applications — PapersNo Access

EFFICIENT CONTROL OF ACCELERATOR MAPS

JEHAN BOREUX

Namur Center for Complex Systems, naXys, University of Namur, Rempart de la Vierge 8, Namur 5000, Belgium

Search for more papers by this author

TIMOTEO CARLETTI

Namur Center for Complex Systems, naXys, University of Namur, Rempart de la Vierge 8, Namur 5000, Belgium

Search for more papers by this author

CHARALAMPOS SKOKOS

Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany

Center for Research and Applications of Nonlinear Systems, University of Patras, GR-26500 Patras, Greece

Search for more papers by this author

YANNIS PAPAPHILIPPOU

CERN, CH-1211 Geneva 23, Switzerland

Search for more papers by this author

, and

MICHEL VITTOT

Centre de Physique Théorique, Aix-Marseille Universite, CNRS-UMR 7332, USTV, FRUMAM F-13288 Marseille, cedex 9, France

Search for more papers by this author

https://doi.org/10.1142/S0218127412502197Cited by:15 (Source: Crossref)

Abstract

Recently, the Hamiltonian Control Theory was used in [Boreux et al., 2012] to increase the dynamic aperture of a ring particle accelerator having a localized thin sextupole magnet. In this paper, these results are extended by proving that a simplified version of the obtained general control term leads to significant improvements of the dynamic aperture of the uncontrolled model. In addition, the dynamics of flat beams based on the same accelerator model can be significantly improved by a reduced controlled term applied in only one degree of freedom.

Keywords:

References

J. Boreuxet al., Commun. Nonlin. Sci. Numer. Simulat. 17, 1725 (2012), DOI: 10.1016/j.cnsns.2011.09.037. Crossref, Web of Science, Google Scholar
N. Bourbaki , Eléments de Mathématiques: Groupes et Algèbres de Lie ( Hermann Ed , Paris , 1972 ) . Google Scholar
T. Bountis and S. Tompaidis, Future Problems in Nonlinear Particle Accelerators, eds. G. Turchetti and W. Scandale (World Scientific, Singapore, 1991) p. 112. Google Scholar
T. Bountis and Ch. Skokos, Nucl. Instr. Meth. Phys. Res. — Sect. A 561, 173 (2006), DOI: 10.1016/j.nima.2006.01.009. Crossref, Web of Science, Google Scholar
T. Bountis and Ch. Skokos, Phys. Lett. A 358, 126 (2006), DOI: 10.1016/j.physleta.2006.05.011. Crossref, Web of Science, Google Scholar
C. Chandreet al., Physica D 208, 131 (2005), DOI: 10.1016/j.physd.2005.06.016. Crossref, Web of Science, Google Scholar
E. Forest , Beam Dynamics, A New Attitude and Framework ( Harwood Academic , Chur, Switzerland , 1998 ) . Google Scholar
Laskar, J. [1999] "Introduction to frequency map analysis," Proc. 3DHAM95 NATO Advanced Institute, ed. Simoó, C. (SAgaro, June 1995) . Google Scholar
Ch. Skokos, J. Phys. A 34, 10029 (2001), DOI: 10.1088/0305-4470/34/47/309. Crossref, Google Scholar
Ch. Skokoset al., Prog. Theor. Phys. Supp. 150, 439 (2003), DOI: 10.1143/PTPS.150.439. Crossref, Google Scholar
Ch. Skokoset al., J. Phys. A 37, 6269 (2004), DOI: 10.1088/0305-4470/37/24/006. Crossref, Google Scholar
Ch. Skokos, T. Bountis and Ch. Antonopoulos, Physica D 231, 30 (2007), DOI: 10.1016/j.physd.2007.04.004. Crossref, Web of Science, Google Scholar
M. Vittot, J. Phys. A 37, 6337 (2004), DOI: 10.1088/0305-4470/37/24/011. Crossref, Google Scholar
M. N. Vrahatis, H. Isliker and T. C. Bountis, Int. J. Bifurcation and Chaos 7, 2707 (1997). Link, Web of Science, Google Scholar
H. Widemann , Particle Accelerator Physics ( Springer Verlag Ed , NY , 2007 ) . Google Scholar