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  • Open Access

Innovative method to measure the extent of the stable phase-space region of proton synchrotrons

E. H. Maclean1,2, M. Giovannozzi2,*, and R. B. Appleby3

  • 1University of Malta, Msida MSD 2080, Malta
  • 2Beams Department, CERN, 1211 Geneva 23, Switzerland
  • 3The University of Manchester and Cockcroft Institute, Manchester M13 9PL, United Kingdom

  • *Corresponding author. massimo.giovannozzi@cern.ch
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Phys. Rev. Accel. Beams 22, 034002 – Published 12 March, 2019

DOI: https://doi.org/10.1103/PhysRevAccelBeams.22.034002

Abstract

The advent of circular accelerators based on superconducting magnets has revolutionized the field of beam dynamics, with particle motion turning from linear to nonlinear due to unavoidable high-order field errors generated by the ring magnets. Nonlinear dynamics was already well mastered, e.g., in the close field of celestial mechanics as similar problems had been considered and successfully tackled. Hence, several results were available to aid comprehension of the behavior of charged particle beams under the influence of nonlinear forces. Here, we discuss how concepts derived from the theory of dynamical systems, linked with the fundamental Kolmogorov–Arnold–Moser theory and Nekhoroshev theorem, can be successfully applied to the analysis of nonlinear motion of charged particles in a circular accelerator. Based on these ideas, an innovative method to measure the extent of the phase-space region within which bounded motion occurs is presented, which has been successfully tested for the first time at the CERN LHC.

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References (46)

  1. N. M. Gelfand, in Proceedings of SSC Workshop on Accelerator Physics Issues for a Superconducting Super Collider, Ann Arbor, MI, USA, 1983, edited by M. Tigner (Michigan Trout Unlimited, Ann Arbor, MI, 1984), p. 190.
  2. V. Visnjic, in Proceedings of 1991 Particle Accelerator Conference, edited by J. Chew and L. Lizama (IEEE, Piscataway, NJ, 1991), p. 1701.
  3. V. Visnjic, in Proceedings of Workshop On Nonlinear Problems In Future Particle Accelerators, edited by W. Scandale and G. Turchetti (World Scientific, Singapore, 1991).
  4. R. Brinkmann and F. Willeke, DESY Report No. DESY-HERA-88-08, 1988.
  5. F. Zimmermann and F. Willeke, DESY Report No. DESY-HERA-91-08, 1991.
  6. F. Zimmermann, SLAC Report No. SLAC-PUB-6458, 1994.
  7. O. S. Brüning et al., Comparison of measured and computed dynamic aperture for the SPS and the HERA proton ring, Part. Accel. 54, 223 (1996).
  8. Y. Luo et al., in Proceedings of 2007 Particle Accelerator Conference, edited by C. Petit-Jean-Genaz (IEEE, Piscataway, NJ, 2007), p. 4363.
  9. T. Sen, A. Chao, and Y. Yan, in Proceedings of 1991 Particle Accelerator Conference, edited by L. Lizama and J. Chew (IEEE, Piscataway, NJ, 1991), p. 345.
  10. L. Schachinger and Y. Yan, SSC Laboratory Report No. SSC-N-664, 1989.
  11. O. Brüning et al., CERN Report No. CERN-2004-003-V-1, 2004.
  12. E. Todesco and M. Giovannozzi, Dynamic aperture estimates and phase-space distortions in nonlinear betatron motion, Phys. Rev. E 53, 4067 (1996).
  13. D. R. Douglas and A. J. Dragt, MARYLIE: The maryland lie algebraic transport and tracking code, IEEE Trans. Nucl. Sci. 30, 2442 (1983).
  14. A. J. Dragt, Elementary and advanced Lie algebraic methods with applications to accelerator design, electron microscopes, and light optics, Nucl. Instrum. Methods Phys. Res., Sect. A 258, 339 (1987).
  15. A. J. Draft, F. Neri, G. Rangarajan, D. R. Douglas, L. M. Healy, and R. D. Ryne, Lie algebraic treatment of linear and nonlinear beam dynamics, Annu. Rev. Nucl. Part. Sci. 38, 455 (1988).
  16. A. Bazzani, P. Mazzanti, G. Servizi, and G. Turchetti, Normal forms for Hamiltonian maps and nonlinear effects in a particle accelerator, Nuovo Cimento Soc. Ital. Fis. 102B, 51 (1988).
  17. E. Forest, M. Berz, and J. Irwin, Normal form methods for complicated periodic systems, Part. Accel. 24, 91 (1989).
  18. A. Bazzani, G. Servizi, E. Todesco, and G. Turchetti, Normal forms and invariants in the description of a magnetic lattice, Nucl. Instrum. Methods Phys. Res., Sect. A 298, 102 (1990).
  19. M. Giovannozzi, Proposed scaling law for intensity evolution in hadron storage rings based on dynamic aperture variation with time, Phys. Rev. ST Accel. Beams 15, 024001 (2012).
  20. M. Hénon and C. Heiles, The applicability of the third integral of motion: Some numerical experiments, Astron. J. 69, 73 (1964).
  21. C. Froeschlé, Numerical study of a four-dimensional mapping, Astron. Astrophys. 16, 172 (1972).
  22. G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn, Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; A method for computing all of them. Part 2: Numerical application, Meccanica 15, 21 (1980).
  23. F. Schmidt, F. Willeke, and F. Zimmermann, Fast indicators of long-term stability, Part. Accel. 35, 249 (1991).
  24. E. Todesco, M. Giovannozzi, and W. Scandale, Prediction of long-term stability in large hadron colliders, Part. Accel. 55, 273 (1995).
  25. M. Giovannozzi, W. Scandale, and E. Todesco, Dynamic aperture extrapolation in presence of tune modulation, Part. Accel. 56, 195 (1996).
  26. M. Giovannozzi, W. Scandale, and E. Todesco, Dynamic aperture extrapolation in the presence of tune modulation, Phys. Rev. E 57, 3432 (1998).
  27. M. Giovannozzi and E. McIntosh, Development of parallel codes for the study of nonlinear beam dynamics, Int. J. Mod. Phys. C 08, 155 (1997).
  28. W. Wan and J. R. Cary, Increasing the Dynamic Aperture of Accelerator Lattices, Phys. Rev. Lett. 81, 3655 (1998).
  29. W. Wan and J. R. Cary, Method for enlarging the dynamic aperture of accelerator lattices, Phys. Rev. ST Accel. Beams 4, 084001 (2001).
  30. C. L. Siegel and J. Moser, Lectures in Celestial Mechanics (Springer Verlag, Berlin, 1971).
  31. N. Nekhoroshev, An exponential estimate of the time of stability of nearly-integrable hamiltonian systems, Russ. Math. Surv. 32, 1 (1977).
  32. A. Bazzani, S. Marmi, and G. Turchetti, Nekhoroshev stability estimates for symplectic maps and physical applications, Cel. Mech. 47, 333 (1990).
  33. G. Turchetti, in Proceedings of Number Theory and Physics, edited by J. M. Luck, P. Moussa, and M. Waldschmidt, Springer Proceedings in Physics (Springer Verlag, Berlin, 1990), Vol. 47, p. 223.
  34. T. Collins et al., in Proceedings of the 1984 Snowmass Workshop on Design and Utilization of the Superconducting Super Collider, Snowmass, Colorado, 1984, edited by R. Donaldson and J. G. Morfin (Division of Particles and Fields of the American Physical Society, New York, 1984), p. 361.
  35. J. M. Peterson et al., in Proceedings of the 1988 European Particle Accelerator Conference, edited by S. Tazzari (World Scientific, Singapore, 1988), p. 266.
  36. W. Fischer, M. Giovannozzi, and F. Schmidt, Dynamic aperture experiment at a synchrotron, Phys. Rev. E 55, 3507 (1997).
  37. F. Willeke, in Proceedings of 1995 Particle Accelerator Conference (IEEE Service Center, Piscataway, 1996), p. 2747.
  38. E. H. Maclean, R. Tomás, F. Schmidt, and T. H. B. Persson, Measurement of nonlinear observables in the Large Hadron Collider using kicked beams, Phys. Rev. ST Accel. Beams 17, 081002 (2014).
  39. M. Albert et al., in Proceedings of the 3rd International Particle Accelerator Conference, New Orleans, LA, 2012, edited by C. Eyberger and F. Zimmermann (IEEE, Piscataway, NJ, 2012), p. 1362.
  40. M. Giovannozzi et al., in Proceedings of the 4th International Particle Accelerator Conference, IPAC-2013, Shanghai, China, 2013, edited by Z. Dai, C. Petit-Jean-Genaz, V. R. W. Schaa, and C. Zhang (JACoW, Shanghai, China, 2013), p. 2606.
  41. S. Fartoukh and M. Giovannozzi, Dynamic aperture computation for the as-built CERN Large Hadron Collider and impact of main dipoles sorting, Nucl. Instrum. Methods Phys. Res., Sect. A 671, 10 (2012).
  42. http://sixtrack.web.cern.ch/SixTrack/.
  43. E. H. Maclean et al. (to be published).
  44. J. Barranco et al., LHC@Home: a BOINC-based volunteer computing infrastructure for physics studies at CERN, Open Eng. 7, 378 (2017).
  45. E. H. Maclean, R. Tomás, M. Giovannozzi, and T. H. B. Persson, First measurement and correction of nonlinear errors in the experimental insertions of the CERN Large Hadron Collider, Phys. Rev. ST Accel. Beams 18, 121002 (2015).
  46. G. Apollinari et al., CERN Report No. CERN-2015-005.

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Phys. Rev. Accel. Beams 22, 034002– Published 12 March, 2019
  • Received 10 January 2019
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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