Skip to main content
SpringerLink
Log in

A canonical 8-dimensional formalism for classical spin-orbit motion in storage rings

II. Normal forms and the n-axis

  • Theoretical Physics
  • Published:
Zeitschrift für Physik C Particles and Fields

Abstract

The two real canonical spin variables α and β introduced in an earlier paper to describe spin motion in storage rings [1] are combined with the six canonical variables of coupled synchro-betatron motion to form a system of eight canonical spin-orbit variables in which spin and orbital motion are treated on the same level. In these variables on turn maps are origin preserving and the usual techniques of canonical perturbation theory can be applied. By writing the Hamiltonian in normal form the spin detuning terms as well as the so calledn-axis, the semiclassical spin axis which is needed in the theory of radiative polarization, can be constructed. The equations derived are valid for arbitrary particle velocity (below and above transition energy).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D.P. Barber, K. Heinemann, G. Ripken: in this issue of Z. Phys. C.; see also DESY 91-047 by the same authors

  2. A.W. Chao: Nucl. Instrum. Methods 180 (1981) 29, also in: Physics of High Energy Particle Accelerators, American Institute of Physics Proceedings 87, p. 395, 1982

    Google Scholar 

  3. K. Yokoya: DESY Report 86-57, 1986

  4. Y.S. Derbenev: University of Michigan, Ann Arbor Preprint. UM HE 90-23, 1990; Y.S. Derbenev: University of Michigan, Ann Arbor Preprint, UM HE 90-30, 1990; Y.S. Derbenev: University of Michigan, Ann Arbor Preprint, UM HE 90-32, 1990

  5. Y.S. Derbenev, A.M. Kondratenko: Sov. Phys. JETP 37 (6) (1973) 968

    Google Scholar 

  6. D.P. Barber, K. Heinemann, G. Ripken: DESY M-92-04, 1992

  7. G. Ripken, F. Willeke: DESY 90-001, 1990; Part. Acc. 27 (1990) 203

  8. K. Yokoya: Nucl. Instrum. Methods A258 (1987) 149

    Google Scholar 

  9. K. Yokoya: KEK Preprint KEK 92-06, 1992

  10. Yu. Eidelman, V. Yakimenko: Proceedings of the 1991 IEEE Particle Accelerator Conference, San Francisco, USA, p. 269, 1991

  11. Yu. Eidelman, V. Yakimenko: Proceedings of the 1993 IEEE Particle Accelerator Conference, Washington DC, USA, p. 450, 1993

  12. V. Balandin, N. Golubeva: Proceedings of the XV International Conference on High Energy Particle Accelerators, Int. J. Mod. Phys. A (Proc. Suppl.) 2B (1992) 998

    Google Scholar 

  13. V. Balandin, N. Golubeva: Proceedings of the 1993 IEEE Particle Accelerator Conference, Washington DC, USA, p. 441, 1993

  14. S.R. Mane: Phys. Lett. A177 (1993) 411

    Google Scholar 

  15. D. Bohm: Quantum theory. New York: Prentice-Hall 1951

    Google Scholar 

  16. L. Thomas: Phil. Mag. 3 (1927) 1

    Google Scholar 

  17. V. Bargmann, L. Michel, V.L. Telegdi: Phys. Rev. Lett. 2 (1959) 435

    Google Scholar 

  18. A.O. Barut: Electrodynamics and classical theory of fields and particles: New York: Macmillan 1964

    Google Scholar 

  19. G. Ripken: DESY 85-84, 1985

  20. D.P. Barber, G. Ripken, F. Schmidt: DESY 87-36, 1987

  21. E. Courant, H. Snyder: Ann. Phys. 3 (1958) 1

    Google Scholar 

  22. G. Ripken, E. Karantzoulis: DESY 86-29, 1986

  23. H. Mais, G. Ripken: DESY 83-62, 1983

  24. H. Mais, G. Ripken: DESY M-82-05, 1982

  25. K. Yokoya: KEK Report 92-6, 1992

  26. S.R. Mane: Phys. Rev. A36 (1987) 105

    Google Scholar 

  27. F. Willeke, G. Ripken: DESY 88-114, 1988; also in: Physics of Particle Accelerators; American Institute of Physics Conference Proceedings 184, p. 758, 1989

  28. D.P. Barber, K. Heinemann, H. Mais, G. Ripken: DESY 91-146, 1991

  29. A. Schoch: CERN 57-21, 1958

  30. G. Guignard: CERN 78-11, 1978

  31. F. Willeke: Fermi National Accelerator Laboratory, FN-422, 1985

  32. D.P. Barber, H. Mais, G. Ripken, F. Willeke: DESY 86-147, 1986

  33. H. Goldstein: Classical mechanics, New York: Addison-Wesley 1980

    Google Scholar 

  34. F.D. Courant, R.D. Ruth, W.T. Weng: SLAC-PUB-3415, 1984; also in: Physics of High Energy Particle Accelerators: American Institute of Physics Conference Proceedings 127, p. 294, 1985

  35. S.R. Mane: DESY 85-125, 1985

  36. M. Berz, E. Forest: J. Irwin: Part. Acc. 24 (1989) 91

    Google Scholar 

  37. K. Symon: in: The physics of particle accelerators: American Institute of Physics Conference Proceedings 249, p. 277, 1992

  38. H. Mais, G. Ripken: DESY 86-29, 1986

  39. G. Ripken: DESY R1-70/04, 1970

  40. D.P. Barber, K. Heinemann, G. Ripken: Submitted to Z. Phys. C.

Download references

Author information

Authors and Affiliations

  1. Deutsches Elektronen-Synchrotron Desy, D-22603, Hamburg, Germany

    D. P. Barber, K. Heinemann & G. Ripken

Authors
  1. D. P. Barber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Heinemann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. Ripken
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barber, D.P., Heinemann, K. & Ripken, G. A canonical 8-dimensional formalism for classical spin-orbit motion in storage rings. Z. Phys. C - Particles and Fields 64, 143–167 (1994). https://doi.org/10.1007/BF01557244

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01557244

Keywords

Search

Navigation