Polarization Issues

  • Michiko G. Minty
  • Frank Zimmermann
Open Access
Part of the Particle Acceleration and Detection book series (PARTICLE)


The study of spin dynamics in synchrotrons has evolved over the years as has the desire for achieving polarized particle beams of the highest possible beam energies. A selection of reviews of the dynamics of polarized beams may be found in [1]–[9]. In this chapter, we focus on experimental data and describe spin transport in circular accelerators and transport lines. Except where explicitly mentioned, radiative effects in electron accelerators or very high energy proton accelerators are not treated here. We begin with a review of the Thomas-BMT equation for spin motion. This will be given in terms of the SU(2) spinor representation. Spinor algebra will be introduced and applied in the description of techniques used for preserving the beam polarization during acceleration through depolarizing resonances at moderate beam energies.


Closed Orbit Spin Motion Spin Precession Resonance Strength Resonance Tune 
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  1. 1.
    E.D. Courant: Bull. Am. Phys. Soc. 7, 33 (1962); E.D. Courant, R.D. Ruth: The Acceleration of Polarized Protons in Circular Accelerators. BNL 51270 (1980)Google Scholar
  2. 2.
    A.W. Chao: Polarization of a Stored Electron Beam. In: Proc. 1981 Fermilab Summer School, Batavia, 1981 vol. 1, p. 395Google Scholar
  3. 3.
    A.W. Chao: Nucl. Instr. Meth. A 180, 29 (1981)CrossRefADSGoogle Scholar
  4. 4.
    A.W. Chao, K. Yokoya: An Alternative Longitudinal Polarization Scheme for Tristan. KEK 81–7 (1981)Google Scholar
  5. 5.
    B.W. Montague: Phys. Rep. 113, 1 (1984)CrossRefADSGoogle Scholar
  6. 6.
    S.Y. Lee: Spin Dynamics and Snakes in Synchrotrons ( World Scientific, Singapore, 1997 )CrossRefGoogle Scholar
  7. 7.
    D.P. Barber: Electron and Proton Spin Polarization in Storage Rings — an Introduction. In: Proc. Advanced ICFA Beam Dynamics Workshop on Quantum Aspects in Beam Physics ed. by P. Chen ( World Scientific, Singapore, 1999 )Google Scholar
  8. 8.
    G.H. Hoffstaetter: A Modern View of High Energy Polarized Proton Beams, Springer Tracts in Modern Physics, to be publishedGoogle Scholar
  9. 9.
    M. Vogt: Bounds on the Maximum Attainable Equilibrium Spin Polarization of Protons at High Energy in HERA. Ph.D. thesis, University of Hamburg, DESY-THESIS-2000–054 (2000)Google Scholar
  10. 10.
    L.H. Thomas: Philos. Mag. 3, 1 (1927)CrossRefGoogle Scholar
  11. 11.
    V. Bargman, L. Michel, V.L. Telegdi: Phys. Rev. Lett. 2, 435 (1959)CrossRefADSGoogle Scholar
  12. 12.
    J.D. Jackson: Classical Electrodynamics ( Wiley and Sons, New York, 1975 )zbMATHGoogle Scholar
  13. 13.
    T. Roser: In Handbook of Accelerator Physics and Engineering ed. by A.W. Chao, M. Tigner, second edition (World Scientific, Singapore, Singapore, 2002 )Google Scholar
  14. 14.
    T. Limberg, P. Emma, R. Rossmanith: The North Arc of the SLC as a Spin Rotator. In: Proc. IEEE PAC 93, Washington, DC, 1993 ( IEEE, Piscataway 1993 ) p. 429Google Scholar
  15. 15.
    P. Emma, T. Limberg, R. Rossmanith: Depolarization in the SLC Collider Arcs. In: Proc. EPAC 94, London, 1994 ( World Scientific, Singapore 1994 )Google Scholar
  16. 16.
    T. Khoe, R.L. Kustom, R.L. Martin et al.: Part. Accel. 6, 213 (1975)Google Scholar
  17. 17.
    E. Grorud, J.L. Laclare, G. Leleux et al.: ‘Crossing of Depolarization Resonances at Saturne (Saclay)’. In: Proc. High Energy Spin Physics(Brookhaven, 1982)Google Scholar
  18. 18.
    F.Z. Khiari, P.R. Cameron, G.R. Court et al.: Phys. Rev. D 39, 45 (1989)CrossRefADSGoogle Scholar
  19. 19.
    H. Sato, D. Arakawa, S. Hiramatsu et al.: Nucl. Instr. Meth. A 272, 617 (1988)CrossRefADSGoogle Scholar
  20. 20.
    A.D. Krisch, S.R. Mane, R.S. Raymond, et al.: Phys. Rev. Lett. 63, 1137 (1989)CrossRefADSGoogle Scholar
  21. 21.
    J.E. Goodwin, H.O. Meyer, M.G. Minty et al.: Phys. Rev. Lett. 64, 2779 (1990)CrossRefADSGoogle Scholar
  22. 22.
    J.E. Goodwin: Ph.D. dissertation, Indiana University (1990)Google Scholar
  23. 23.
    H. Spinka, D. Underwood, L. Ahrens et al.: ‘Commissioning and Future Plans for Polarized Protons in RHIC’. In: Proc. PAC 2001, Chicago, Illinois, 2001 ( IEEE, Piscataway 2001 )Google Scholar
  24. 24.
    D.P. Barber, M. Boge, H.D. Bremer et al.: Nucl. Instr. Meth. A 338, 166 (1994)CrossRefADSGoogle Scholar
  25. 25.
    R. Rossmanith, R. Schmidt. Nucl. Instr. Meth. A 236, 231 (1985)Google Scholar
  26. 26.
    D.P. Barber, G. Ripken: In: A. Chao, M. Tigner (eds.): Handbook of Accelerator Physics and Engineering, second edition ( World Scientific, Singapore, 2002 )Google Scholar
  27. 27.
    M. Böge, R. Brinkmann. Optimization of Electron Spin Polarization by Application of a Beam Based Alignment Technique in the HERA Electron Ring. In: Proc. 1995 Conf. in Accelerator Alignment, Tsukuba, Japan, 1995, p. 412Google Scholar
  28. 28.
    R. Brinkmann, M. Boege: Beam Based Alignment and Polarization Optimization in the HERA Electron Ring. In: Proc. EPAC 94, London, 1994 ( World Scientific, Singapore 1994 )Google Scholar
  29. 29.
    E. Gianfelice: Measurement of Beam Polarization and a 72°/72° Spin Matched Optics. In: HERA Accelerator Studies 2000 ed. by G. Hoffstaetter. DESY HERA 00–07 (2000)Google Scholar
  30. 30.
    R. Assmann, A. Blondel, B. Dehning et al.: ‘Deterministic Harmonic Spin Matching in LEP’. In: Proc. EPAC 94, London, 1994 ( World Scientific, Singapore 1994 ) p. 932Google Scholar
  31. 31.
    A.A. Sokolov, I.M. Ternov: Soy. Phys. Dokl. 8, 1203 (1964)ADSGoogle Scholar
  32. 32.
    M. Froissart, R. Stora: Nucl. Instr. Meth. 7, 297 (1960)CrossRefGoogle Scholar
  33. 33.
    Y. Cho, R.L. Martin, E.F. Parker et al. In: Proc. of High Energy Spin Symposium, Argonne, 1976 AIP Conf. Proc. 35(12), 396 (1976)Google Scholar
  34. 34.
    D.D. Caussyn, Ya.S. Derbenev, T.J.P. Ellison et al.: Phys. Rev. Lett. 73, 28572859 (1994)Google Scholar
  35. 35.
    S. Tepikian, S.Y. Lee, E.D. Courant: Part. Accel. 17, 1 (1986)Google Scholar
  36. 36.
    Ya.S. Derbenev, A.M. Kondratenko: In: Proc. of the 10th Intl. Conf. on High Energy Accel., Protvino, 1977 v. 2, p. 70Google Scholar
  37. 37.
    Ya.S. Derbenev: Part. Accel. 8, 115 (1978)Google Scholar
  38. 38.
    K. Steffen: Note on the Choice of Siberian Snake Configurations in Proton Rings. DESY HERA 85–24 (1985)Google Scholar
  39. 39.
    K. Steffen: Design of an Orthogonal Snake Pair for Proton Rings in the Few Gev Energy Range. DESY HERA 87–11 (1987)Google Scholar
  40. 40.
    K. Steffen: How to Avoid Imperfection Spin Resonances in a Protron Ring with Snakes. DESY 89–024 (1989)Google Scholar
  41. 41.
    E.D. Courant: Hybrid Helical Snakes and Rotators for RHIC. BNL-61920, BNLAD-133 (1995)Google Scholar
  42. 42.
    E. Courant, W. Fischer, A. Luccio et al.: ‘The Use of Helical Dipole Magnets in the RHIC Project’. In: Proc. Spin 96, Amsterdam, 1996Google Scholar
  43. 43.
    D.P. Barber, M. Boge, H.D. Bremer et al.: Phys. Lett. B343, 436 (1995)CrossRefGoogle Scholar
  44. 44.
    B.W. Montague: CERN/ISR-LTD/76–2 (1976)Google Scholar
  45. 45.
    J. Buon: Prescriptions for 90-Percent Spin Rotators in Electron Rings. LAL/RT/81–08 (1981)Google Scholar
  46. 46.
    S.Y. Lee, S. Tepikian: Phys. Rev. Lett.56, 1635 (1986)CrossRefADSGoogle Scholar
  47. 47.
    R.A. Phelps, V.A. Anferov, B.B. Blinov et al.: Phys. Rev. Lett. 78, 2772 (1997)CrossRefADSGoogle Scholar
  48. 48.
    T. Roser. In: Proc. 1990 Partial Siberian Snake Workshop, Brookhaven, NY, 1990Google Scholar
  49. 49.
    B. Blinov, C.M. Chu, E.D. Courant et al.: Phys. Rev. Lett. 73, 1621 (1994)CrossRefADSGoogle Scholar
  50. 50.
    H. Huang, L. Ahrens, J.G. Alessi, et al.: Phys. Rev. Lett. 73, 2982 (1994)CrossRefADSGoogle Scholar
  51. 51.
    M. Bai, L. Ahrens, J.G. Alessi et al.: Phys. Rev. Lett. 80, 21, 4673 (1998)CrossRefADSGoogle Scholar
  52. 52.
    D.A. Crandell, V.A. Anferov, B.B. Blinov et al.: Phys. Rev. Lett. 77, 1763, 4673 (1996)Google Scholar
  53. 53.
    S.Y. Lee: Prospects for Polarization at RHIC and SSC. In: AIP Conf. Proc. 224, (1991) p.35Google Scholar

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Authors and Affiliations

  • Michiko G. Minty
    • 1
  • Frank Zimmermann
    • 2
  1. 1.DESY - MDEHamburgGermany
  2. 2.AB Division, ABP GroupCERNGeneva 23Switzerland

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