1. Accelerating Polarized Protons to High Energy Mei Bai Collider Accelerator Department Brookhaven National Laboratory

2. Outline General introduction of accelerator physics spin dynamics Accelerating polarized protons to high energy RHIC: the first polarized proton collider brief history of RHIC pp program achieved performance of RHIC pp Summary

3. Synchrotron The acceleration comes from the electric field with an oscillating frequency synchronized with the particle’s revolution frequency Alternating gradient A proper combination of focusing and de- focusing quadrupoles yields a net focusing force in both horizontal and vertical planes FODO cell: most popular building block for synchrotrons QF QD QF L L Rf cavity

4. Particle motion in a synchrotron Transverse Betatron oscillation: Betatron tune: number of betatron oscillations in one orbital revolution Beta function: the envelope of the particle’s trajectory along the machine

5. Spin motion in a circular accelerator Thomas BMT equation In a perfect accelerator, spin vector precesses around its guiding field, i.e. vertical Spin tune Qs: number of precessions in one orbital revolution. In general, horizontal field kicks the spin vector away from its stable direction, i.e. vertical, and can lead to  Depolarization resonance when the spin vector gets kicked at a frequency close to the frequency it precesses y x z beam direction

6. Depolarizing spin resonances For protons, imperfection spin resonances are spaced by 523 MeV

7.  Break the resonance condition: Full Siberian snake  Rotates spin vector by 180 o  Cancels the kicks on the spin vector in between the snakes  Keeps the spin tune independent of energy Challenge in accelerating polarized protons to high energy: preserve beam polarization Partial snake  rotates spin vector by an angle of  <180 o  Keeps the spin tune away from integer Tune jump  Jump the betatron tune as quickly as possible  Intrinsic resonance only and can cause emittance blow up

8.  Change the resonance strength Minimize the resonance strength  Harmonic close orbit correction Imperfection resonance Operationally difficult for high energy accelerators Enhance the resonance strength to achieve full spin flip with normal resonance crossing rate  Induce full spin flip using an ac dipole Can only be applied to strong intrinsic spin resonances not ideal for coupling resonances Challenge in accelerating polarized protons to high energy: preserve beam polarization

10. Polarized proton acceleration complex at BNL  AGS (Alternating Gradient Synchrotron) Energy: 2.3 GeV ~ 23.8 GeV A total of 41 imperfection resonances and 7 intrinsic resonances from injection to extraction  One 5.9% partial snake plus one 10~15% partial snake    

11. Spin tune with two partial snakes Courtesy of T. Roser Spin tune Extraction 36+ Q y intrinsic resonance GG Vertical betatron tune Vertical component of stable spin

12. Tune scan with the AGS dual snake setup 15% cold snake +5.9% warm snake Courtesy of H. Huang Operating working point Snake resonances

13. Results of AGS dual snake setup  The dual snake setup in the AGS was successfully commissioned. With the four new trim quadrupoles located at the entrance and exit of the cold and the warm snakes for compensating the optics distortion from the focusing fields from the snakes, 1.5x10 11 protons with a beam polarization of 65% were accelerated with the vertical tune close to 9. H. Huang’s talk: “Polarized Proton Acceleration in the AGS with Two Helical Partial Snakes”, Oct. 2, 17:00, Hall II

14. Polarized proton acceleration complex at BNL  RHIC: Energy: 23.8 GeV ~ 250 GeV (maximum store energy) A total of 146 imperfection resonances and about 10 strong intrinsic resonances from injection to 100 GeV.  Two full Siberian snakes

15. snake depolarization resonance  Condition  even order resonance When m is an even number Disappears in the two snake case like RHIC if the closed orbit is perfect  odd order resonance When m is an odd number Driven by the intrinsic spin resonances Ramp working pt. Store working pt. 3/4 5/6 7/8 5/8

16. Snake resonance observed in RHIC ¼ snake resonance Coupled 3/14 snake resonance Maximum vertical tune|Horizontal tune – 3/14|

17. Snake resonance observed in RHIC 7/10 snake resonance polarized protons were accelerated to an energy of G  =63, a location of a strong intrinsic spin resonance

18. How to avoid a snake resonance  Keep the spin tune as close to 0.5 as possible snake current setting  Keep the vertical closed orbit as flat as possible Flat orbit: Sum of kicks on the spin vector from quads as well as the dipole correctors = 0

19. How to avoid a snake resonance  Keep the spin tune as close to 0.5 as possible snake current setting  Keep the vertical closed orbit as flat as possible  Keep the betatron tunes away from snake resonance locations Precise tune control

20. Polarized proton collisions in RHIC

21. Design parameters for RHIC pp ParameterUnitp-p relativistic , injection …25.9 relativistic , store …266.5 no of bunches, n b …112 ions per bunch, N b 10 11 2.0 emittance e N x,y 95% mm-mrad20 average luminosity 10 30 cm -2 s -1 150 polarization,store%70

22. Milestones of RHIC pp development 2000  New polarized proton source (OPPIS) commissioned  One snake was installed in Blue ring and commissioned  CNI polarimeter in Blue installed and commissioned 2002  All snakes for both rings installed and commissioned  CNI polarimeter in Yellow installed and commissioned 2003  Spin rotators installed and commissioned 2004  RHIC absolute polarimeter using H Jet target installed and commissioned  AGS 5% helical warm snake installed and commissioned 2005  New super-conducting solenoid was installed in the OPPIS source  Polarized protons in RHIC were accelerated to 205 GeV with about 30% polarization at top energy  AGS strong super-conducting helical snake installed and commissioned 2006  The AGS dual snake configuration was commissioned in the AGS. This configuration (10% cold snake + 5.9% warm snake) yields a polarization of 65% at the AGS extraction with 1.5x10 11 protons per bunch  Polarized protons were accelerated to 250 GeV with a polarization of 45%

23. RHIC pp achieved performance ParameterUnit20022003200420052006 No. of bunches--55 56106111 bunch intensity10 11 0.7 0.91.3 store energyGeV100 100 100 ** m3111 1 peak luminosity10 30 cm -2 s -1 2661035 average luminosity 10 30 cm -2 s -1 1446 20 Collision points--44432 Time in store%3041385646 average polarization, store %153546 47 47 60~65 Ptitsyn’s talk: “RHIC Performance with Polarized Protons in Run-6”, Oct. 2, 16:45, Hall II

24. one week shutdown RHIC pp performance: delivered luminosity  FY05: Provided a total of 12.6pb -1 luminosity with longitudinal polarization at STAR and PHENIX  FY06: faster setup, higher luminosity and higher polarization

25. Blue average polarization: 49.5% Yellow average polarization:44.5% RHIC pp performance: average store polarization FY2005 FY2006 Goal!

26. RHIC pp performance: polarization transmission efficiency

27. 45% First look of beam polarization at 250 GeV

28. Intrinsic spin resonance Q x =28.73, Q y =29.72, emit= 10 achieved RHIC intrinsic spin resonance strength

29. Resonance around 138 GeV Polarization 250 GeV ramp measurement

30. Outlook of RHIC polarized protons Luminosity:  Goal:  At 100 GeV: 60x10 30 cm -2 s -1 20x10 30 cm -2 s -1 (x3) Improve bunch intensity/emittance:  Injector Improvement  improve beam transfer efficiency  Eliminate beam emittance growth during ramp Improve luminosity lifetime:  10 Hz feedback loop to fight against the 10 Hz orbit jitter: work-in-progress  minimize non-linear triplet errors to improve the tolerance to beam-beam effect  At 250 GeV: 150x10 30 cm -2 s -1 (x2.5 compared w. 100 GeV)

31. Outlook of RHIC polarized protons Polarization Goal: 70% 65% AGS: operating the AGS with both betatron tunes placed in the spin tune gap that dual snakes provide.

32. Outlook of RHIC polarized protons Polarization Goal: 70% 65% AGS: operating the AGS with both betatron tunes placed in the spin tune gap that dual snakes provide RHIC: Snake current setting is critical to make sure the spin precession tune is very close to 0.5 Multiple techniques of measuring spin precession tune in RHIC are under development. Precise tune control Tune+decoupling feedback system comissioned in FY06 Precise orbit control Re-alignment of the machine Improve the quality as well as the robustness of the BPM system to achieve the rms value of the orbit distortion below 0.3mm

33. Summary  Over the past 5 years, all the essential hardware and diagnostic apparatus for polarized beam were put in place and successfully commissioned. RHIC has successfully accelerated polarized protons to 100 GeV with no polarization loss.  The performance of RHIC pp in Run 2006 was greatly improved due to the great success of the AGS dual snake setup as well as the improvement of RHIC systems.  The 500 GeV development demonstrated a beam polarization of 45% at 250 GeV and also identified the location of depolarizing resonances.  With the success in the AGS and improvements in RHIC, the RHIC 2006 has achieved a faster setup as well as higher luminosity.

34. Acknowledgement L. Ahrens, I.G. Alekseev, J. Alessi, J. Beebe-Wang, M. Blaskiewicz, A. Bravar, J.M. Brennan, D. Bruno, G. Bunce, J. Butler, P. Cameron, R. Connolly, J. Delong, T. D’Ottavio, A. Drees, W. Fischer, G. Ganetis, C. Gardner, J. Glenn, T. Hayes, H-C. Hseuh. H. Huang, P. Ingrassia, U. Iriso-Ariz, O. Jinnouchi, J. Laster, R. Lee, A. Luccio, Y. Luo, W.W. MacKay, Y. Makdisi, G. Marr, A. Marusic, G. McIntyre, R. Michnoff, C. Montag, J. Morris, A. Nicoletti, P. Oddo, B. Oerter, J. Piacentino, F. Pilat, V. Ptitsyn, T. Roser, T. Satogata, K. Smith, D.N. Svirida, S. Tepikian, R. Tomas, D. Trbojevic, N. Tsoupas, J. Tuozzolo, K. Vetter, M. Milinski. A. Zaltsman, A. Zelinski, K. Zeno, S.Y. Zhang.

35. Results of AGS dual snake setup Courtesy of L. Ahrens and K. Brown Beam intensity AGS bending magnet field Vertical betatron tune (8.98) Horizontal betatron tune 9.0 8.8 8.6

36. How to avoid a snake resonance  Keep the spin tune as close to 0.5 as possible snake current setting set the vertical tune to 0.745 measure the beam polarization with different snake current expect no depolarization if the corresponding spin tune is very close to 0.5

37. AGS Horizontal resonance Courtesy of F. Lin: “Exploration of Horizontal Intrinsic Spin Resonance in the AGS”, April 22, C14.00005 Target position P P 10% Cold snake 5.9% Warm snake 15% Cold snake 5.9% Warm snake The tilted stable spin direction also causes about ~5% depolarization at the locations of horizontal tunes