1. RHIC Spin and Collider Mei Bai

2. Outline  Introduction: why polarized protons  spin “crisis”  accelerate polarized protons to high energy  RHIC: the first polarized proton collider  brief history of RHIC spin program  achieved performance of RHIC pp  Conclusion  plan for RHIC improvements

3. What is Spin? From Google… revolve quickly and repeatedly around one's own axis, "The dervishes whirl around and around without getting dizzy" twist and turn so as to give an intended interpretation, "The President's spokesmen had to spin the story to make it less embarrassing" a distinctive interpretation (especially as used by politicians to sway public opinion), "the campaign put a favorable spin on the story"

4. What is Spin? Classical definition the body rotation around its own axis Particle spin: an intrinsic property, like mass and charge a quantum degree freedom associated with the intrinsic magnetic moment. G: anomalous gyromagnetic factor, describes the particle internal structure. For particles: point-like: G=0 electron: G=0.00115965219 muon: G=0.001165923 proton: G=1.7928474 m: particle mass q: electrical charge of particle

5.  Spin: single particle  pure spin state align along a quantization axis  Spin vector S: a collection of particles  the average of each particle spin expectation value along a given direction spin vector and spin-orbit interaction S N  Spin orbit interaction SN  I S

6. Discovery of Spin: 1925 “This is a good idea. Your idea may be wrong, but since both of you are so young without any reputation, you would not lose anything by making a stupid mistake.” --- Prof. Ehrenfest G.E. Uhlenbeck and S. Goudsmit, Naturwissenschaften 47 (1925) 953. A subsequent publication by the same authors, Nature 117 (1926) 264,

7. Spin Crisis: what makes up the proton spin? P u d Sum of spins of all quarks CERN EMC and SLAC SMC:  ~ 20%!

8. Current model: Proton spin sum-rule Orbital angular momentum of quarks and gluons? Spin contribution from all the gluons?

9. gg q gluon spin contribution quark/antiquark spin contribution g High energy proton proton collisions: gluon gluon collision and gluon quark collision Quest to unveil the proton spin structure:

10. STAR RHIC: world’s first polarized proton collider

11. RHIC spin physics STAR Excellent calorimeter granularity and muon detection electrons, muons, photons and leading hadrons  measure gluon spin contribution  g  measure quark and anti quark spin contribution Large acceptance with Time Projection Chamber and calorimeters Jets and photons and electrons

12. 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

13. Figure of merit of polarized proton collider  Luminosity:  number of particles per unit area per unit time. The higher the luminosity, the higher the collision rates  beam polarization  Statistical average of all the spin vectors.  zero polarization: spin vectors point to all directions.  100% polarization: beam is fully polarized if all spin vectors point to the same directions. Transverse beam size # of particles in one bunch # of bunches

14. Basics of circular accelerator bending dipole Constant magnetic field Keeps particles circulating around the ring quadrupole Magnetic field proportional to the distance from the center of the magnet. Keeps particles focused radio frequency cavities Electric field for acceleration and keeping beam bunched longitudinally

15. Closed orbit in a circular accelerator Closed orbit in a machine with dipole errors Closed orbit in a perfect machine: center of quadrupoles Courtesy of Lingyun Yang Closed orbit: particle comes back to the same position after one orbital revolution

16. Betatron oscillation in a circular accelerator Beta function Betatron tune: number of oscillations in one orbital revolution Courtesy of Lingyun Yang

17. Spin motion in circular accelerator: Thomas BMT Equation In a perfect accelerator, spin vector precesses around the bending dipole field direction: vertical Spin tune Qs: number of precessions in one orbital revolution. In general, Spin vector in particle’s rest frame B beam

18. polarized proton acceleration challenges: preserve beam polarization Depolarization(polarization loss) mechanism  Come from the horizontal magnetic field which kicks the spin vector away from its vertical direction  Spin depolarizing resonance : coherent build-up of perturbations on the spin vector when the spin vector gets kicked at the same frequency as its precession frequency x y z beam Initial x y z beam 1 st full betatron Oscillation period x y z beam 2nd full betatron Oscillation period

19. spin depolarizing resonance Imperfection resonance Source: dipole errors, quadrupole mis- alignments Resonance location: G  = k k is an integer Intrinsic resonance Source: horizontal focusing field from betatron oscillation Resonance location: G  = kP±Qy, P is the periodicity of the accelerator, Qy is the vertical betatron tune

20. Intrinsic spin resonance Q x =28.73, Q y =29.72, emit= 10 Spin depolarization resonance in RHIC For protons, imperfection spin resonances are spaced by 523 MeV the higher energy, the stronger the depolarizing resonance

21.  First invented by Derbenev and Kondratenko from Novosibirsk in 1970s  A group of dipole magnets with alternating horizontal and vertical dipole fields  rotates spin vector by 180 o Innovative polarized proton acceleration techniques: Siberian snake

22. Particle trajectory in a snake:

23.  Use one or a group of snakes to make the spin tune to be at ½ How to preserve polarization using Siberian snake(s) y z beam y z  Break the coherent build- up of the perturbations on the spin vector

24. Accelerate polarized protons in RHIC

26. Polarized proton in the AGS  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    

27. AGS polarized proton development 1988Harmonic correction Fast tune jumpMonths21.70.10842 imperfectionintrinsicSetup timeEnergy GeV Int [10 11 ] Pol [%] 19945%solenoid partial snake Fast tune jump2 weeks23.00.0531 19985%solenoid partial snake AC dipole @ 3 strong intrinsic resonance 2 weeks23.00.0537 20055%helical partial snake AC dipole @ 4 strong intrinsic resonance 2 weeks23.81.050 2000New polarized H- source with high current high polarization 20055% helical partial snake +10% super-conducting helical partial snake 2 weeks23.81.565

28. Polarized proton acceleration setup in 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

29. Polarized proton acceleration in RHIC

30. 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

31. z beam y -x y z beam z y -x z beam y -x z beam y -x z beam y -x

32. Snake resonance observed in RHIC 7/10 snake resonance

33. How to avoid a snake resonance  Keep the spin tune as close to ½ as possible 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 snake current setting

34. How to avoid a snake resonance  Keep the vertical closed orbit as flat as possible rms: 0.45mm

35. How to avoid a snake resonance  Keep the spin tune as close to ½ as possible  snake current setting  Keep the vertical closed orbit as flat as possible  orbit control  Keep the betatron tunes away from snake resonance locations Precise tune control

36. Betatron tune along the ramp flattop *=2m 10 seconds after flattop beta1 *=2m ¾ snake resonance 7/10 snake resonance

37. Milestones of RHIC pp development 2000  New polarized proton source  One snake installed in Blue ring of RHIC  New fast polarimeter in Blue 2002  All 4 snakes for both rings and CNI polarimeter in Yellow 2003  Spin rotators 2004  RHIC absolute polarimeter using H Jet target  AGS 5% helical warm snake 2005  New super-conducting solenoid for the polarized H- source  205 GeV polarized protons with ~ 30% polarization  AGS strong super-conducting helical snake 2006  Dual snake configuration for the AGS and reached a polarization of 65% at the AGS extraction with 1.5x10 11 protons per bunch  250 GeV polarized protons in RHIC with a polarization of 45%

38. RHIC pp performance Courtesy of W. Fischer

39. RHIC pp performance: polarization transmission efficiency

40. Intrinsic spin resonance Q x =28.73, Q y =29.72, emit= 10 Achieved Physics Run RHIC intrinsic spin resonance strength Design goal

41. 45% ! First look of beam polarization at 250 GeV

42. Resonance around 138 GeV Polarization 250 GeV ramp measurement

43. Plan for RHIC polarized protons

44. Improve luminosity performance  Increase the average luminosity at 100 GeV from 6.0x10 30 cm -2 s -1 to 20x10 30 cm -2 s -1 (x3)  Luminosity limit beam-beam effect  Accelerator developments to mitigate the beam- beam effect  increase bunch intensity  eliminate emittance grow  At 250 GeV: 150x10 30 cm -2 s -1

45. Reach polarization of 70% or higher  AGS:  operating the AGS with both betatron tunes in the spin tune gap to avoid additional polarization loss due to horizontal betatron oscillation as observed in RHIC 2006 Run  RHIC:  preserve beam polarization to 250 GeV Improve the tune control technique Improve the orbit control system to control the orbit distortion within 0.3mm or less.

46. Conclusion  Over the past 5 years,  all the essential hardware and diagnostic apparatus for polarized beam were put in place and successfully commissioned.  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, we expect RHIC to achieve the design goal in the near future.

47. Great physics is ahead of us, stay tuned in …

48. 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.

49. Acknowledgement

50. Special Thanks to my mentors Prof. S. Y. Lee, Indiana University Dr. Thomas Roser, C-A Department Dr. Mike Syphers, Fermi Lab.