1. Thomas Roser SPIN 2008 October 10, 2008 The Future of High Energy Polarized Proton Beams Spin dynamics and depolarizing resonances Early multi-GeV polarized proton acceleration Polarized protons at BNL: from AGS to 250 GeV at RHIC Designing high energy colliders for polarized protons. From polarized protons at RHIC to polarized protons at LHC Polarimeters and spin diagnostics for high energy beams

2. Spin Dynamics in Rings Precession Equation in Laboratory Frame: (Thomas [1927], Bargmann, Michel, Telegdi [1959]) dS/dt = - (e/  m) [(1+G  B  + (1+G) B II ]  S Lorentz Force equation: dv/dt = - (e/  m) [ B  ]  v For pure vertical field: Spin rotates G  times faster than motion, sp = G  For spin manipulation: At low energy, use longitudinal fields At high energy, use transverse fields

3. Spin tune and Depolarizing Resonances Depolarizing resonance condition: Number of spin rotations per turn = Number of spin kicks per turn Spin resonance strength  = spin rotation per turn / 2  Imperfection resonance (magnet errors and misalignments): sp = n Intrinsic resonance (Vertical focusing fields): sp = Pn± Q y P: Superperiodicity [AGS: 12] Q y : Betatron tune [AGS: 8.75] Weak resonances: some depolarization Strong resonances: partial or complete spin flip Illustration by W.W. MacKay

4. Spin Resonance Crossing Froissart-Stora:  : crossing speed] Non-adiabatic (  2 /  1)  Adiabatic (  2 /  1) P f /P i = 1 P f /P i =  1  KGKG  G  K   KGKG G  =K

5. Spin Resonance Crossing Non-adiabatic (  2 /  1)  Adiabatic (  2 /  1) P f /P i = 1 P f /P i =  1 Imperfection Resonances: Correction Dipoles (  small) Partial Snake (  large) Intrinsic Resonances: Pulsed Quadrupoles (  large) RF Dipole (  large) Lattice modifications (  small) Strong Partial Snake (  large)

6. Polarized proton accelerations at the ZGS ZGS (up to 70% at 12 GeV/c) Weak resonances (  max ~ 0.002) Timing of betatron tune jump using polarization measurement

7. Polarized proton accelerations at the AGS AGS (up to 42% at 22 GeV/c) Strong resonances (  max ~ 0.03) Timing of betatron tune jump and adjusting dipole correction strength using polarization measurement

8. Siberian Snakes (Local Spin Rotators) cos(180  sp ) = cos(  /2) · cos(180  G  )   0   sp  n No imperfection resonances Partial Siberian snake (AGS)  = 180   sp = ½ No imperfection resonances and No Intrinsic resonances Full Siberian Snake (Ya.S. Derbenev and A.M. Kondratenko) Two Siberian Snakes (RHIC): sp = (      /180  (   : angles between snake axis and beam direction) Orthogonal snake axis: sp = ½ and independent of beam emittance (SRM, S. Mane)

9. RHIC – First Polarized Hadron Collider Without Siberian snakes: sp = G  = 1.79 E/m  ~1000 depolarizing resonances With Siberian snakes (local 180  spin rotators): sp = ½  no first order resonances Two partial Siberian snakes (11  and 27  spin rotators) in AGS

10. Siberian Snakes  AGS Siberian Snakes: variable twist helical dipoles, 1.5 T (RT) and 3 T (SC), 2.6 m long  RHIC Siberian Snakes: 4 SC helical dipoles, 4 T, each 2.4 m long and full 360  twist 2.6 m

11. Strong Partial Siberian Snake for AGS A strong partial Siberian snake generates large spin tune gap for G  = n. With strong enough snake, gap is large enough to cover both imperfection and intrinsic spin resonances. Note: With a strong snake, the stable spin direction will deviate from vertical direction Intrinsic resonance Imperfection resonance

12. Betatron Tune and Spin Tune     warm snake cold snake 9.00 8.90 8.95 8.85 sp and Q y GG 36+Q y 0+Q y 24-Q y 12+Q y 36-Q y 24+Q y 48-Q y

13. Ramp Measurement GG Polarimeter asymmetry

14. AGS Polarization  Dual Partial Snake in AGS avoided depolarization from most vertical depolarizing resonances and largely eliminated intensity dependence

15. Spin Resonances in RHIC w/o Snakes Intrinsic resonance strength for 10  mm mrad particle Imperfection resonance strength for corrected orbit (  = 0.15 mm) Imperfection resonance strength for uncorrected orbit (  = 28 mm)

16. Beam Polarization Near a Single Strong Intrinsic Resonance Without snakes: spin flip, width ~ ± 5  With snakes: opening/closing of “spin cone”, nodes at ± 2 Resonance strength  = 0.3, 0.6 GG With Snakes: Resonance crossing during acceleration is adiabatic with no polarization loss. GG

17. Snake Resonances single snake or two snakes with orbit errors two snakes (m: odd) New tune working point 1/6 3/14 3/10 1/10 Old tune working point 0.60.70.80.9 Stable polarization on resonance,  = 0.3 Higher order resonance condition sp + mQ y = k (m, k = integer) driven by interaction of intrinsic resonance G  + Q y = k with large spin rotations of dipoles and snakes. No non-linear drive term necessary – combination of rotations is already non-linear. “Snake resonance strength” depends on intrinsic resonance strength and therefore energy For sp =1/2+  sp  Q y = (2k-1)/2m-  sp /m First analytical solution of isolated resonance with snakes by S.R. Mane, NIM A 498 (2003) 1 1/4 3/8 1/6 1/10 1/8 1/123/10 0.60.70.80.9 Stable polarization on resonance,  = 0.3

18. Spin tracking through strongest RHIC resonances Two Siberian snakes 1 mm rms misalignment (Survey: < 0.5 mm) 0.2 mm rms closed orbit 20   m emittance (95%) Whole beam Edge particle

19. Luminosity and Polarization Lifetimes in RHIC at 100 GeV 19:0021:0023:0001:0003:00 20 40 60 0 50 0 0 10 20 Polarization [%] Luminosity [10 30 cm -2 s -1 ] Protons [10 11 ] Start of collisions Start of acceleration ramp 60 % polarization 100 150 30 Collimation complete

20. Polarized Proton Acceleration to 250 GeV 250 GeVinjection 45 % polarization on first acceleration to 250 GeV!

21. Ramp Measurement to 250 GeV Loss at strong intrinsic resonance (136 GeV) Horizontal tune close to 0.7

22. Limits for Siberian Snakes Spin rotation of Siberian snake (  ) > Spin rotation of resonance driving fields (  ) “Spin rotation of Siberian snake drives strong imperfection resonance” More realistically:  tot ~ 2  max Imperfection resonances   Energy Intrinsic resonances    Energy E max /GeV  E max /GeV Partial Siberian snakes (AGS,  ~ 27° )  <  24 5 One full snake  < 0.25 Two full snakes (RHIC)  < 0.5 250 16 16 full snakes (LHC?)  < 4 7000 84

23. Multiple Siberian Snakes For high energy rings with resonance strengths larger than ~ 0.5 multiple snake pairs need to be used. Many choices of snake axis angles give sp = ½ ! Which is best? K. Steffen (1985) and G. Hoffstaetter (2004) proposed to choose snake axes angles to minimize spin-orbit integrals or effective intrinsic resonance strength. Possible snake axis angles for 8 snakes in ring with 4-fold symmetry (HERA-p):

24. Multiple Siberian Snakes (cont’d) S.R. Mane showed that for a single strong intrinsic resonance the spin tune does not depend on the beam emittance if the snake axes angle increases in equal steps from one snake to the next. This may be a good starting point for a multiple snake design. 2 Snakes (RHIC)  = 90  4 Snakes (HERA-p?)  = 45  6 Snakes (Tevatron?)  = 30 , 90  8 Snakes (HERA-p?)  = 22.5 , 67.5  16 Snakes (LHC, replace 2 dipoles per arc with snakes,  E ~ 1.4%)  = 11.25 , 33.75 , 56.25 , 78.75 

25. Global imperfection resonances – ultimate energy limit? BPM Quad Corrector Correct orbit to minimize kicks: Orbit going through center of BPM’s Orbit without kicks  Residual orbit distortion after orbit correction drives imperfection resonance with a strength that is not affected by (multiple) Siberian snakes  Resonance strength needs to be less than 0.05 ( S. Y. Lee and E. D. Courant, Phys. Rev. D 41, 292 (1990))  At RHIC (250 GeV) this corresponds to ~250  m residual orbit error (OK)  At LHC (7 TeV) this corresponds to ~10  m residual orbit error ! (LHC orbit accuracy ~ 200  m)  Need beam based quadrupole offset measurement, using trim-quadrupoles (?)  Flatten actual beam orbit using H,V - beam position monitors ( ) and correctors (?) at each quadrupole:

26. Polarization at low beta IR RHIC LHC Strong focusing in final focus triplets reduces beam polarization at IR Spin rotation in triplet: ___ P  /P 0 ___ P 

27. Proton-Carbon Coulomb-Nuclear Interference Polarimeter Ultra-thin carbon ribbon target ~ 100 mono-layers think, 10  m wide beam view 1 3 4 5 6 2 Si strip detectors for recoil carbon (TOF, E C ) 30cm  A N  0.015, originates from anomalous magnetic moment of proton  At high energy A N is independent of beam energy  Negligible emittance growth per polarization measurement  Due to radiation cooling carbon target survives beam heating  Measures polarization and beam profile

28. Spin Flipper  Use spin resonance driven by AC dipole(s) to induce spin flip  Single AC dipole (oscillation) drives two resonances that interfere at sp = 0.5, only partial spin flip  Two AC dipoles with vertical spin precession in between creates rotating drive field AC dipole -45  90  One AC dipole Two AC dipoles

29. Spin Tune Measurement  Use AC dipoles to excite coherent spin precession (drive tune  spin tune,  d >>  sp )  Measure radial polarization component as Fourier component of turn-by- turn asymmetry measurement.  Ratio of vertical over radial component (or “cone opening”) measures difference of drive tune and spin tune VERTICAL RADIAL Beam

30. Summary l High proton beam polarization reached at high energy: n 65 -70 % polarization reached in AGS at 24 GeV n 60 - 65 % polarization reached in RHIC at 100 GeV n 45 % polarization reached in RHIC at 250 GeV l Experience at RHIC confirms that it is plausible to accelerate polarized protons to significantly higher energy - LHC might be possible

31. Are there alternatives to acceleration? l Polarization build-up at high energy through synchrotron radiation: n Worked well for electrons up to 30 GeV (HERA-e) and partially at LEP  pol ~ M 7 /E 5 : Proton energy ~ 1000 TeV for same  pol as HERA-e In addition since  depol ~ 1/  ~ 1/E and P eq ~P ST (  depol /(  depol +  pol )): proton energy ~ 30000 TeV for same P eq as HERA-e