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Spin Dynamics in Rings

Possibility for polarized beam at J-PARC Summary of Satellite Workshop on Polarized Proton Beam at J-PARC.

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Spin Dynamics in Rings

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  1. Possibility for polarized beam at J-PARCSummary of Satellite Workshop on Polarized Proton Beam at J-PARC Satellite Workshop Program:Overview of the status of J-PARC (Shin'ya Sawada)Feasibility of Polarized Proton Beam at J-PARC (Hikaru Sato)Overview and Source, RCS (Thomas Roser )50 GeV Main Ring numerical studies (Alfredo Luccio)Polarimeter (Kazu Kurita)Spin dynamic overview AGS experience with strong partial snake Possible plans for J-Parc

  2. Spin Dynamics in Rings • Precession Equation in Laboratory Frame: • (Thomas [1927], Bargmann, Michel, Telegdi [1959]) • dS/dt = - (e/gm) [(1+Gg)B + (1+G) BII] S • Lorentz Force equation: • dv/dt = - (e/gm) [ B ] v • For pure vertical field:Spin rotates Gg times faster than motion, nsp = Gg • For spin manipulation:At low energy, use longitudinal fieldsAt 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 Imperfection resonance (magnet errors and misalignments): Gg = nsp = n Intrinsic resonance (Vertical focusing fields): Gg = nsp = Pn ± Qy P: Superperiodicity [AGS: 12] Qy: Betatron tune [AGS: 8.75] Weak resonances: some depolarization Strong resonances: partial or complete spin flip Illustration by W.W. MacKay

  4. Siberian Snakes (Local Spin Rotators) cos(180 nsp) = cos(d/2) · cos(180 Gg) d 0 nsp  n No imperfection resonances Partial Siberian snake (AGS) d= 180 nsp = ½ No imperfection resonances and No Intrinsic resonances Full Siberian Snake (Ya.S. Derbenev and A.M. Kondratenko) Two Siberian Snakes in RHIC

  5. (Naïve) Limits for Siberian Snakes • Spin rotation of Siberian snake (d) > Spin rotation of driving fields (e) • “Spin rotation of Siberian snake drives strong imperfection resonance” • Imperfection resonances e Energy • Intrinsic resonances eEnergy • Partial Siberian snake(AGS, d = 9°)e < d/360° • One full snakee < 1/2 • Two full snakes(RHIC)e < 1 • N full snakes(LHC? N  16)e < N/2

  6. RHIC – first polarized hadron collider pC Polarimeters Absolute Polarimeter (H jet) BRAHMS PHOBOS Siberian Snakes Siberian Snakes PHENIX STAR Spin Rotators (longitudinal polarization) Spin flipper Spin Rotators (longitudinal polarization) Solenoid Partial Siberian Snake Pol. H- Source LINAC BOOSTER 5% Helical Partial Siberian Snake AGS 200 MeV Polarimeter Internal Polarimeter pC Polarimeter Rf Dipole 25% Helical Partial Siberian Snake Without Siberian snakes: nsp = Gg = 1.79 E/m  ~1000 depolarizing resonances With Siberian snakes (local 180spin rotators): nsp = ½  no first order resonances Achieved ~ 50% beam polarization at 100 GeV Achieved ~ 30% beam polarization at 205 GeV on first try!

  7. High intensity polarized H- source KEK OPPIS upgraded at TRIUMF 80 - 85 % Polarization 151011 protons/pulse at source 61011 protons/pulse at end of LINAC

  8. Simulation and measurement at 25 GeV 1997 2000 2002 2003 2004 Proton polarization at the AGS • Full spin flip at all imperfection and strong intrinsic resonances using partial Siberian snake and rf dipole • Ramp measurement with new AGS pC CNI polarimeter: raw asymmetry = AN · PB • Remaining polarization loss from coupling and weak intrinsic resonances • New helical partial snake (RIKEN funded) eliminated coupling resonances • Strong super-conducting helical partial snake will eliminate all depolarization. 2005: 55%, 1x1011 ppb

  9. Strong Partial Siberian Snake in AGS partial snake resonance Polarization Imperfection resonance Intrinsic resonance desired vertical betatron tune to avoid depolarization Challenges:1. SC element in warm machine 2. Lattice disturbances cos(180nsp) = cos(d/2) · cos(180Gg)

  10. Multiple partial Siberian snakes Single partial snake rotating by angle d : Two partial snakes rotating by angle d1and d2and separated by 1/m of ring: • Max. effective snake strength at Gg = mn: d1 + d2 (n: integer) • Min. effective snake strength at Gg = mn + m/2: d1 - d2 • For max. strength at intrinsic resonances m needs to be a common factor of both vertical tune and super-periodicity (Gg = Pn ± ny) • To avoid minimum strength at imperfection resonances m needs to be an odd integer.

  11. Two partial Siberian snakes in the AGS (J-PARC MR) Vertical tune ~ 9 (21), super-periodicity = 12 (3) m = 3 Two partial snakes rotating by angle d1and d2and separated by 1/3 of ring: Max. effective snake strength at Gg = 3n (energy of AGS intrinsic resonances): dtot = d1 + d2 Min. effective snake strength at Gg = 3n + 1.5 (energy of AGS injection/extraction): dtot = d1 - d2 At this energy the stable spin direction is close to vertical, which simplifies spin matching. Two equal partial snakes give perfect spin matching.

  12. Warm helical partial Siberian snake • Replaced solenoidal partial snake • Same design as cold snake (dual pitch) • 1.5 Tesla field • ~ 6 % partial snake (w/o generating coupling) • Funded by RIKEN, built by Takano Ind.

  13. 25 % AGS super-conducting helical snake Completed helical dipole coil Correction solenoid and dipoles Measured twist angle 2 deg/cm in the middle ~ 4 deg/cm at ends

  14. Vertical component of stable spin Fractional part of spin tune Two partial snakes in the AGS E20 5% A20 15% Deviation from integer Gg Injection First intrinsic resonance (0+n)

  15. Tune Measurement on Ramp (Haixin Huang) 35+y 37+y 12+y 24+y 36+y 36-y 48-y 1+y 0+y -1+y (Jeff Wood) 8.98 2T+1.53T Snake: Spin tune (7)=.957 Spin tune (8)=.957 Spin tune (9)=.925

  16. Tune Scan around 36+ (2T+1.53T) (Haixin Huang) • The vertical tune should be > 9.985 for 2T case.For tune range of 8.90-8.96, the depolarization is a combination of 36+nu and 37+. • For vertical tune >8.97, there is no effect from 37+ and 55-: the betatron tune is already high enough for all G. It is possible a few percents polarization loss due to the tight tune space.

  17. Ramp Measurement The ramp measurements pattern look similar, there is no catastrophic polarization drop. Higher asymmetry with cold snake. There may still be polarization loss around 36+. 2.5T 2T 1.5T

  18. Horizontal resonances Caused by horizontal component of stable spin direction Horizontal resonances are always weak but there are many of them Horizontal resonances are much weaker than the counterparts of vertical ones. 55-Qy 38+Qy 38+Qx 34.9/49.2=.71 41.4/49.8=.83

  19. Polarization losses C2.5T C2.5T,W1.5T C2T,W1.5T AC dipole Hori. res.1: 0.94 0.89 0.94 0.99 Low y at 36+1: 0.95 0.95 0.95 1.00 Inj./Ext.: 0.92 0.97 0.99 0.99 Weak intrinsic 1.00 1.00 1.00 0.85 Total2 0.82 0.82 0.89 0.83 Measured3 0.77 0.76 0.80 0.80 • The polarization loss due to horizontal res. and low y at 36+ is given as the upper limit, especially in the two snake cases (total snake strength varies). • There is also possible loss at early part of ramp when vertical tune is outside the tune window. It is estimated to be no more than a couple percents but spin tracking will follow. • 80% source polarization assumed.

  20. Polarized proton beams at J-Parc 50 GeV polarized protons for slow extracted beam primary fixed target experiments Low intensity (~ 1012 ppp), low emittance (10 p mm mrad) beams pC CNI Polarimeter Extracted Beam Polarimeter Pol. H- Source Rf Dipole 180/400 MeV Polarimeter 25-30% Helical Partial Siberian Snakes

  21. Polarized proton beams in J-PARC Linac and RCS • Optically Pumped Polarized Ion Source: 1012 Hminus per 0.5 ms pulse and > 5 Hz rep. rate, 85% polarization • Bunch emittance: ~ 5 p mm mrad and 0.3 eVs for 2 x 1011 protons (required for polarized beam acceleration) • Linac: No depolarization • RCS (ny = 6.35, P = 3, Ekin = .18 … 3 GeV, Gg = 2.2 … 7.5) • Harmonic correction of 5 imperfection resonances • Intrinsic resonances: • Gg = 2.65 (9- ny), 3.35 (-3+ ny), 5.65 (12- ny), 6.35 (0+ ny) • Full spin flip with rf dipole: 20 Gm gives > .99 spin-flip (seems feasible) • Avoid depolarization with tune jump: Dny = 0.2 in 6 turns  large aperture ferrite quadrupoles with fast pulsing power supplies (difficult)

  22. Intrinsic resonances in RCS (Mei Bai) • emittance: 10 mm-mrad, 95% • repetition rate 25Hz • sinusoidal ramping • kinetic energy: 180MeV – 3GeV • intrinsic resonance strength for a particle at an emittance of 10 mm-mrad =6.18x10-5 Full spin flip by a rf dipole Fast tune jump? =6.60x10-5 =7.63x10-5 =2.33x10-5

  23. Polarized proton beams in J-PARC Main Ring • Main ring (ny ~ 20.8, P = 3, Ekin = 3 … 50 GeV, Gg = 7.5 … 97.5) • Two strong 30% partial Siberian snakes installed in two of the three straight sections: • Avoid all vertical depolarizing resonances if vertical tune is set to ~ 20.92 • For injection and extraction energies of 3 GeV (Gg = 7.5) and 50 GeV (Gg = 97.5), respectively, perfect spin matching at injection and extraction. • Setting horizontal tune to 22.88 (or 22.12) avoids depolarization from horizontal motion with stable spin direction not vertical.

  24. Vertical component of stable spin Fractional part of spin tune Two partial snakes in J-PARC MR ny nx 30% 30% Gg Injection Intrinsic resonance

  25. Possible locations of partial snakes in MR First 30% snake Second 30% snake

  26. Spin tracking in 50 GeV MR (Alfredo Luccio) • nx,y = 22.128,20.960 • Two 30% snakes • 12 particles at 1.5 beam sigma

  27. Conclusions • Strong partial Siberian snakes can overcome intrinsic depolarizing resonances. Operation is analogous to full snake situation. • If vertical tune and super-periodicity have common factor that is odd multiple partial snakes can be used to give larger effective strength • With proper choice of injection and extraction energy multiple partial snakes can solve the spin matching problem • Horizontal resonances can be avoided by placing horizontal tune close to integer also. • Polarized beam acceleration in J-Parc is possible with a rf dipole in the RCS and two strong partial Siberian snakes in Main Ring.

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