J-PARC Spin Physics Workshop1 Polarized Proton Acceleration in J-PARC M. Bai Brookhaven National Laboratory

J-PARC Spin Physics Workshop2 Outline Introduction Challenges in accelerating polarized protons in circular accelerator Polarized proton acceleration in J-PARC LINAC RCS Main Ring Setup for preserving polarization Conclusion

J-PARC Spin Physics Workshop3 Spin motion in a circular accelerator 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

J-PARC Spin Physics Workshop4 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 Depolarizing mechanism in circular accelerator

J-PARC Spin Physics Workshop5 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

J-PARC Spin Physics Workshop6 Layout of J-PARC Pol. H - Source 180/400 MeV Polarimeter Rf Dipole 25-30% Helical Partial Siberian Snakes pC CNI Polarimeter Extracted Beam Polarimeter 50 GeV polarized protons for slow extracted beam primary fixed target experiments Low intensity (~ ppp), low emittance (10  mm mrad) beams Optically Pumped Polarized Ion Source: H - per 0.5 ms pulse and > 5 Hz rep. rate, 85% polarization, emittance: ~ 5  mm-mrad and 0.3 eVs for 2 x protons. Courtesy of T. Roser

J-PARC Spin Physics Workshop7 Harmonic correction J-PARC accelerators for pp LINAC: polarization transparent RCS: Energy: 180 MeV – 3 GeV (G  : ) Periodicity 3, Working point: Qx=6.735, Qy= imperfection resonances: With the RCS acceleration rate, keep the rms orbit distortion better than 0.38mm Harmonic orbit correction should also help to reserve the polarization Provided by Hikaru Sato

J-PARC Spin Physics Workshop8 Intrinsic Spin Resonance at RCS 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 Full spin flip by a rf dipole  =2.33x10 -5  =6.18x10 -5  =7.63x10 -5  =6.60x10 -5 Fast tune jump? G  = 2.65(9- Qy), 3.35(-3+ Qy), 5.65(12- Qy), 6.35(0+ Qy)

J-PARC Spin Physics Workshop9 AC dipole for RCS Magnet gap: 95mm Beta function at the ac dipole: 24 m Maximum coherent amplitude: 10  Coherence amp [mm] Freq [kHz]B Gaussm Current 4- turn magnet

J-PARC Spin Physics Workshop10 Alternative: Tune jump Advantage: can handle the first weak resonance However, tune needs to get jumped by about 0.06 at the second resonance, this can cause emittance blowup

J-PARC Spin Physics Workshop11 Accelerating polarized protons in Main Ring Beam energy: 3 GeV ~ 50 GeV (G  = ) Design working point: Qx = , Qy = Many imperfection resonances Strong intrinsic resonance

J-PARC Spin Physics Workshop12 Spin tracking: A. Luccio Spin tracking of one particle at the nominal tune of the lattice.  =10  mm. mrad. No snakes. The polarization is lost at the resonances, located at G  = 3N +-

J-PARC Spin Physics Workshop13 Full Snake in Main Ring? Needs two snakes to maintain vertical stable spin direction Limited space

J-PARC Spin Physics Workshop14 Main ring pp setup – dual snake: T. Roser Vertical component of stable spin Fractional part of spin tune Injection Intrinsic resonance GG  Qy = Qx = 20.12

J-PARC Spin Physics Workshop15 Possible locations of partial snakes in MR First 30% snakeSecond 30% snake Courtesy of T. Roser

J-PARC Spin Physics Workshop16 Spin tracking with dual snake setup: A. Luccio Single particle at 4  mm-mrad Working point: Qx = Qy =

J-PARC Spin Physics Workshop17 Conclusion  Scenarios for preserving polarization through the J- PARC accelerator complex are explored. We should be able to accelerate polarized protons to 50 GeV  RCS:  imperfection resonance: harmonic correctors  intrinsic resonance: ac dipole  50 GeV Main Ring:  a pair of AGS type 30% partial snakes  operate at working point Qx=20.12, Qy=20.96  The design requires the polarized proton beam size of 10  mm-mrad. The smaller beam size, the less polarization loss.

J-PARC Spin Physics Workshop18 Remaining issues RCS Can we raise the injection energy higher than the first intrinsic resonance? A moderate fast quad to jump through the 1 st intrinsic resonance To achieve > 80% polarization at 50 GeV Source pol Transmission efficiency RCS mini trans efficiency MR Ignore 1 st resonance Correct/ inj above 1 st resonance

J-PARC Spin Physics Workshop19 Remaining issues Main ring Optics design for dual snake setup Correction quadrupoles on either side of each partial snake are necessary to compensate the optics distortion due to the strong focusing field from the snake The effect goes down with energy and is strongest at injection. It is very possible that both horizontal and vertical tune have to stay farther away from integer at injection to allow stable operation.

J-PARC Spin Physics Workshop20 Betatron tune path: A. Luccio additional polarization losses at -9+Qy 6 horizontal resonances

J-PARC Spin Physics Workshop21 Remaining issues Main ring Optics design for dual snake setup What’s the best tune path Keep Qy high at low energy and ramp Qx up to 0.12 between injection and gamma=10 Can the slow extraction be done with near integer tunes? Spin matching between RCS and Main Ring