Polarized Proton Acceleration in J-PARC

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

2. 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 Workshop

3. B beam Spin motion in a circular accelerator Spin vector in particle’s rest frame • 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, J-PARC Spin Physics Workshop

4. Depolarizing mechanism in circular accelerator • 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 y y y beam beam beam z z z x x x 1st full betatron Oscillation period 2nd full betatron Oscillation period J-PARC Spin Physics Workshop Initial

5. 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 Workshop

6. Courtesy of T. Roser Layout of 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 • Optically Pumped Polarized Ion Source: 1012 H- per 0.5 ms pulse and > 5 Hz rep. rate, 85% polarization, emittance: ~ 5 mm-mrad and 0.3 eVs for 2 x 1011 protons. J-PARC Spin Physics Workshop

7. J-PARC accelerators for pp • LINAC: polarization transparent • RCS: • Energy: 180 MeV – 3 GeV (G: 2.2 -- 7.5) • Periodicity 3, Working point: Qx=6.735, Qy=6.356 • 5 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 Harmonic correction Provided by Hikaru Sato J-PARC Spin Physics Workshop

8. 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 Intrinsic Spin Resonance at RCS G = 2.65(9- Qy), 3.35(-3+ Qy), 5.65(12- Qy), 6.35(0+ Qy) J-PARC Spin Physics Workshop

9. AC dipole for RCS • Magnet gap: 95mm • Beta function at the ac dipole: 24 m • Maximum coherent amplitude: 10 J-PARC Spin Physics Workshop

10. 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 Workshop

11. Accelerating polarized protons in Main Ring • Beam energy: 3 GeV ~ 50 GeV (G = 7.5 -- 97.5) • Design working point: Qx = 22.339, Qy = 20.270 • Many imperfection resonances • Strong intrinsic resonance J-PARC Spin Physics Workshop

12. Spin tracking of one particle at the nominal tune of the lattice. e =10p mm.mrad. No snakes. The polarization is lost at the resonances, located at Gg = 3N +- n Spin tracking: A. Luccio J-PARC Spin Physics Workshop

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

14. Vertical component of stable spin Fractional part of spin tune Main ring pp setup – dual snake: T. Roser Qy = 20.96 30% 30% Gg Qx = 20.12 Injection Intrinsic resonance J-PARC Spin Physics Workshop

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

16. Spin tracking with dual snake setup: A. Luccio • Single particle at 4 mm-mrad • Working point: • Qx = 20.128 • Qy = 20.960 J-PARC Spin Physics Workshop

17. 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 10p mm-mrad. The smaller beam size, the less polarization loss. J-PARC Spin Physics Workshop

18. Remaining issues • To achieve > 80% polarization at 50 GeV • RCS • Can we raise the injection energy higher than the first intrinsic resonance? • A moderate fast quad to jump through the 1st intrinsic resonance J-PARC Spin Physics Workshop

19. 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 Workshop

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

21. 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 J-PARC Spin Physics Workshop