1. Thomas Roser SPIN 2006 October 3, 2006 A Study of Polarized Proton Acceleration in J-PARC A.U.Luccio, M.Bai, T.Roser Brookhaven National Laboratory, Upton, NY 11973, USA A.Molodojentsev, C.Ohmori, H.Sato High Energy Accelerator Research Organization, Tsukuba, Ibaraki, Japan H.Hatanaka Research Center for Nuclear Physics, Osaka University, Japan

2. Layout of J-PARC for polarized proton acceleration 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 (~ 10 12 ppp), low emittance (10  mm mrad) beams

3. Setup for accelerating polarized protons at J-PARC l Optically Pumped Polarized Ion Source: 10 12 H - per 0.5 ms pulse and > 5 Hz rep. rate, 85% polarization (similar to KEK-TRIUMF-BNL OPPIS) Bunch emittance: ~ 5   rad and 0.3 eVs for 2  10 11 protons (required for polarized beam acceleration) l Linac: No depolarization RCS (25 Hz, y = 6.35, P = 3, E kin =.18 … 3 GeV, G  = 2.2 … 7.5) 5 imperfection resonances; harmonic correction needed for G  = 7 n Intrinsic resonances:  G  = 2.65 (9- y ), 3.35 (-3+ y ), 5.65 (12- y ), 6.35 (0+ y ) m Full spin flip with rf dipole: 20 Gm gives >.99 spin-flip (seems feasible)  Avoid depolarization with tune jump:  y = 0.2 in 6 turns  large aperture ferrite quadrupoles with fast pulsing power supplies (difficult)

4. Intrinsic Spin Resonance at RCS – Rapid Cyclic Synchrotron emittance: 10   rad, 95% repetition rate 25Hz sinusoidal ramping kinetic energy: 180MeV – 3GeV intrinsic resonance strength for a particle at an emittance of 10   rad Full spin flip by a rf dipole  =2.33x10 -5  =6.18x10 -5  =7.63x10 -5  =6.60x10 -5 Fast tune jump?

5. 10   rad emittance Issues of accelerating polarized protons in Main Ring l Beam energy: 3  50 GeV (G  = 7.5  97.5) Design working point: x = 22.34; y = 20.27 l Many imperfection resonances l Strong intrinsic resonances l No space for full snake installation

6. Spin tracking without partial snakes  Spin tracking of single particle at the nominal tune of the lattice.   =10  mm. mrad. No snakes.  The polarization is lost at the resonances, located at G  = 3N  y

7. Solution of accelerating polarized protons in Main Ring Vertical component of stable spin Fractional part of spin tune Injection Intrinsic resonance GG  y = 20.96 x = 22.12

8. Spin tracking 12 particles at 4   rad (1.5 beam sigma) l Two 30% synthetic snakes l Working point: x = 22.128 y = 20.960

9. Possible locations of partial snakes in MR First 30% snakeSecond 30% snake

10. Main Ring Partial Snake  AGS type of cold snake  magnetic field strength: 3.4 Tesla  snake strength 30% (54 0 spin rotation angle) at injection and gets weaker at higher energy according to:

11. horizontal orbital offset focusing field in both planes both effects become weaker at higher energy Effect of Snake magnetic field on orbital motion

12. Matching of the INSA with snake at the energy  =11

13. Matching snakes to the lattice Because of the strong focusing of the snakes in both planes, they produce a substantial perturbation on the optics of the lattice at low energy, especially at injection. Can be solved by using correcting quadrupoles at the entrance and exit of each snake to compensate the distortion, as demonstrated in the AGS. Due to the constraint of limited space in MR, we present a solution using existing quadrupoles in MR QDT,QFP,QFT and QFS. Instead of building new quadrupoles, this solution only needs additional power supplies for these 4 magnets

14. Solution of Correcting Quadrupoles x = 22.12 y = 20.96

15. Betatron tune l No stable lattice found with MAD with both horizontal and vertical tune close to integer at injection. Real machine is probably stable (as in AGS) but tune swing is also possible. l The spin depolarization resonances in MR at low energy are very weak, and the amount of depolarization is negligible for a 10  mm- mrad beam. This allows one to ramp the two betatron tunes to (22.12, 20.96).

16. Conclusion  Possible to accelerate polarized protons of 10  mm-mrad in the J-PARC Main Ring using two 30% partial snakes of AGS type.  The perturbation on the MR optics from snakes is significant at low energy. This can be minimized by using a correcting quadrupole doublet each at the entrance and exit of each snake.  Tracking with the code Spink using synthetic snakes with variable strength and a static lattice shows good polarization survival.