1. Polarization of CEPC M. Bai Collider Accelerator Department Brookhaven National Laboratory, Upton, NY 11973 Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

2. Outline Challenges of high energy polarized electrons – Depolarizing mechanism – Achieved polarization in circular accelerators VEPP, ELSA, LEP and HERA A preliminary look at CEPC polarization What can be done to reach high energy polarized electrons? – Think out of the box Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

3. Spin motion in a circular accelerator Spin vector in particle’s rest frame Magnetic field perpendicular to the particle’s velocity  G is the anomoulous g- factor, for proton, G=1.7928474   : Lorenz factor Magnetic field along the direction of the particle’s velocity Thomas BMT Equation: (1927, 1959) Spin tune Q s : number of precessions in one orbital revolution: L. H. Thomas, Phil. Mag. 3, 1 (1927); V. Bargmann, L. Michel, V. L. Telegdi, Phys, Rev. Lett. 2, 435 (1959) Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

4. Depolarizing mechanism in a synchrotron horizontal field kicks the spin vector away from its vertical direction, and can lead to polarization loss  dipole errors, misaligned qadrupoles, imperfect orbits  betatron oscillations  other multipole magnetic fields  other sources x y z beam Initial x y z beam 1 st full betatron Oscillation period x y z beam 2nd full betatron Oscillation period

5. Depolarizing Resonance  Intrinsic resonance: Focusing field due to the intrinsic betatron oscillation Location: G  = kP±Q y P: super periodicity of the accelerator, Q y : vertical betatron tune Resonance strength: Proportional to the size of the betatron oscillation  Imperfection resonance: Source: dipole errors, quadrupole misalignments Resonance location: G  = k, k is an integer Resonance strength: Proportional to the size of the vertical closed orbit distortion Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

6. Depolarizing Resonances@ SPERA Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

7. Sokolov-Ternov Radiative Polarization Limit Synchrotron radiation has a weak dependence on the spin direction of the particle Spin flip transition rate Beam polarization for the case of a uniform magnetic field with Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

8. In a planar circular accelerator The magnetic field is distributed piece-wisely instead of uniformly Clearly, a single snake or other configurations which lays the stable spin direction in the horizontal plane, can cancel the S-T radiative polarization build-up Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

9. Now, let’s add in spin diffusion An emission of a photon yields a sudden change of the particle’s energy, as well as its spin phase Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

10. Synchrotron Sideband Spin tune is modulated due to synchrotron oscillation Hence, the spin-orbit coupling factor averaged over all synchrotron phase becomes C. Biscari, J. Buon, B. Montague, CERN/LEP-TH/83-8

11. Enhancement factor due to synchrotron motion For a spin tune spread distribution of Spin-orbit coupling factor becomes C. Biscari, J. Buon, B. Montague, CERN/LEP-TH/83-8

12. LEP Enhancement Factor Synchrotron tune ~0.07, momentum spread ~ 0.0007 At beam energy 51.5GeV, ~50% vertical polarization was achieved with careful spin matching to minimize the resonance strength Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

13. Achieved Electron Polarization www.desy.de/~mpybar/psdump/amspap2.ps.gz‎

14. Current CEPC Design SPECs Qin, et al, Preliminary Accelerator Design of a Circular Higgs Factory in China, TUPBA03, NAPAC13

15. Preliminary Estimate S-T polarization build-up time for beam energy at 120 GeV Enhancement factor due to synchrotron motion ~120.72GeV Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

16. Preliminary Estimate of Equilibrium Polarization For both cases, a resonance strength of 0.001 is assumed Momentum spread 0.0013 Momentum spread 0.0007 Synchrotron tune Equilibrium polarization Beam Energy ~ 120.68 GeV

17. Preliminary Estimate of Equilibrium Polarization For both cases, a resonance strength of 0.001 is assumed Momentum spread 0.001 Momentum spread 0.0007 Synchrotron tune Equilibrium polarization Beam Energy ~ 90.245 GeV

18. For Polarized CEPC/TLEP Careful lattice design from day one to make sure a good spin matching to minimize the depolarizing resonance strength Careful choices of beam parameters including longitudinal to avoid depolarization – betatron tunes and synchrotron tune – small momentum spread Excellent spin matching and very precise beam control, i.e. closed orbit, betatron tune, are required to minimize the depolarizing resonance strength – In general, the depolarizing resonance gets stronger at higher energies. This means the tolerance to closed orbit distortion as well as other beam parameters is much tighter than LEP Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

19. Preliminary Estimate of Equilibrium Polarization However, one may still have to make compromise between luminosity and polarization due to the beam-beam induced tune spread, which pushes particles to the spin resonances. Such an effect has been seen at LEP, HERA. In addition, one still has to build spin rotator In summary, it seems very daunting to have polarized beams at ~50% or higher polarization at the energy of CEPC or TLEP

20. Criterion for Keeping Polarization Keep the stable spin direction along the main B field direction – To allow ST polarization built-up Reduce spin chromaticity – Improve equilibrium polarization – Minimize synchrotron side band Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

21. Can Siberian Snake Help? In a storage ring like RHIC, a pair of Siberian snakes located diametrically to yield a spin tune of ½, energy independent. This is good However, the same advantage of completely cancels out Sokolov-Ternov effect, which is bad  So, one could conceive the scenario of accelerate pre- polarized electrons to the top energy. But, – What about positron? One way to solve this, is to have a polarizer ring for both e+ and e- beam at lower energy to establish polarization – Even with dual snake, it may still not efficient enough to suppress the spin-orbit coupling factor[J. Buon, LAL-RT-84-05]. But, what about three pairs? Detailed analysis including simulation needs to be done. Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

22. With Siberian Snakes Low energy polarizer ring – Reasonable polarization time – > 50% polarization – Both injector and main ring are equipped with snakes. Main ring needs spin rotators Polarization wigglers for the injector – No need of low energy polarizer ring – Both injector and main ring are equipped with snakes, plus the spin rotator for main ring – However, challenge is whether one can achieve >50% polarization within reasonable time snake Dec. 16-17, 2013 International workshop on Future High Energy Circular Colliders, IHEP, Beijing

23. Conclusion It is very challenge to establish polarized electron-positron beam with > 50% polarization at CEPC/TLEP Several critical R&D items – Lattice design with spin matching – Local spin rotator for high energy electron/positron beam – Explore the feasibility of applying dual snake or odd pairs of snake to overcome the strong depolarizing mechanism due to quantum excitation Wigglers or other beam manipulations to generate S-T polarization – In addition to existing algorithms for spin-coupling factor calculations, SLIM, SODOM, etc, a robust numerical simulation code for high energy polarized electron- positron collider