1. Possible Approach for Reaching High Energy Polarized Electron- Positron Beams M. Bai, T. Roser Collider Accelerator Department Brookhaven National Laboratory, Upton, NY 11973 Z. Duan IHEP, Beijing, Collider Accelerator Dept., BNL Feb. 12-13, 2014 Polarized Lepton, Mainz, Germany

2. Outline Challenges of high energy polarized electron/positron – Depolarizing mechanism – achieved polarization in circular accelerators VEPP, ELSA, LEP and HERA – A preliminary look at CEPC/TLEP polarization What can be done to reach high energy polarized electron/positron beams? – Think out of the box Summary Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

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 electron, G~0.00116   : 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) Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

4. Spin motion in a circular accelerator  Polarized source  Spin manipulation to accelerating polarized beam to high energy  Depolarization dominated by orbital  Rely on spin manipulation to maintain polarization at store for high energy Thomas BMT Equation: (1927, 1959)  un-polarized source  accelerate to high energy  radiative polarized build-up  rely on careful spin matching to obtain/maintain polarization.  Depolarization due to spin diffusion  solenoid snake for longitudinal polarization at low energy Proton/ion Electron/positron At high energy, rotators for providing non- vertical polarization at detector

5. In a planar circular accelerator where the magnetic field is distributed piece-wisely 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 Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

6. 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 Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

7. 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

8. Depolarizing Resonances@ SPERA Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

9. 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

10. 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

11. Achieved Polarized Electron Beams J. Buon, J. P. Koutchouk, Polarization of Electron and Proton Beams, CAS Lecture

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

13. Preliminary Estimate S-T polarization build-up time for beam energy at 120 GeV Enhancement factor due to synchrotron motion ~120.72GeV Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

14. 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 Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

15. 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 Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

16. For Polarized Circular Higgs Factory 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 Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

17. 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 solely based on S-T effect EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, GermanyFeb. 12-13, 2014

18. 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 EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, GermanyFeb. 12-13, 2014

19. 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 accelerating 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 EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, GermanyFeb. 12-13, 2014

20. 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 Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

21. Low Energy Polarizer Scenario Beam Energy: ~ 20GeV With bending field ~ 0.3 [T-m], S-T polarizing time < 10 mins Size the ring is ~ 1km, and reasonable synchrotron radiation power Polarization direction: along the direction of the guiding field Beam Energy [GeV] Bending Stregnth [T-m] S-T time[min] 50 10 40 30 100 50 1 0.5 Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany 20

22. Possible Scenario for injector Beam Energy: ~ 20GeV – ~ 100 GeV for top-off injection Same size as the collider Equipped with snakes to help preserve beam polarization – propose to have 3 pairs of snakes – The spin rotation axis of each snake alternates between 45 degrees and −45 degrees with respect to beam direction for all six snakes. – Yields spin tune at ½, and stable spin vector along guiding field direction, independent of beam energy. In the absence of errors, the spin tune is also independent of beam betatron amplitude Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

23. Depolarization time in the presence of snakes One of the critical the advantage of snake is the spin tune becomes quasi energy independent Spin chromaticity in the presence of 6 snakes then becomes very weakly dependent on energy, especially at high energy Together with vertical polarization direction, reasonable depolarization time may be achievable Beam energy [GeV] A simple minded model of a smooth ring with evenly distributed 3 pairs of snake with axes perpendicular for each pair Effect of synchrotron radiation at snakes on depolarization is not included in this simple minded model.

24. Possible Scenario for Collider Beam Energy: ~100 GeV Requires longitudinal polarization at the detector for physics program Scenario 1: – Equip with similar amount of snakes, plus local spin rotators around the detector – More synchrotron radiation due to snake/spin rotators. Need to verify these impact on the spin diffusion Scenario 2: – Odd number of snakes – The stable spin direction then stays in the horizontal plane. Snakes can be chosen in a way to produce longitudinal polarization at detector – But, one still needs to match the spin from injector to collider Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

25. Odd number of snakes* Proposed by Koop et al for BINP Tau-charm factory Spin chromaticity becomes inversely proportional to the square of number of snakes A very attractive solution for low energy But, at high energy solenoid can’t be used. And also it is not clear that at high energy, this is enough to obtain long enough depolarization time *A Koop, A V Bogomyagkov, A V Otboev, Longitudinally polarized electrons in Novosibirsk c-tau factory, Proceedings of 19 th International Spin Symposium, 2010

26. Summary It is very challenge to establish polarized electron-positron beam with > 50% polarization at future circular Higgs factory – Polarization of ~10% can be very useful for precise energy calibration of the lepton beams as demonstrated at LEP Option of establishing polarization at lower energy for both electron and positron beams, together with accelerating both beams with multiple snakes may be one of the possible approaches – Technique of using odd number of snakes to get longitudinal polarization may not be applicable for this high energy – Local rotators can still be the option Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

27. Summary Critical R&D items for the snake-option – Verify the effect of snakes on suppressing the spin-orbit coupling factor. As Buon pointed out decades ago, even with dual snake, it may still not efficient enough to suppress the spin-orbit coupling factor[J. Buon, LAL-RT-84- 05]. Detailed analysis including simulation to verify whether 3-pairs can be an option – Snake/spin rotator design How to minimize the orbit excursion as well as synchrotron radiation? – Verify the effect of spin diffusion due to snakes/spin rotators on beam polarization Feb. 12-13, 2014EUCARD workshop "Spin optimization at Lepton accelerators”, Mainz, Germany

28. I have a dream!