1. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 1 Ion Polarization Control in MEIC Rings Using Small Magnetic Field Integrals Ya.S. Derbenev 1, F. Lin 1, V.S. Morozov 1, Y. Zhang 1, A.M. Kondratenko 2, M.A. Kondratenko 2 and Yu.N. Filatov 3,4 1 Jefferson Lab, Newport News, VA 2 Science and Technique Laboratory Zaryad, Novosibirsk, Russia 3 Joint Institute for Nuclear Research, Dubna, Russia 4 Moscow Institute of Physics and Technology, Dolgoprydny, Russia University of Virginia, Charlottesville, VA, USA September 9 - 13, 2013 The XV th International Workshop on Polarized Sources, Targets and Polarimetry (PSTP 2013)

2. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 2 1.Introduction 2.Polarization preservation during acceleration in the pre-booster and large booster 3.Deuteron polarization control scheme with “small” solenoids for the collider 4.Proton polarization control with “small” radial fields in the collider 5.Compensation of the 0 th harmonic of the spin perturbation in the collider ring. Spin response function and its suppression in the interaction points. 6.Conclusions Outline

3. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 3 Schematic Layout of Medium-Energy Electron-Ion Collider (MEIC) at Jefferson Lab Warm large booster (up to 20 GeV/c) Warm 3-12 GeV electron collider ring Medium-energy IPs with horizontal beam crossing Injector 12 GeV CEBAF Prebooster SRF linac Ion source Cold 20-100 GeV/c proton collider ring Three Figure-8 rings stacked vertically

4. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 4 Major Components of MEIC Ion Complex The MEIC ion beam polarization design requirements are: High polarization (over 70%) for protons or light ions (d, 3 He ++, and possibly 6 Li +++ ). Both longitudinal and transverse polarization at all IPs. Sufficiently large lifetime to maintain high beam polarization. Spin flipping at a high frequency. to high-energy collider ring Ion source SRF linac Prebooster (accumulator ring) Large booster Medium-energy collider ring Cooling

5. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 5  The figure-8 structure provides unique capabilities for manipulating the beam polarization In an ideal structure (without perturbations) all solutions are periodic It has an energy-independent (zero) spin tune It allows control of the beam polarization with small fields without orbit perturbation It eliminates depolarization problem during acceleration It becomes possible to efficiently control the polarization of a beam of particles with any anomalous magnetic moment including particles with small anomalous moments, such as deuterons Makes possible ultra-high precision experiments with polarized beams Spin Motion in “Figure-8” Rings

6. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 6 Control of Polarization during Acceleration B || L of only 3 T  m provides deuteron polarization stability up to 100 GeV. A conventional ring at 100 GeV would require B || L of 1200 T  m or B  L of 400 T  m. The polarization is stable if  w 0 (w 0 is the «zero» spin resonance strength)

7. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 7 Acceleration and Spin Matching in MEIC Pre-booster (1 solenoid) 0.785 / 3.830.06 / 0.28600.003 / 0.01 Large booster (1 solenoid) 3.83 / 200.28 / 1.51200.003 / 0.01 Conventional ~20 GeV accelerators require

8. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 8 Control of Deuteron Polarization in Collider Ring is the spin rotation angle between the solenoids is the orbit rotation angle between the solenoids is the angle between the polarization and velocity directions are the spin rotation angles in the solenoids A scheme for obtaining any polarization direction Beam injected longitudinally polarized, accelerated and then desired spin orientation adjusted

9. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 9 Control of Deuteron Polarization in Collider Ring (B || L) 1,2 (T  m) vs. p (GeV/c) longitudinal polarization radial polarization (B || L) 1 (B || L) 2

10. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 10 Control of Proton Polarization in Collider Ring Last two arc dipoles (B  L) i (T  m) vs. p (GeV/c) longitudinal polarization radial polarization (BxL)1(BxL)2(BxL)3(BxL)4(BxL)1(BxL)2(BxL)3(BxL)4

11. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 11 Control of Proton Polarization in Collider Ring Vertical excursion of the reference orbit

12. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 12 Spin Response Function Zero-harmonic spin resonance strength can be calculated using spin “response function” Response function is determined by the accelerator’s design lattice and represents the spin response to a  -function perturbation at an azimuthal angle : Such a dipole generates the following strength of the zero-harmonic resonance: For a flat figure-8 orbit, the response function is given by where is the spin rotation angle in the collider’s bending dipoles, is the Floquet function are the vertical betatron function and betatron tune

13. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 13 Response Function in Collider Ring is the periodic response function describing effect of any radial fields and allowing one to calculate the zero-resonance strength. IP IR Highest error sensitivity in the IR’s but error control requirements high anyway for dynamic reasons.

14. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 14 Response Function and Zero Spin Resonance Strength The total zero-harmonic resonance strength: is composed of  coherent part due to closed orbit excursion  due to transverse and longitudinal emittance The coherent part arises due to radial fields from  dipole roll  vertical quadrupole misalignment

15. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 15 Compensation of Zero-Harmonic Spin Resonance Strength In the linear approximation, the zero-harmonic spin resonance strength is determined by two components of the spin perturbation lying in the ring’s plane: and can be compensated by correcting devices whose spin rotation axis lies in the same plane insertion for spin control insertion for strength compensation insertion for strength compensation insertion for spin control With compensation of the “coherent” component of the spin resonance:

16. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 16 Conclusions Schemes were developed for MEIC figure-8 rings that eliminate depolarization problem during acceleration allow control of the beam polarization with small fields without significant orbit perturbation efficiently control the polarization of particles with any anomalous magnetic moment including those with small anomalous moments, such as deuterons allow adjustment of polarization orientation in either of the two straights allow single-turn as well as multi-turn spin-flipping schemes make possible ultra-high precision experiments with polarized beams Future plans optimization of the developed schemes integration into the ring lattices validation by spin tracking development of spin-flipping techniques

17. Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13 V.S. Morozov et al., Ion Polarization Control in MEIC Rings Using Small Magnetic Fields Integrals. PSTP 13, University of Virginia, Charlottesville, VA, USA, September 9-13, 2013 17 http://www.jlab.org/conferences/eic2014/index.html