Deuteron Polarization in MEIC

1. Deuteron Polarization in MEIC Vasiliy Morozov for MEIC Study Group using results of IUCF and COSY SPIN Collaborations led by A.D. Krisch figure-8 concept originally proposed by Ya.S. Derbenev and develop by Yu.N. Filatov, A.M. Kondratenko, and M.A. Kondratenko High Energy Nuclear Physics with Spectator Tagging Old Dominion University, March 10, 2014

2. Deuteron polarization Spin dynamics and spin resonances Figure-8 concept Summary Outline

3. Spin-1 state Mathematical expectation of an operator Mathematical expectation for an ensemble of particles where is the fraction of particles in the state. If all beam particles are in the eigenstates then Spin Density Matrix

4. Cartesian vector and tensor spin operators Density matrix representation If all particles are in the eigenstates the only non-zero expectation values Rotations Vector and Tensor Polarizations

5. COSY’s polarized ion source Polarized Ion Source Deuterium hyperfine states (in strong magnetic field)

6. Differential spin-dependent cross-section (using lab-frame polarizations) Polarizations extractedusing azimuthal count rate dependence and effective analyzing powers Spin-1 Polarimetry

7. Spin tune (number of spin precession per turn) in a conventional ring A spin resonance occurs whenever the spin precession becomes synchronized with the frequency of spin perturbing fields Imperfection resonances due to alignment and field errors Intrinsic resonances due to betatron oscillations RF-induced resonances Coupling and higher-order resonances Spin Resonances

8. Convenient controllable resonance model for experiments Can be used for spin flipping Experiment using 1.85 GeV/c deuteron beam at COSY RF-Induced Spin Resonance

9. Sweeping an rf magnet’s frequency through a spin resonance can flip the polarization Spin rotation and Froissart-Stora formula Spin Flipping

10. Device rotating the spin by some angle about an axis in horizontal plane A “full” Siberian snake rotates the spin by 180 Overcomes all imperfection and most intrinsic resonances Spin tune with a snake Solenoidal snake at low energies Dipole snake at high energies Siberian Snake

11. Figure-8 shape has been chosen for all MEIC rings to achieve high ion (and electron) polarization Spin precession in one arc is exactly cancelled in the other Zero spin tune independent of energy Spin control and stabilization with small solenoids or other compact spin rotators Advantages of the figure-8 scheme for ions Efficient preservation of ion polarization during acceleration Energy-independent spin tune High polarization of all light ions Ease of spin manipulation Any desired polarization orientation at the IP Spin flip A simple way to accommodate polarized deuterons Particles with small anomalous magnetic moment Spin control without affecting the beam dynamics Figure-8 Concept

12. Pre-Acceleration & Spin Matching BIIL Booster beam from Linac to Collider Ring • Polarization in Booster stabilized and preserved by a single weak solenoid • 0.7 Tm at 9 GeV/c • d / p = 0.003 / 0.01 • Longitudinal polarization in the straight with the solenoid • Conventional 9 GeV accelerators require B||L of ~30 Tm for protons and ~110 Tm for deuterons

13. Linear optics without solenoid Linear optics with solenoid Betatron tune shift Optical Effect of Solenoid

14. “3D spin rotator” rotates the spin about any chosen direction in 3D and sets the stable polarization orientation nx control module(constant radial orbit bump) ny control module(constant vertical orbit bump) nz control module Polarization Control in Collider x y z z Control of longitudinal (nz)spin component Control of vertical (ny)spin component Control of radial (nx)spin component IP

15. Placement of the 3D spin rotator in the collider ring Integration of the 3D spin rotator into the collider ring’s lattice Seamless integration into virtually any lattice Another 3D spin rotator suppresses the zero-integer spin resonance strength Polarization Control in Collider 3D Spin Rotator IP Spin-control solenoids Vertical-field dipoles Radial-field dipoles Lattice quadrupoles

16. Radial polarization at IP assuming d = 2.510-4, p = 100 GeV/c Vertical polarization at IP Longitudinal polarization at IP Deuteron Polarization Behavior nx ny nz

17. The universal 3D spin rotator can be used to flip the polarization Consider e.g. longitudinal polarization at the IP at 100 GeV/c Polarization is flipped by reversing the fields of the solenoids in the radial and longitudinal spin control modules Polarization is preserved if The spin tune is kept constant No resonant depolarization The rate of change of the polarization direction is slow compared to the spin precession rate >0.1 ms for protons and >3 ms for deuterons Spin Flipping

18. Dynamics of the deuteron vector and tensor polarizations in an accelerator are not independent. They are connected through rotations. Preserving the vector polarization also preserves the tensor polarization. Manipulation of the vector and tensor polarizations can be understood in terms of rotations and controlled accordingly. Figure-8 is an elegant solution for preservation and control of the polarization of any particle species: acceleration, orientation, spin flip. Summary