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
F. Lin

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

3. Spin Density Matrix 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

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

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

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

7. Spin Resonances
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

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

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

10. Siberian Snake
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

11. Figure-8 Concept
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

12. Pre-Acceleration & Spin Matching
Polarization in Booster stabilized and preserved by a single weak solenoid
0.7 Tm at 9 GeV/c
d / p = / 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
beam from Linac
Booster
to Collider Ring
BIIL

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

14. Polarization Control in Collider
“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
Control of radial (nx) spin component
Control of vertical (ny) spin component
Control of longitudinal (nz) spin component IP z x z y

15. Polarization Control in Collider
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
3D Spin Rotator IP
Spin-control solenoids
Vertical-field dipoles
Radial-field dipoles
Lattice quadrupoles

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

17. Spin Flipping
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

18. Summary
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.