1. JLEIC Weekly R&D Meeting
Spin-Tracking the JLEIC Ion Collider Ring: Polarization Control and Spin Flip
A.M. Kondratenko, M.A. Kondratenko, and Yu.N. Filatov presented by V.S. Morozov
JLEIC Weekly R&D Meeting
June 23, 2016
F. Lin

2. Outline Ideal figure-8 collider ring 3D spin rotator
Reference particle
Particle with non-zero betatron amplitudes
3D spin rotator
Ideal collider ring with spin motion stabilized by a 3D spin rotator
Effect of lattice imperfections
Closed orbit distortion
Coherent part of the zero-integer spin resonance strength
Spin control with a single 3D spin rotator
Spin control with compensation of the coherent part by a 2nd rotator
Spin flip
Summary and conclusions

3. Ideal Figure-8 Collider Lattice
A sanity check
60 GeV/c reference proton with initially vertical (Sy) spin
60 GeV/c reference deuteron with initially longitudinal (Sz) spin

4. Effect of Betatron Oscillations
Incoherent component of the zero-integer spin resonance strength
60 GeV/c proton launched with 25/5 m x/y offset at the IP
Particles with initially vertical and longitudinal spins
The incoherent component is vertical as expected
The incoherent part has a strength of 1.810-5 for protons (0.710-9 for deuterons)

5. 3D Spin Rotator
Three modules for control of the radial, vertical, and longitudinal spin components
Module for control of the radial component (fixed radial orbit bump)
Module for control of the vertical component (fixed vertical orbit bump)
Module for control of the longitudinal component

6. 3D Rotator Integration Placement of 3D spin rotator elements
Location in the lattice

7. Transverse Proton Polarization
Reference proton in an ideal lattice with a 3D spin rotator launched with initially radial and vertical spins; spin tune = 10-2
Proton in an ideal lattice with a 3D spin rotator launched with initially radial and vertical spins with 25/5 m x/y offset at the IP

8. Longitudinal Deuteron Polarization
Reference deuteron in an ideal lattice with a 3D spin rotator launched with initially radial and vertical spins; spin tune = 10-4
Deuteron in an ideal lattice with a 3D spin rotator launched with initially radial and vertical spins with 25/5 m x/y offset at the IP

9. Lattice Imperfections
Transverse quadrupole misalignments
Horizontal and vertical closed orbit distortions

10. New Stable Spin Orientation
Longitudinally polarized proton and deuteron launched along closed orbit
 Coherent parts of the resonance strengths are 2.5210-3 for protons and 1.14 10-5 for deuterons
Proton and deuteron launched along closed orbit with their spins along the stable direction determined by the coherent strength component

11. Stabilization by 3D Spin Rotators
Vertical proton polarization stabilized by a single 3D spin rotator giving a spin tune of 10-2
Oscillations because spin tune of 10-2 is not “much greater” than the coherent resonance strength component of 2.5210-3
After compensation of the coherent component by a 2nd 3D rotator

12. Spin Flip
Adiabaticity criterion: spin reversal time must be much longer than spin precession period
 flip >> 1 ms for protons and 0.1 s for deuterons
Vertical and longitudinal stable spin direction components as set by the spin rotator vs time
Spin tune vs time, changes due to piece-wise linear shape above

13. Spin Flip Simulation
Protons
Deuterons at different rates

14. Summary and Conclusions
The ability of a 3D spin rotator to control the ion polarization in the JLEIC energy range has been verified
The incoherent part of the resonance strength has been calculated for protons and deuterons setting the limit on the 3D spin rotator strength
The coherent part of the resonance strength has been calculated for protons and deuterons using the statistical model
Compensation of the coherent part of the resonance strength has been numerically demonstrated
A spin flipping system implemented using a 3D rotator for protons and deuterons has been numerically modeled
All results obtained so far agree with earlier theoretical and analytical predictions