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

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

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

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)

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

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

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

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

Lattice Imperfections Transverse quadrupole misalignments Horizontal and vertical closed orbit distortions

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

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

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

Spin Flip Simulation Protons Deuterons at different rates

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