1. JLEIC Collaboration meeting Spring 2016 Ion Polarization with Figure-8
March 29-31, 2016,
Thomas Jefferson National Accelerator Facility Newport News, Virginia USA
Ion Polarization with Figure-8
A.M. Kondratenko 1, Ya.S. Derbenev 2, Yu.N. Filatov 3, M.A. Kondratenko 1, F. Lin 2, V.S. Morozov 2 and Y. Zhang 2
1 Science and Technique Laboratory Zaryad, Novosibirsk, Russia
2 Jefferson Lab, Newport News, VA
3Moscow Institute of Physics and Technology, Dolgoprydny, Russia

2. Outline Features of ion polarization control in figure-8 rings
Ion polarization stability in figure-8 rings. Coherent and incoherent parts of the zero-integer spin resonance strength
Verification of analytic predictions by spin tracking
Analysis of ion polarization stability in the JLEIC collider up to 200 GeV
Summary
Future plans
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

3. Spin Motion in Figure-8 Rings
Spin transparency in a figure-8 structure
Spin precessions in the two arcs are exactly cancelled
In an ideal structure (without perturbations) all solutions are periodic
The spin tune is zero independent of energy
n = 0
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

4. Polarization Preservation during Ion Acceleration
To preserve the beam polarization during acceleration, it is sufficient to stabilize the spin motion in the zero-integer spin resonance region using one weak solenoid
The required solenoid field integral does not exceed 1 Tm at the top energy of the booster.
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

5. Control of Ion Polarization in Collider Ring
3D spin rotator allows one to adjust any polarization orientation at the interaction point
Polarization stability condition
The spin tune induced by the PC solenoids must significantly exceed the strength of the zero-integer spin resonance
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

6. Strength of Zero-Integer Spin Resonance
The resonance strength is determined by the average spin perturbation component and consists of coherent and incoherent parts.
caused by closed orbit distortions
caused by emittances of the synchrotron and betatron oscillations
lies in the ring plane
is vertical
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

7. Figure-8 Booster Original 3 GeV/c booster scaled to 8 GeV/c
Stabilizing solenoid with B||l < 0.35 Tm
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

8. Incoherent Part of Resonance Strength in Figure-8 Booster
Ideal figure-8 booster, on-momentum particles with 1 cm offsets in x and y
Stable polarization direction vertical as expected!
Incoherent part of the resonance strength
protons
vertical
(Zgoubi)
(Zgoubi)
longitudinal
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

9. Coherent Part of Resonance Strength in Figure-8 Booster
Stable spin direction due to coherent part lies in the horizontal plane
RMS closed orbit distortion of a few hundred m
On-momentum particle launched along CO
Precession rate gives the value of the coherent part of the spin resonance strength
protons
vertical
(Zgoubi)
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

10. Stabilization of Proton Spin in Figure-8 Booster
Figure-8 booster with transverse quadrupole misalignments
0.35 Tm (maximum) spin stabilizing solenoid (=510-3)
On-momentum particle with 1 cm offsets in x and y
protons
(Zgoubi)
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

11. Incoherent Part of Resonance Strength in Figure-8 Booster
Ideal figure-8 booster, on-momentum particles with 1 cm offsets in x and y
Stable polarization direction vertical as expected!
Incoherent part of the resonance strength <10-8
deuterons
vertical
(Zgoubi)
(Zgoubi)
longitudinal
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

12. Coherent Part of Resonance Strength in Figure-8 Booster
Same transverse quadrupole misalignments as for protons
On-momentum particle launched along CO, coherent strength part <10-6
0.35 Tm solenoid (=1.510-3), p/p=0 particle with 1 cm offsets in x and y
deuterons
vertical
(Zgoubi)
longitudinal
(Zgoubi)
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

13. Coherent Part of Resonance Strength in the JLEIC Collider
Assuming RMS closed orbit distortion of ~200 m
2T4m control solenoids allow setting proton and deuteron spin tunes to p= and d=10-4.
This is sufficient for stabilization and control of polarization in the JLEIC collider up to 60 GeV without compensation and up to GeV with compensation.
Going above 100 GeV requires additional measures.
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

14. Compensation of Coherent Part of Resonance Strength up to 100 GeV
The first 3D rotator located in the straight containing the interaction point directly controls the polarization.
The second 3D rotator with constant solenoid fields is located in the other straight and is used to compensate the coherent part of the zero-integer spin resonance strength.
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

15. Incoherent Part of Resonance Strength vs Momentum in JLEIC
Assuming normalized vertical beam emittance of 0.07 m rad
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

16. Summary
For stability of ion polarization, the spin tune induced by the 3D spin rotator must significantly exceed the strength of the zero-integer spin resonance.
Calculations of resonance strength for JLEIC show that its coherent part related to closed orbit distortion is a few orders of magnitude greater than its incoherent part related to beam emittances.
3D rotators with 2 T solenoids provide control of proton and deuteron polarizations in the JLEIC collider up to 100 GeV.
Analysis of ion polarization stability in the JLEIC collider up to 200 GeV indicates that one has to take additional measures to preserve and control the polarization, e.g. better orbit control, stronger spin control solenoids, and/or small transverse spin control fields.
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA

17. What is next? Future Plans
Spin tracking simulations using verified existing codes
Optics optimization and development of ion polarization scheme for up to 200 GeV/c
Evaluation and compensation of the spin effect of the detector solenoid
Study of non-linear spin effects
Evaluation of beam-beam effect on ion polarization and optimization of the response function at the IP
Development of ion polarization measurement scheme and spin- flipping system for high precision experiments at the JLEIC collider
A. Kondratenko et al, Ion Polarization with Figure-8. JLEIC Collaboration Meeting Spring 2016, March 29-31, 2016, Newport News, Virginia, USA