1. JLEIC Weekly R&D Meeting
Effects of acceleration and transition energy crossing on ion polarization
A.M. Kondratenko, M.A. Kondratenko, Yu.N. Filatov, Ya.S. Derbenev, F. Lin, V.S. Morozov, Y. Zhang
JLEIC Weekly R&D Meeting
February 2, 2017
F. Lin

2. Outline Acceleration Transition energy crossing for protons
Deuterons
Transition energy crossing for protons
Hardt’s scheme
Phase-jump scheme
Start-to-end acceleration
Conclusions

3. Incoherent and Coherent Resonance Strengths
Analytically calculated proton incoherent spin resonance strength for 𝜀 𝑥,𝑦 𝑁 =1 𝜇𝑚  Need a spin tune of ~ 10 −2
Analytically calculated proton vertical orbit excursion due to quadrupole misalignments and resulting coherent spin resonance strength

4. Proton Acceleration
Closed orbit excursion due to random quadrupole misalignments
Acceleration on the closed orbit at different rates

5. Emittance Impact Acceleration of a proton with 𝜀 𝑥,𝑦 𝑁 =1 𝜇𝑚
Orbital dynamics

6. Effect of Adiabaticity Violation
Proton polarization near interference maximum with a well-corrected orbit
Proton polarization near interference maximum with large orbit excursion

7. Incoherent and Coherent Resonance Strengths
Analytically calculated deuteron incoherent spin resonance strength for 𝜀 𝑥,𝑦 𝑁 =0.5 𝜇𝑚  Need a spin tune of ~3⋅ 10 −3
Analytically calculated deuteron vertical orbit excursion due to quadrupole misalignments and resulting coherent spin resonance strength

8. Deuteron Acceleration
Closed orbit excursion due to random quadrupole misalignments
Acceleration along the closed and with 𝜀 𝑥,𝑦 𝑁 =0.5 𝜇𝑚

9. Effect of Momentum Spread
Three deuterons with Δ𝑝/𝑝 = 0 (red) and ± 10 −3 (blue and green)

10. Transition Energy Crossing Scheme I
Constant acceleration rate
Transition energy jump according to the below picture
RF phase flip at the instant of crossing during the jump 
106.6
t = s
 2 = 0.5
12.45
tr
 = 1
8.53
t = 60 ms
2.4 60
t (s)

11. Transition Energy Modification
Scheme by W. Hardt (1974)
Two quadrupole doublets are used in one arc
Horizontal and vertical betatron phase advances between the quadrupoles in each pair are 
Horizontal and vertical betatron phase advances between the pairs are 
The doublets excite dispersion wave around the ring thus modifying the transition energy
Excited dispersion is large. Dispersion increase is unavoidable, but it can be minimized using additional doublets.
This is the worst case scenario.
The betatron tunes and the chromaticities change very little during the jump. We can first ignore their changes.

12. Unperturbed Lattice with tr = 12.453

13. Transition Jump Lattice with tr = 11.452

14. Parameter Table |Δ𝑘1| ( 𝑚 −2 ) 𝑘 1 𝑄𝑇𝑅𝐶𝑅01 ( 𝑚 −2 )
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
𝑘 1 𝑄𝑇𝑅𝐶𝑅01 ( 𝑚 −2 )
𝑘 1 𝑄𝑇𝑅𝐶𝑅02 ( 𝑚 −2 )
0.2045
Δ𝛾 𝑡𝑟
𝛾 𝑡𝑟
12.453
𝜈 𝑥
24.22
𝜈 𝑦
23.16
𝜕 𝜈 𝑥 /𝜕(Δ𝑝/𝑝)
0.9555
𝜕 𝜈 𝑦 /𝜕(Δ𝑝/𝑝)
1.2277
1.2382
1.2626

15. Transition Energy Crossing Procedure
Acceleration starts below transition at 𝑑𝛾/𝑑𝑡= 𝑠 −1
When 𝛾 reaches 𝛾 𝑡𝑟 −Δ𝛾/2=12.453−0.5=11.953, RF is turned off
Strengths of quadrupoles QTRCR01 and QTRCR02 are ramped from the initial values of 𝑘 1 𝑖 ≡ 𝑘1 𝑖 𝑄𝑇𝑅𝐶𝑅01 = 𝑘1 𝑖 𝑄𝑇𝑅𝐶𝑅02 = 𝑚 −2 to the final values of 𝑘1 𝑓 𝑄𝑇𝑅𝐶𝑅01 =𝑘 1 𝑖 −Δ𝑘1= − = 𝑚 −2 𝑘1 𝑓 𝑄𝑇𝑅𝐶𝑅02 =𝑘 1 𝑖 +Δ𝑘1= = 𝑚 −2 in 𝑡 𝑗𝑢𝑚𝑝 of 60 ms
RF is turned on with its phase flipped
Strengths of quadrupoles QTRCR01 and QTRCR02 are returned to their initial values 𝑘 1 𝑖 in 𝑡 𝑐𝑟𝑜𝑠𝑠 of 612 ms
Acceleration continued normally

16. Transition Energy Crossing with Protons
Field ramps in Zgoubi: dipole ramp rate is 3 T/min

17. Proton Dynamics During Crossing
On-momentum particle
Particle with Δ𝑝/𝑝 = 1⋅ 10 −3

18. Proton Spin During Crossing
On-momentum particle
Particle with Δ𝑝/𝑝 = 1⋅ 10 −3

19. Crossing Scheme II: Simple Phase Jump
On-momentum particle
Particle with Δ𝑝/𝑝 = 1⋅ 10 −3

20. Proton Spin in Scheme II
On-momentum particle
Particle with Δ𝑝/𝑝 = 1⋅ 10 −3

21. Impact of Synchrotron Phase
On-momentum particle
Five particles uniformly distributed on an ellipse with Δ𝑝/𝑝 = 1⋅ 10 −3

22. Start-to-End Acceleration
Proton with 𝜀 𝑥,𝑦 𝑁 =1 𝜇𝑚 and Δ𝑝/𝑝 = 0 in an ideal lattice

23. Incoherent Resonance Strength Part
Simulated is large compared to predicted by a factor of ~5
Possible reasons: lack of phase averaging and coupling

24. Conclusions
Simulated spin dynamics of protons and deuterons during acceleration  Looks good but one must pay attention to closed orbit correction and spin resonance interference peaks
Developed a transition energy crossing scheme and simulated orbital and spin dynamics during crossing  Orbital dynamics looks good and there is no effect on spin
Start-to-end simulations are in progress and will be presented at IPAC’17  Qualitatively the results look good but further studies are needed, which are already a part of the original plan