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

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

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

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

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

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

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

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

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

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 = 0.612 s  2 = 0.5 12.45 tr  = 1 8.53 t = 60 ms 2.4 60 t (s)

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.

Unperturbed Lattice with tr = 12.453

Transition Jump Lattice with tr = 11.452

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 0.04574 𝑘 1 𝑄𝑇𝑅𝐶𝑅01 ( 𝑚 −2 ) 0.15876 0.15376 0.14876 0.14376 0.13876 0.13376 0.12876 0.12376 0.11876 0.11302 𝑘 1 𝑄𝑇𝑅𝐶𝑅02 ( 𝑚 −2 ) 0.16376 0.16876 0.17376 0.17876 0.18376 0.18876 0.19376 0.19876 0.2045 Δ𝛾 𝑡𝑟 -0.01333 -0.05311 -0.11866 -0.20892 -0.32246 -0.45756 -0.61225 -0.78445 -1.00089 𝛾 𝑡𝑟 12.453 12.43977 12.39999 12.33444 12.24418 12.13064 11.99554 11.84085 11.66865 11.45221 𝜈 𝑥 24.22 24.21997 24.2199 24.21977 24.21959 24.21936 24.21907 24.21874 24.21835 24.21784 𝜈 𝑦 23.16 23.15998 23.15996 23.15993 23.15988 23.15983 23.15977 23.1597 23.15961 𝜕 𝜈 𝑥 /𝜕(Δ𝑝/𝑝) 0.9555 0.94107 0.89831 0.82797 0.73135 0.61025 0.46702 0.30456 0.12635 -0.09234 𝜕 𝜈 𝑦 /𝜕(Δ𝑝/𝑝) 1.2277 1.23282 1.2382 1.24385 1.24978 1.25602 1.2626 1.26956 1.27696 1.28605

Transition Energy Crossing Procedure Acceleration starts below transition at 𝑑𝛾/𝑑𝑡=1.6343 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 =0.15876 𝑚 −2 to the final values of 𝑘1 𝑓 𝑄𝑇𝑅𝐶𝑅01 =𝑘 1 𝑖 −Δ𝑘1=0.15876−0.04574=0.11302 𝑚 −2 𝑘1 𝑓 𝑄𝑇𝑅𝐶𝑅02 =𝑘 1 𝑖 +Δ𝑘1=0.15876+0.04574=0.2045 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

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

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

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

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

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

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

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

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

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