About polarized protons acceleration at U-70

1. A.Otboyev,P.Shatunov, Yu.Shatunov BINP, Novosibirsk S.Ivanov,S.Nurushev IHEP, Protvino About polarized protons acceleration at U-70 Dubna Spin-05

3. Spin in accelerator Orbital motion doesn’t depend on spin and determines fields acting on spin -”spin closed orbit” - spin tune φ - “spin field”, distributed around . In linear approximation: 1970-1974 A.Skrinsky,Ya.Derbenev, A.Kondratenko, ……. -semi-classical Hamiltonian with spin

4. Precise energy calibration Intrinsic resonances: - emittance z electron: ΔE = 440.652 MeV; proton: ΔE = 523.342 MeV Imperfection resonances: spin response function x “Ideal” flat machine:

5. Single resonance model -resonance strength; - tuning - tuning rate • spin phase advance in • resonance zone Fast crossing: ( 1)   - spin harmonic matching; coupling compensation - Q-jump; pulse shunting: Spin in accelerator Froissart-Stora:spin resonance crossing Adiabatic crossing:(  1)   -? - partial snake; RF-dipole ,

6. Proton synchrotron U-70(in operation from 1968) E = 70 GeV 400 linear spin resonances LINAC 12 super-periods FODO BOOSTER

7. Vertical closed orbit in U-70 (Δ≈ ±5mm)

8. Spin resonances: proton synchrotron U -70 (Protvino) νx = 9.8 νz = 9.87 νy = 0.002 (P = 12) imperfection ν = k = q·P ν = k = q·10 Zs ≈ 1 мм intrinsic ν = q·P ± νz ν = q·10 ± νz (εz ) norm = 10 mm·mrad S = -(99% S0) δS = 99% S0 γ 10 20 30 40 50 60 70

9. φ = π; z x y 2 Snakes z x Siberian snakes – remedy against spin resonances Ya.Derbenev, A.Kondratenko (1974)

10. 0 y x ( z ) x x y ( z ) 2λ - 0.031 y 2λ 0 z 1 Rotating frame -Ap Spin precession around (ap=1.79284735); with frequency -1 Ap ≈ 0.5 by h = 5T; λ = 3m In laboratory frame after one period spin rotates around λ λ λ λ by angle φ = 2π(νs -1) p2 -p2 -p1 p1 1) No outside orbit distortions due to mirror symmetry 2) Moderate orbit deviations inside 3) Spin rotation by any angle around arbitrary axis in medium plane 4) Low focusing p1 Helical dipole magnets

11. Сибирские змейки (RHIC) V.Ptitsyn, Yu.Shatunov (1994)

12. Siberian snake at RHIC 4 superconducting full twist helical magnets: magnetic field4T, λ= 2.4 m,

13. Partial snake (φ<π) ν = 38 - νz ν = 18 + νz ν0

14. Bz Bx By PARTIAL SIBERIAN SNAKEBASED ON HELICAL MAGNETS FOR U-70

15. Partial snake at U-70

16. corrector corrector Helix 3.4 m ( = 0.75 m) Bx(z) and By(z) on the snake axis

17. corrector corrector Helix 3.4 m ( = 0.75 m) Proton’s trajectory in the snake E=25 ГэВ x

18. Spin “trajectory” in the snake φy ≈ 1.14

19. Snake strength: |ws| =φ/2π (%) |wk| 0.20 0.15 0.10 0.05 40 30 25 10

20. 1 ● ● ● ● ● ν = k = m P/4 ν = k= (m +1/2) P/4 - + + + 1 1 2 2 3 3 У-70 ● ● 2 ● ● ● ● ● 3 Partial snakes at U-70

21. Optical functions

22. γ

24. Vertical polarization with snakes

25. Summary ◘Acceleration of polarized protons at U-70 is possible with three partial snakes (|ws|≈ 0.18) ◘ Requirements: ♣develophelical magnets(λ = 0.75 м ; L=3.4 m; B = 4.5 Т); ♣ bending magnets alignment ≤ 5 мм ; ♣ normalized emittance εz = 10-15 мм мрад ; ♣ betatron tunes: νz= 9.9; νx =9.8 . ◘ Further study (spin tracking) ☺