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

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

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

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

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

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

8. imperfection ν = k = q·P ν = k = q·10 Z s ≈ 1 мм intrinsic ν = q·P ± ν z ν = q·10 ± ν z (ε z ) norm = 10 mm· mrad (P = 12) Spin resonances: proton synchrotron U -70 (Protvino) S = -(99% S 0 ) δS = 99% S 0 ν x = 9.8 ν z = 9.87 ν y = 0.002 γ 10 20 30 40 50 60 70

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

10. In laboratory frame after one period spin rotates around by angle φ = 2π(ν s -1) p1p1 λλλλ p1p1 -p 1 p2p2 -p 2 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 Rotating frame with frequency Spin precession around Ap ≈ 0.5 by h = 5T; λ = 3m (a p = 1.79284735); -Ap x y 2λ2λ 0 0.031  xz() yz() 10z x 2λ2λ y Helical dipole magnets

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

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

13. Partial snake (φ<π) ν0ν0 ν = 38 - ν z ν = 18 + ν z

14. PARTIAL SIBERIAN SNAKE BASED ON HELICAL MAGNETS FOR U-70 BxBx BzBz ByBy

15. Partial snake at U-70

16. B x (z) and B y (z) on the snake axis Helix 3.4 m ( = 0.75 m) corrector

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

18. Spin “trajectory” in the snake φ y ≈ 1.14

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

20. ● ● ● ● ● ● ● ● ● ●● ● У-70 1 2 3 ν = k = m P/4 ν = k= (m +1/2) P/4 123 ++ 123 -+ 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 (|w s | ≈ 0.18) ◘ Requirements: ♣ develop helical magnets (λ = 0.75 м ; L=3.4 m; B = 4.5 Т); ♣ bending magnets alignment ≤ 5 мм ; ♣ normalized emittance ε z = 10-15 мм мрад ; ♣ b etatron tunes: ν z = 9.9; ν x =9.8. ◘ Further study (spin tracking) ☺