1. Praha- Dubna SPIN2013 Helical magnets Siberian snakes I.Koop, A.Otboyev, P.Shatunov Yu.Shatunov Budker Institute for Nuclear Physics Novosibirsk

2. Helical magnet yoke cm coil yoke coil

3. Transverse cross section of the field map BzBz kGs cm BxBx kGs cm ByBy kGs cm

4. Helix field components on the axis (λ=2.5 m) BxBx ByBy

5. Particle and spin motion equations in the Cartesian frame (Bρ is a rigidity)

6. Field in helical magnet

7. Orbit in helical magnet (zero approximation) x y

8. Spin in helical magnet (zero approximation) e3e3 e1e1 e2e2 S -k-k For protons (a=1.793) p=1 by b 0 λ=19.6 Tm

9. Siberian snakes and spin rotators 1.Spin rotation 2.No orbit disturbing and coupling outside α1α1 α2α2 α3α3 α4α4 R1R1 R2R2 R3R3 R4R4 p1p1 p2p2 p3p3 p4p4 R 1 =R 4 ; R 2 =R 3 p 1 =-p 4 ; p 2 =-p 3 snakes rotators.

10. Siberian snakes and spin rotators for RHIC (field)

11. Siberian snakes and spin rotators for RHIC (orbit E=25 GeV)

12. Siberian snakes and spin rotators for RHIC (spin)

13. Siberian Snake in RHIC 4 superconducting helical dipoles : Magnetic field 4T, length 2.4 m each with 360° twist, coil inner aperture 100 mm.

14. RHIC polarization E=255 GeV L=5·10 31 cm -2 s -1 S~50%

15. Snake from 2 helical magnets BxBx ByBy ξ = + ξ = - z (cm)

16. Optimal particle trajectory y x z (cm) (cm)

17. Spin trajectory S(0)=S y → -Sy z (cm) SySy SxSx SzSz

18. Spin trajectory z (cm) SzSz SxSx SySy S(0)=S z → -S z

19. Partial snakes

20. Partial snakes (field on axis) Helix 3.4 m ( λ =0.75 m) corrector

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

22. Spin in partial snake (33%)

23. ACCELERATION OF POLARIZED PROTONS IN THE AGS WITH TWO HELICAL PARTIAL SNAKES H. Huang, L.A. Ahrens, M. Bai, K. Brown, E. D. Courant, C. Gardner, J.W. Glenn, R. C. Gupta, A.U. Luccio, W.W. MacKay, V. Ptitsyn, T. Roser, S. Tepikian, N. Tsoupas, E. Willen, A. Zelenski,K. Zeno, BNL, Upton, USA M. Okamura, J. Takano, Radiation Laboratory, RIKEN, Saitama, Japan, F. Lin, Indiana University, Bloomington 13% 6% AGS S=70%

24. Partial snakes at U-70

25. Partial snakes at U-70 (spin tune)

26. NICA polarization?

27. NICA polarization ( protons 10 GeV) Helical magnet snake B=4 T; L=10 m Δx~Δz~1-2 mm Solenoid snake B=4T; L=10 m (coupling?) lr ⊗ ⊙

28. transverse longitudinal IBS diffusion rate (s -1 ) NICA polarization + luminosity L e

29. “Rotating” quads angle I 1 /I 2

30. Luminosity considerations Coulomb scattering cross-section: Limitations: ● ● space-charge effect instabilities in electron cooler: ● beam-beam effect bunches. Assumptions: ● ● ● ● round beams electron cooling will squeeze beams to the space charge limit ●

31. Luminosity considerations E k (GeV) N p =10 11

32. Conclusion Thanks for attention! Let’s do it!