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Praha- Dubna SPIN2013

Helical magnets Siberian snakes. I.Koop, A.Otboyev, P.Shatunov Yu.Shatunov Budker Institute for Nuclear Physics Novosibirsk. Praha- Dubna SPIN2013. yoke. coil. Helical magnet. cm. yoke. coil. cm. B z. B x. B y. kGs. kGs. kGs. cm. cm. cm. cm. cm. cm.

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Praha- Dubna SPIN2013

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

  2. yoke coil Helical magnet cm yoke coil cm

  3. Bz Bx By kGs kGs kGs cm cm cm cm cm cm Transverse cross section of the field map

  4. Bx By Helix field components on the axis(λ=2.5 m)

  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. e2 S e3 -k e1 Spin in helical magnet(zero approximation) For protons (a=1.793) p=1 by b0λ=19.6 Tm

  9. Siberian snakes and spin rotators • Spin rotation • No orbit disturbing and coupling outside α3 α4 α1 α2 R3 R4 R1 R2 p3 p4 p1 p2 rotators snakes . R1=R4; R2 =R3 p1=-p4; p2 =-p3

  10. Siberian snakes and spin rotatorsfor RHIC (field)

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

  12. Siberian snakes and spin rotatorsfor 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=5·1031cm-2s-1 S~50%

  15. Snake from 2 helical magnets ξ = - ξ = + By Bx z (cm)

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

  17. Spin trajectory S(0)=Sy→ -Sy Sz Sy Sx z (cm)

  18. Spin trajectory S(0)=Sz→ -Sz Sz Sy Sx z (cm)

  19. Partial snakes

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

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

  22. Spin in partial snake (33%)

  23. ACCELERATION OF POLARIZED PROTONS IN THE AGS WITH TWOHELICAL 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, USAM. Okamura, J. Takano, Radiation Laboratory, RIKEN, Saitama, Japan, F. Lin, Indiana University, Bloomington S=70% 6% AGS 13%

  24. Partial snakes at U-70

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

  26. NICA polarization?

  27. l r ⊗ ⊙ 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?)

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

  29. “Rotating” quads angle I1/I2

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

  31. Np=1011 Ek (GeV) Luminosity considerations

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

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