About polarized protons acceleration at U70 A Otboyev

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

Spin in accelerator 1970 -1974 A. Skrinsky, Ya. Derbenev, A. Kondratenko, ……. -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: . φ

“Ideal” flat machine: Precise energy calibration z x Intrinsic resonances: Imperfection resonances: - emittance electron: ΔE = 440. 652 Me. V; proton: ΔE = 523. 342 Me. V spin response function

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

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

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

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% S 0 ) δS = 99% S 0 10 20 30 40 50 60 70 γ

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

Helical dipole magnets 0 y x( z) xx y ( z) 2λ - 0. 031 0 z y 2λ 1 Rotating frame -Ap -1 Spin precession around (ap= 1. 79284735); Ap ≈ 0. 5 by h = 5 T; λ = 3 m with frequency In laboratory frame after one period spin rotates around λ p 1 λ p 2 λ -p 2 λ by angle φ = 2π(νs -1) -p 1 1) No outside orbit distortions due to mirror symmetry 2) Moderate orbit deviations inside 3) Spin rotation by anypangle around arbitrary axis in medium plane 1 4) Low focusing

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

Siberian snake at RHIC 4 superconducting full twist helical magnets: magnetic field 4 T, λ= 2. 4 m,

Partial snake (φ<π) ν = 38 - νz ν = 18 + νz ν 0

PARTIAL SIBERIAN SNAKE BASED ON HELICAL MAGNETS FOR U-70 By Bx Bz

Partial snake at U-70

Bx(z) and By(z) on the snake axis corrector Helix 3. 4 m ( = 0. 75 m)

Proton’s trajectory in the snake E=25 Гэ. В corrector Helix 3. 4 m x ( = 0. 75 m) corrector

Spin “trajectory” in the snake φy ≈ 1. 14

Snake strength: |ws| =φ/2π 40 (%) |wk| 0. 20 30 0. 15 25 0. 10 10 0. 05

Optical functions

Vertical polarization with snakes

Summary ◘ Acceleration of polarized protons at U-70 is possible with three partial snakes (|ws| ≈ 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 εz = 10 -15 мм мрад ; ♣ betatron tunes: ◘ νz = 9. 9; νx =9. 8. Further study (spin tracking) ☺