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Polarized Proton Acceleration in AGS and RHIC

Polarized Proton Acceleration in AGS and RHIC. Spin dynamics and depolarizing resonances Partial and Full Siberian Snakes Polarization development in the AGS Polarization development in RHIC Spin flipper and spin tune meter. RHIC – a High Luminosity (Polarized) Hadron Collider. Jet Target

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Polarized Proton Acceleration in AGS and RHIC

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  1. Polarized Proton Acceleration inAGS and RHIC Spin dynamics and depolarizing resonances Partial and Full Siberian Snakes Polarization development in the AGS Polarization development in RHIC Spin flipper and spin tune meter

  2. RHIC – a High Luminosity (Polarized) Hadron Collider Jet Target 12:00 o’clock (PHOBOS) 10:00 o’clock e-cooling (BRAHMS) 2:00 o’clock RHIC PHENIX 8:00 o’clock RF 4:00 o’clock STAR 6:00 o’clock LINAC NSRL EBIS Booster AGS Operated modes (beam energies): Au–Au 4.6, 10, 28, 31, 65, 100 GeV/n d–Au* 100 GeV/n Cu–Cu 11, 31, 100 GeV/n p–p 11, 31, 100, 205, 250 GeV Possible future modes: Au – Au 2.5 GeV/n (AGS, SPS c.m. energy) p – Au* 100 GeV/n (*asymmetric rigidity) Achieved peak luminosities (100 GeV, nucl.-pair): Au–Au 1201030 cm-2 s -1 p–p 351030 cm-2 s -1 Other large hadron colliders (scaled to 100 GeV): Tevatron (p – pbar) 291030 cm-2 s -1 LHC (p – p, design) 1401030 cm-2 s -1 Tandems

  3. Spinning Quarks or Gluons Spinning Proton Spinning Proton Quark, Gluon, Photon, Electron or Neutrino from W or Z Decay RHIC Spin Physics • Spin structure functions of gluon and anti-quarks • Parity violation in parton-parton scattering • Requires high beam polarization and high luminosity

  4. Delivered Luminosity and Polarization

  5. Spin Dynamics in Rings • Precession Equation in Laboratory Frame: • (Thomas [1927], Bargmann, Michel, Telegdi [1959]) • dS/dt = - (e/gm) [(1+Gg)B + (1+G) BII] S • Lorentz Force equation: • dv/dt = - (e/gm) [ B ] v • For pure vertical field:Spin rotates Gg times faster than motion, nsp = Gg • For spin manipulation:At low energy, use longitudinal fieldsAt high energy, use transverse fields

  6. Spin tune and Depolarizing Resonances Depolarizing resonance condition: Number of spin rotations per turn = Number of spin kicks per turn Spin resonance strength e = spin rotation per turn / 2p Imperfection resonance (magnet errors and misalignments): nsp = n Intrinsic resonance (Vertical focusing fields): nsp = Pn± Qy P: Superperiodicity [AGS: 12] Qy: Betatron tune [AGS: 8.75] Weak resonances: some depolarization Strong resonances: partial or complete spin flip Illustration by W.W. MacKay

  7. Spin Resonance Crossing Froissart-Stora: [a: crossing speed] Non-adiabatic (e2/a << 1)  Adiabatic (e2/a >> 1) Pf /Pi = 1 Pf /Pi = - 1 e Gg-K Gg-K e e K-Gg K-Gg e Gg=K

  8. Spin Resonance Crossing Non-adiabatic (e2/a << 1)  Adiabatic (e2/a >> 1) Pf /Pi = 1 Pf /Pi = - 1 Imperfection Resonances: Correction Dipoles (e small) Partial Snake (e large) Intrinsic Resonances: Pulsed Quadrupoles (a large) RF Dipole (e large) Lattice modifications (e small) Strong Partial Snake (e large)

  9. AGS polarization with (weak) partial snake and rf dipole 0.015 36 -  ~1 ms bin width 0.01 Raw asymmetry = AN Pbeam 0.005 0 -0.005 36 +  -0.01 -0.015 25 30 35 40 45 12 14 16 18 20 22 24 Ebeam Asymmetry flips sign at every G = N and intrinsic res.

  10. Siberian Snakes (Local Spin Rotators) cos(180 nsp) = cos(d/2) · cos(180 Gg) d 0 nsp  n No imperfection resonances Partial Siberian snake (AGS) d= 180 nsp = ½ No imperfection resonances and No Intrinsic resonances Full Siberian Snake (Ya.S. Derbenev and A.M. Kondratenko) Two Siberian Snakes in RHIC

  11. (Naïve) Limits for Siberian Snakes • Spin rotation of Siberian snake (d) > Spin rotation of driving fields (e) • “Spin rotation of Siberian snake drives strong imperfection resonance” • Imperfection resonances e Energy • Intrinsic resonances eEnergy • Partial Siberian snake(AGS, d = 9°)e < d/360° • One full snakee < 1/2 • Two full snakes(RHIC)e < 1 • N full snakes(LHC? N  16)e < N/2 • Ultimate energy limit: Imperfection resonance strength for corrected orbit ~ 0.05 • RHIC (250 GeV)  200 mm residual error  • LHC (7 TeV)  ~20 mm residual error ?

  12. RHIC – First Polarized Hadron Collider pC Polarimeters Absolute Polarimeter (H jet) BRAHMS PHOBOS Siberian Snakes Siberian Snakes PHENIX STAR Spin Rotators (longitudinal polarization) Spin flipper Spin Rotators (longitudinal polarization) Pol. H- Source LINAC BOOSTER 5.9% Helical Partial Siberian Snake AGS 200 MeV Polarimeter Internal Polarimeter pC Polarimeter 10-25% Helical Partial Siberian Snake Without Siberian snakes: nsp = Gg = 1.79 E/m  ~1000 depolarizing resonances With Siberian snakes (local 180spin rotators): nsp = ½  no first order resonances Two partial Siberian snakes (11 and 27 spin rotators) in AGS

  13. 2.6 m 2.6 m Siberian Snakes Major funding by RIKEN, Japan RT helical dipole constructed at Tokano Ind., Japan SC helical dipoles constructed at BNL AGS Siberian Snakes: variable twist helical dipoles, 1.5 T (RT) and 3 T (SC), 2.6 m RHIC Siberian Snakes: 4 SC helical dipoles, 4 T, each 2.4 m long and full 360 twist

  14. Strong Partial Siberian Snake for AGS • A strong partial Siberian snake generates large spin tune gap for G = n. With strong enough snake, gap is large enough to cover both imperfection and intrinsic spin resonances. • Note: With a strong snake, the stable spin direction will deviate from vertical direction (18 degree for 20% snake). Imperfection resonance Intrinsic resonance

  15. E20 5.9% A20 10~15% Two partial snakes in the AGS Vertical betatron tune 36+Qy intrinsic resonance Extraction Vertical component of stable spin Gg Spin tune warm snake cold snake

  16. Betatron Tune and Spin Tune Courtesy of H. Huang

  17. Ramp Measurement

  18. AGS Polarization Dual Partial Snake (Run 6) AC Dipole plus Partial Snake (Run 5) • Dual Partial Snake in AGS avoided depolarization from all vertical depolarizing resonances and largely eliminated intensity dependence • Plan to study low energy polarization loss and also increase acceleration rate at low energy  goal to reach 70% polarization at AGS extraction energy.

  19. Spin Resonances in RHIC w/o Snakes Imperfection resonance strength for corrected orbit with 150 mm residual error Intrinsic resonance strength for 10 p mm mrad particle

  20. Beam Polarization Near a Strong Intrinsic Resonance Without snakes: spin flip, width ~ ± 5e With snakes: opening/closing of “spin cone”, nodes at ± 2 With Snakes:Resonance crossing during acceleration is adiabatic with no polarization loss. Resonance strength e = 0.3, 0.6 Gg

  21. Old tune working point New tune working point 1/12 3/10 3/14 3/10 1/8 3/8 1/6 1/10 1/4 1/10 1/6 Stable polarization on resonance, e = 0.3 Stable polarization on resonance, e = 0.3 0.9 0.8 0.7 0.6 0.9 0.8 0.7 0.6 Snake Resonances • Higher order resonance condition nsp + mQy = k (m, k = integer) driven by interaction of intrinsic resonance Gg + Qy = k with large spin rotations of dipoles and snakes. • No non-linear drive term necessary – combination of rotations is already non-linear. • “Snake resonance strength” depends on intrinsic resonance strength and therefore energy • For nsp=1/2+Dnsp Qy = (2k-1)/2m-Dnsp/m • First analytical solution of isolated resonance with snakes by S.R. Mane, NIM A 498 (2003) 1 single snakeor two snakes with orbit errors two snakes (m: odd)

  22. Luminosity and Polarization Lifetimes in RHIC at 100 GeV Start of acceleration ramp Start of collisions 150 100 Protons x 1011 Collimation complete 50 0 30 Luminosity 1030 cm-2 s-1 20 10 0 60 60 % polarization 40 % Polarization 20 0 19:00 21:00 23:00 01:00 03:00

  23. Polarized Proton Acceleration to 250 GeV injection 250 GeV 45 % polarization on first acceleration to 250 GeV!

  24. Ramp Measurement to 250 GeV Loss at strong intrinsic resonance (136 GeV)

  25. Spin Flipper (plan) • Use spin resonance driven by AC dipole(s) to induce spin flip • Single AC dipole (oscillation) drives two resonances that interfere at nsp = 0.5, only partial spin flip • Two AC dipoles with vertical spin precession in between creates rotating drive field AC dipole AC dipole -45 90 -45 Two AC dipoles One AC dipole

  26. Spin Tune Measurement (plan) • Use AC dipoles to excite coherent spin precession (drive tune  spin tune, ed >> Dnsp) • Measure radial polarization component as Fourier component of turn-by-turn asymmetry measurement. • Ratio of vertical over radial component (or “cone opening”) measures difference of drive tune and spin tune • nsp - nd = ed Pv/Pr VERTICAL RADIAL Beam

  27. Summary • 65 -70 % polarization reached in AGS at 24 GeV • 60 - 65 % polarization reached in RHIC at 100 GeV • 45 % polarization reached in RHIC at 250 GeV

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