Spin-Manipulating Polarized Deuterons *

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1 Jefferson Lab, Newport News, VA 28 May 2009 Spin-Manipulating Polarized Deuterons * V.S. Morozov 1, A.W. Chao 1,, A.D. Krisch 1, M.A. Leonova 1, R.S. Raymond 1, D.W. Sivers 1, V.K. Wong 1 ; A.M. Kondratenko 2 ; E.J. Stephenson 3 1 Spin Physics Center, University of Michigan, Ann Arbor, MI , USA 2 GOO Zaryad, Russkaya St. 41, Novosibirsk, Russia 3 IUCF, Indiana University, Bloomington, IN , USA * This research was supported by grants from the German BMBF Science Ministry and its FFE program at COSY. also at SLAC, 2575 Sand Hill Rd., Menlo Park, CA

2 OUTLINE Motivation Experimental apparatus at Forschungszentrum Jülich Manipulation of deuteron vector and tensor polarizations Chao s new matrix formalism for describing spin dynamics Kondratenko Crossing to overcome depolarizing resonances Possible improvement of Kondratenko Crossing Summary 2

3 MOTIVATION Manipulation of deuteron vector and tensor polarizations: precise control over deuteron polarizations reduce systematic errors in polarized scattering experiments Chao s new matrix formalism for describing spin dynamics: analytic calculation of polarization at any time during piecewise-linear spin resonance crossing Kondratenko Crossing to overcome depolarizing resonances: better preserve polarization when going through spin resonance even with moderate crossing rate Possible improvement of Kondratenko Crossing: easier practical implementation, possibly less sensitive to beam s momentum spread 3

4 COSY COoler SYnchrotron Deuterons: 1.85 GeV/c D source cycled through 5 (P V,P T) spin states LE Polarimeter monitored injected polarization e-cooler reduced momentum spread at injection RF Dipole or RF Solenoid EDDA detector as polarimeter 4

5 POLARIZED H - /D - ION SOURCE 5

6 FERRITE RF DIPOLE Ceramic vacuum pipe Brms dl = 0.54 T mm at ~917 khz 6

7 RF SOLENOID Ceramic vacuum pipe Brms dl = 0.67 T mm at ~917 khz 7

EDDA DETECTOR as deuteron polarimeter Beam pipe Beam C or CH2 fiber target Two cylindrical double layers Outer double layer: 32 scintillator slabs (Δφ = 11.

8 EDDA DETECTOR as deuteron polarimeter Beam pipe Beam C or CH2 fiber target Two cylindrical double layers Outer double layer: 32 scintillator slabs (Δφ = ), 2 29 scintillator half-rings (Δθlab = 2.5 ) Inner double layer: 640 scintillating fibers Fast deuteron polarimeter Inclusive scaler counts in Left, Right, Top & Bottom quadrants d 8

9 SPIN-1 BEAM POLARIZATION Deuteron s gyromagnetic anomaly Gd = (~12.5 x smaller than proton s) Three possible spin components along vertical axis: +1, 0 & -1 Vector polarization P V = N+ N N + N + N + 0 Tensor polarization = N 0 PT 1 3 N + + N 0 + N N +, N 0 & N = number of particles in +1, 0 & -1 states., 9

10 SPIN MOTION AND SPIN FLIPPING Unperturbed spin motion precession about vertical axis with frequency νs = Gγ spin tune RF magnet can create spin resonance centered at fr = fc (n ± νs) fc beam s circulation frequency Sweeping rf magnet s frequency through fr flip PV direction Froissart-Stora equation gives final polarization 2 i ( π ε f c ) PV = PV 2 exp 1 Δf/ Δt ε = resonance strength Δf = frequency ramp range Δt = ramp time Spin-flip efficiency η P /P V i V 10

11 ROTATING DEUTERON POLARIZATION Sweeping rf magnet s frequency through fr rotates polarization by an angle θ. vector and tensor polarizations transform as i i 2 P V( θ= ) P 3 1 V cos θ, P T( θ= ) P[ T cos θ ] 2 2 modified Froissart-Stora formula for PV 2 PV ( π ε f c ) i = (1 +ηˆ)exp ˆ P η Δf/ Δt V formula for PT PT 3 PV 1 3 ( π ε f c ) = (1 )exp 1 i i ˆ ˆ P 2 = 2 2 +η η f/ t 2 T P Δ Δ V ˆη limiting spin-flip efficiency 11

12 RESONANCE MAP at fixed frequency December 03 V.S. Morozov et al., Phys. Rev. ST-AB 8, (2005) Measured Resonance Frequency and Width f = ± khz V ω = 40.8 ± 0.8 Hz V f = ± khz T ω = 39 ± 7 Hz T 12

13 VARYING RAMP TIME December 03 V.S. Morozov et al., Phys. Rev. ST-AB 8, (2005) Measured Resonance Strength η ˆ = 100 ± 2% ε V V = (1.17 ± 0.01) 10 6 η ˆ = 100 ± 2% ε T T = (1.14 ± 0.02) 10 6 ε 1 e(1+ Gγ) π2 2 p ~7 too large! B rms dl 13

14 VARYING FREQUENCY RANGE December 03 V.S. Morozov et al., Phys. Rev. ST-AB 8, (2005) 14

15 MULTIPLE SPIN FLIPPING December 03 V.S. Morozov et al., Phys. Rev. ST-AB 8, (2005) P = P ( η ) i V V V η = 96.5 ± 0.6% V n P = P ( η ) i V V V η = 98.5 ± 0.3% V n i 2 PT = P 3 1 T ( ηt) 2 2 η = 98.3 ± 1.0% T n 15

16 CHAO MATRIX FORMALISM A.W. Chao, Phys. Rev. ST-AB 8, (2005) Particle s spin state described by two-component complex spinor Ψ Spinor equation of motion near single spin resonance iνθ r dψ i G γ( θ) ε e = d 2 iνrθ Ψ θ ε e G γθ ( ) θ= 2π fc t = time variable ν = the spin resonance tune r Equation solved analytically for o constant distance between Gγ and ν r o linearly changing distance between Gγ and Spinor evolution described by time-dependent matrix Matrices multiplied sequentially for piece-wise linear crossing pattern Resulting matrix determines final spinor state and polarization ν r 16

17 CHAO TEST SCHEMATIC f start Δf = fixed f end w f end - f r f r f 17

18 CHAO TEST WITH PARTIALLY COOLED BEAM May 07 V.S. Morozov et al., Phys. Rev. Lett. 100, (2008) P V f r (+1, +1) χ 2 /(N-2) = 1.3 (-1/3, -1) χ 2 /(N-2) = 2.1 (-2/3, 0) χ 2 /(N-2) = 2.3 (-1, +1) χ 2 /(N-2) = s e-cooling Δt = 100 ms Δf = 400 Hz = 1.06 x 10-5 ε f r = _ 0.5 Hz = 32 +_ 1 Hz δ f Δ p f end (khz) 18

19 CHAO TEST WITH FULLY COOLED BEAM May 07 V.S. Morozov et al., Phys. Rev. Lett. 100, (2008) P V f r (+1, +1) χ 2 /(N-2) = 3.5 (-1/3, -1) χ 2 /(N-2) = 1.1 (-2/3, 0) χ 2 /(N-2) = 1.1 (-1, +1) χ 2 /(N-2) = s e-cooling Δt = 100 ms Δf = 400 Hz ε = 1.06 x 10-5 f r = _ 0.5 Hz = 23 +_ 1 Hz δ f Δ p f end (khz) 19

20 CHAO TEST WITH FULLY COOLED BEAM May 07 V.S. Morozov et al., Phys. Rev. Lett. 100, (2008) Green line: original prediction from V.S. Morozov et al., PRST-AB 10, (2007) P V / P V i Δf = 400 Hz Δt = 100 ms f r = Hz f = 23 Hz p Chao ε Chao ε = 1.00 x 10-5 = 1.06 x 10-5 Fig. 4 data averaged for all spin states δ Δ [f end - f r ] (Hz) 20

APPLICATION TO KONDRATENKO CROSSING f fast slope link slope ε = 1 10-5 [df /dt]link = [df /dt]fast fc = 1 147

21 APPLICATION TO KONDRATENKO CROSSING f fast slope link slope ε = [df /dt]link = [df /dt]fast fc = Hz δf = 9.8 Hz rms Δt slow = 160 ms Δf slow = 400 Hz Δf fast Δf slow slow slope t Δf gap Δt fast Δt slow 21

22 KONDRATENKO CROSSING SHAPE KC FC f fast slope link slope Δf slow Δf fast slow slope f KC t Δf gap Δt fast Δt slow Shape defined by Δtslow, Δfslow, Δtfast, Δffast, and [df/dt]fast / [df/dt]link ratio 22

23 CHOOSING CROSSING PARAMETERS A.M. Kondratenko, Internal Report, 17 November Suppose [df /dt]link = [df /dt]fast then to overcome spin resonance strength ε with rms spin resonance frequency spread δf [df /dt]fast must satisfy: [df /dt]fast 83 (ε fc) 2 [df /dt]fast 156 (δf ) 2 [fc circulation frequency] and the crossing parameters should be chosen as Δfslow ([df /dt]fast) 1/2 Δtslow = 6.03 Δfslow / [df /dt]fast Δf fast = 1.43 ([df /dt]fast) 1/2 Δtfast = 1.43 / ([df /dt]fast) 1/2 23

24 1.85 GeV/c DEUTERONS AT COSY May 08 V.S. Morozov et al., accepted for publication in Phys. Rev. Lett. P V / P V i (P V, P T ) (+1, +1) (-1/3,-1) (-2/3, 0) ( -1, +1) Δt (s) Fit to Froissart-Stora formula ε = (1.067 ± 0.003)

25 Kondratenko Crossing (KC) & Fast Crossing (FC) May 08 by Varying fkc V.S. Morozov et al., accepted for publication in Phys. Rev. Lett. fr spin resonance center frequency f KC KC shape center frequency Parameters at COSY: 1 ε = δf 10 Hz rms 0.5 f r (unb) P V / P V i Δfslow = 400 Hz Δtslow = 160 ms Δf fast = 185 Hz Δtfast = 12 ms KC (unbunched) FC (unbunched) KC prediction (unb) FC prediction (unb) f KC (khz) KC fit using Chao formalism f r = ± 0.1 Hz δf = 24.4 ± 0.2 Hz fwhm 25

26 Kondratenko Crossing (KC) & Fast Crossing (FC) May 08 by Varying fkc V.S. Morozov et al., accepted for publication in Phys. Rev. Lett. fr spin resonance center frequency f KC KC shape center frequency Parameters at COSY: 1 ε = δf 10 Hz rms P V / P V i 0.5 Δfslow = 400 Hz Δtslow = 160 ms Δf fast = 185 Hz Δtfast = 12 ms f r (unb) f r (bunched) KC (unbunched) FC (unbunched) KC prediction (unb) FC prediction (unb) KC (bunched) FC (bunched) f KC (khz) KC fit using Chao formalism f r = ± 0.1 Hz δf = 24.4 ± 0.2 Hz fwhm 26

27 KC and FC by Varying Δf fast and Δtfast May 08 V.S. Morozov et al., accepted for publication in Phys. Rev. Lett. ε = fr = ± 0.1 Hz δf = 24.4 ± 0.2 Hz fwhm P V / P V i KC (unbunched) FC (unbunched) KC (bunched) FC (bunched) KC prediction (unb) FC prediction (unb) P V / P V i KC (unbunched) FC (unbunched) KC (bunched) FC (bunched) KC prediction (unb) FC prediction (unb) Δf fast (Hz) Δt fast (ms) 27

28 KC and FC by Varying Δtslow and Δfslow May 08 V.S. Morozov et al., accepted for publication in Phys. Rev. Lett. ε = fr = ± 0.1 Hz δf = 24.4 ± 0.2 Hz fwhm 1 Unbunched P V / P V i a) KC (unb) FC (unb) KC prediction FC prediction Δt slow (ms) Δf slow (Hz) b) 28

29 Depolarization Summary at KC Peak May 08 V.S. Morozov et al., accepted for publication in Phys. Rev. Lett. 1 - P V / P V (%) i _ 0.2% _ 0.2% 2.6% 16.4% KC unb. FC unb. KC pred. (unb.) FC pred. (unb.) f KC Δf fast Δt fast Δt slow Δf slow Parameter varied 29

30 Depolarization Summary at KC Peak May 08 V.S. Morozov et al., accepted for publication in Phys. Rev. Lett. 1 - P V / P V (%) i _ 0.2% _ 0.2% 2.6% 16.4% _ 0.3% _ 0.3% KC unb. FC unb. KC pred. (unb.) FC pred. (unb.) KC bunched FC bunched f KC Δf fast Δt fast Δt slow Δf slow Parameter varied 30

31 KC and FC for Different ε Kondratenko Crossing Fast Crossing P V / P V i ε = ε = ε = ε = ε = P V / P V i ε = ε = ε = ε = ε = [f r - f KC ] (Hz) [f r - f KC ] (Hz) 31

32 Kondratenko Triple Crossing ν Gγ - νr νr m or m ± νy Requirements: Spin rotation about vertical axis between crossings Ψ αβ =Ψ βγ = 2π m Spin rotation about horizontal axis 2 θb π θ a =θ c = + ( πε ) f 2 4 where sin exp c θ= 2 Δν/ Δt na Δνi / Δti Tune change ranges Δν i > Δνi = non-adiabatic zone size 2πf link line ab Δt link ν c α β (f KC ) Δν c γ Δν a a b c Δνb t Δt a Δt b bc Δt link Δt c 32

33 Kondratenko Triple Crossing by Ramping νy Gγ, ν y, Gγ - ν y acceleration dν s / dt = 1.81 s -1 ν y Gγ - ν y Δt (ms) 33

34 SUMMARY Achieved 97 ± 1% vector polarization spin-flip efficiency Observed and explained tensor polarization s behavior: transformation of tensor component under rotation Experimentally demonstrated Chao formalism s validity: excellent agreement of observed polarization oscillations with Chao formalism prediction Successfully tested KC concept: ~ 4.7 x reduction in depolarization with unbunched beam ~ x reduction in depolarization with bunched beam Developing KC test with proton intrinsic & imperfection resonances 34

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