Charlottesville VA SPIN 2008 10/10/2008

SPIN@COSY: Spin-Manipulating Polarized Deuterons and Protons *

M.A. Leonova1, A.W. Chao1,†, E.D. Courant1, A.D. Krisch1, V.S. Morozov1, R.S. Raymond1, D.W. Sivers1, V.K. Wong1;

A. Garishvili2,‡, R. Gebel2, A. Lehrach2, B. Lorentz2, R. Maier2, D. Prasuhn2, H. Stockhorst2, D. Welsch2;

F. Hinterberger3, K. Ulbrich3; Ya.S. Derbenev4, A.M. Kondratenko5, Y.F. Orlov6, E.J. Stephenson7.

1 Spin Physics Center, University of Michigan, Ann Arbor, Michigan 48109-1040, USA 2 Forschungszentrum Jülich, Institut für Kernphysik, Postfach 1913, D-52425 Jülich, Germany 3 Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, D-53115 Bonn, Germany

4 J-Lab, Newport News, VA 23606, USA 5 GOO Zaryad, Russkaya St. 41, Novosibirsk, 630058 Russia

6 Laboratory for Elementary-Particle Physics, Cornell University, Ithaca, NY 14853, USA 7 IUCF, Indiana University, Bloomington, Indiana 47408-0768 USA

* This research was supported by grants from the German BMBF Science Ministry, its FFE program at COSY, the U.S. NSF, and the Helmholtz

Association through funds provided to the virtual institute “Spin and strong QCD” (VH-VI-231). † also at SLAC, 2575 Sand Hill Rd., Menlo Park, CA 94025. ‡ also at Erlangen-Nürnberg Univ., D-91058, Germany.

2

OUTLINE

• Introduction • Highly efficient Spin Flipping of polarized Proton beam • Interesting behavior of Deuteron Tensor Polarization • Chao’s new matrix formalism for describing spin dynamics • Kondratenko Crossing to overcome depolarizing resonances

• Studies of RF-Induced Spin Resonance Strength ε at COSY using • RF-Dipole and 2.1 GeV/c polarized Protons • RF-Dipole and 1.85 GeV/c polarized Deuterons • RF-Solenoid and 1.85 GeV/c polarized Deuterons

3

SPIN DYNAMICS

• Thomas-BMT equation

||(1 ) (1 ) ( )1⊥⎡ ⎤γ β×= − + γ + + − γ + ×⎢ ⎥γ + γ⎣ ⎦

q EdS G B G B G Sdt m c

S – spin vector in particle’s rest frame G – particle’s gyromagnetic anomaly [Gp = 1.792847, Gd = −0.142987] B , E – magnetic and electric fields in laboratory frame γ – particle’s Lorentz energy factor

• In ring • Spin precesses around bending dipoles’ vertical magnetic fields • spin tune ≡ number of spin precessions per turn around ring

ν = γs G .

4

SPIN RESONANCES

• Resonance strength 1 (1 ) (1 )2

ν θ⎧ ⎫= + γ + + θ⎨ ⎬π ⎩ ⎭ε ∫ rilr

rmany turns

BBG G e dB B

rB , lB – radial and longitudinal perturbing magnetic fields νr – spin resonance tune θ – particle’s orbital angle

• Radial perturbing magnetic field ∂= +∂

rr

BB yy higher-order multipoles

• Imperfection resonances due to magnet errors & misalignments ν =s n

• Intrinsic resonances due to vertically focusing magnetic fields ν = ± νs yn ,

ν y – vertical betatron tune (number of vertical oscillations per turn)

5

SPIN FLIPPING WITH RF MAGNET

• An rf magnetic field can cause spin resonances centered at r cf f ( )= ± νsn

• Sweeping rf magnet’s frequency through rf ⇒ flip polarization direction

• Froissart-Stora equation describes final polarization 2

cf i

( f )P P 2exp - -1f / t

⎧ ⎫⎡ ⎤π⎪ ⎪= ⎢ ⎥⎨ ⎬Δ Δ⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭

ε

ε – resonance strength fΔ – frequency ramp range tΔ – ramp time

• Spin-flip efficiency f i-P / Pη ≡

6

SPIN-MANIPULATING POLARIZED DEUTERONS & PROTONS at COSY

• Protons: 2.1 GeV/c

• Deuterons: 1.85 GeV/c • H− source

cycled through up & down states

• D− source cycled through 5 V T(P ,P ) spin states

• LE Polarimeter monitored injected polarization

• e-Cooler reduced momentum spread at injection

• RF Dipole or RF Solenoid

• EDDA detector as a polarimeter

7

EDDA DETECTOR proton & deuteron polarimeter

• Two cylindrical double layers

Outer double layer:

− 32 scintillator slabs (Δφ = 11.25°)

− 2 × 29 scintillator half-rings (Δθlab = 2.5°)

Inner double layer:

− 640 scintillating fibers

• C or CH2 fiber target

p

Beam

Beam pipe

8

FERRITE RF DIPOLE

Ceramic vacuum pipe ∫Brms⋅dl = 0.54 T⋅mm at ~917 kHz

9

RF SOLENOID

Ceramic vacuum pipe ∫Brms⋅dl = 0.67 T⋅mm at ~917 kHz

10

SPIN FLIPPING of POLARIZED PROTONS

SPIN RESONANCE SEARCH April 2004

Leonova et al PRL 93, 224801 (2004)

fr = 902.4 ± 0.1 kHz

w = 2.4 ± 0.3 kHz

11

MAXIMIZE SPIN-FLIP EFFICIENCY OPTIMIZE Δf and Δt of FREQUENCY SWEEP April 2004

Leonova et al., PRL 93, 224801 (2004)

-1

-0.5

0

0.5

1

0.001 0.01 0.1 1

P

Δ t (sec)

RF OFF

1 flipΔf/2 = +/- 4 kHz

Set Point

Solid line is fit to Froissart-Stora equation 2

cf

i

( f )P 2exp - -1P f / t⎧ ⎫⎡ ⎤π⎪ ⎪= ⎨ ⎬⎢ ⎥Δ Δ⎪ ⎪⎣ ⎦⎩ ⎭

ε

with ε as fit parameter ⇒ measured εFS

12

MEASURING SPIN-FLIP EFFICIENCY MULTIPLE SPIN-FLIPPING April 2004

Leonova et al., PRL 93, 224801 (2004)

We fit data to

nn iP = P (- )η

nP – polarization after n flips η – spin-flip efficiency

fit gave η = 99.92 ± 0.04%.

13

POLARIZATION OF SPIN-1 DEUTERON BEAM • Deuteron’s gyromagnetic anomaly Gd = –0.142987

~ 12.5 times smaller than proton’s

• Spin-1 particle has 3 possible vertical spin components: +1 , 0 , -1

• Vector polarization + -

V+ 0 -

N - NP = N + N + N

• Tensor polarization 0

T+ 0 -

3NP = 1- N + N + N,

+N , 0N , -N are number of particles in +1 , 0 , -1 states

14

ROTATING DEUTERON POLARIZATION

Sweeping rf magnet’s frequency through spin resonance

• Rotates polarization by angle θ

• Vector and Tensor polarizations transform as ⎡ ⎤⎣ ⎦

i i 2V V T T

3 1P (θ) = P cosθ, P (θ) = P cos θ -2 2

• Modified Froissart-Stora formula for Vector polarization

ˆ ˆ⎡ ⎤⎢ ⎥⎣ ⎦

2V ciV

P (π | | f )= (1+ η)exp - - ηΔf / ΔtPε

• Formula for Tensor polarization

ˆ ˆ⎧ ⎫⎛ ⎞ ⎡ ⎤⎪ ⎪⎨ ⎬⎜ ⎟ ⎢ ⎥⎪ ⎪⎝ ⎠ ⎣ ⎦⎩ ⎭

22 2V cT

i iT V

P (π | | f )P 3 1 3 1= - = (1 + η)exp - - η -2 2 2 Δf / Δt 2P Pε

η̂ ≡ limiting spin-flip efficiency

15

SPIN MANIPULATING POLARIZED DEUTERONS

December 2003

V.S. Morozov et al., Phys. Rev. ST-AB 8, 061001 (2005)

Striking PT behavior of spin-1 bosons

16

SUMMARY of SPIN-FLIPPING at COSY

USING AIR-CORE RF-DIPOLE

• Proton spin-flip efficiency in April 03 η = 99.3 ± 0.1%.

• Deuteron spin-flip efficiency in February 03 η = 48 ± 1%.

USING FERRITE RF-DIPOLE

• Proton spin-flip efficiency in April 04 η = 99.92 ± 0.04%.

• Deuteron spin-flip efficiency in December 03 η = 96 ± 2%.

17

SPIN@COSY CHAO TEST EXPERIMENT

V.S. Morozov et al., Phys. Rev. ST Accel. Beams 10, 041001 (2007) V.S. Morozov et al., Phys. Rev. Lett. 100, 054801 (2008)

fend - fr

f

fr

fstart Δf = fixedfend

w

18

CHAO TEST WITH FULLY COOLED BEAM May 2007 V.S. Morozov et al., Phys. Rev. Lett. 100, 054801 (2008)

fr

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

916.9 917.0 917.1

(+1, +1) χ2/(N-2) = 3.5(-1/3, -1) χ2/(N-2) = 1.1(-2/3, 0) χ2/(N-2) = 1.1(-1, +1) χ2/(N-2) = 4.4

PV

fend (kHz)

25 s e-coolingΔt = 100 msΔf = 400 Hz

= 1.06 x 10 -5 ε

= 916 985.3 0.5 Hz fr f pδ Δ

+_ = 23 1 Hz +_

19

KONDRATENKO CROSSING

Δfslow

Δtslow

f

t

Δffast

Δt fast

link slope

slow slope

fast slope

Δfgap

Shape defined by Δtslow, Δfslow, Δtfast, Δffast, and df/dtlink/ df/dtfast ratio

20

Kondratenko Crossing (KC) May 2008

vs Fast Crossing (FC)

0.2

0.4

0.6

0.8

1

20 40 60

KC prediction (unb)FC prediction (unb)

KC (unbunched)FC (unbunched)KC (bunched)FC (bunched)

PV

/ PV

Δtfast (ms)

i

21

DATA SUMMARY at KC PEAK May 2008

++

+

0

5

10

15

fKC Δffast Δtfast Δtslow Δfslow

KC pred. (unb.)FC pred. (unb.)

KC unb.FC unb.KC bunchedFC bunched

1 - P

V / P

V (%

)

Parameter varied

i

3.3 0.2%_15.6 0.2%_0.8 0.3%_

+15.0 0.3%_2.6%

16.4%

22

STRENGTH of RF SPIN RESONANCE

• The Froissart-Stora equation describes the final polarization 2

f i

( f )P P 2exp 1

f / tπ

= − −Δ Δ

⎧ ⎫⎡ ⎤⎨ ⎬⎢ ⎥

⎣ ⎦⎩ ⎭

ε c

ε − resonance strength fΔ − frequency ramp range tΔ − ramp time

• Widely-used formulae: RESONANCE STRENGTH FOR SOLENOID

(1 )1 12 2

γ→∞+= ∝γπ

⎯⎯⎯→ε ∫Bdl rmse G B dl

p

RESONANCE STRENGTH FOR DIPOLE (1 )1 1

2 2γ→∞+ γ= ∝

βπ⎯⎯⎯→ε ∫Bdl rms

e G B dlp

where e and p are the particle’s charge and momentum.

23

STRENGTH of RF SPIN RESONANCES M.A. Leonova et al., Phys. Rev. ST-AB 9, 051001 (2006)

as of November 2004

0.1

1

10

100

0.1 1 10

a (p, dipole, COSY)b (p, dipole, COSY)c (p, dipole, COSY)d (p, dipole, COSY)e (p, dipole, IUCF)f (p, dipole, IUCF)g (p, dipole, IUCF)h (p, dipole, IUCF)i (p, dipole, IUCF)j (p, dipole, IUCF)k (p, solenoid, IUCF)l (p, solenoid, IUCF)m (d, dipole, COSY)n (d, dipole, COSY)o (d, solenoid, IUCF)p (e, dipole, MIT)

ε FS /

ε Bdl

Δf (kHz)

Ratios of FSε / Bdlε vs. frequency range Δf used in the Δt curves. εFS is obtained by fitting data on Δt curves to Froissart-Stora equation, εBdl is obtained using rf-magnet's ∫B·dl

24

TOTAL RESONANCE STRENGTH

ˆ| - |

⎛ ⎞= + = × +∫ ⎜ ⎟ν ν +⎝ ⎠

ε ε εdipole foy res

B dl kDA

εdipole due to the rf dipole’s field, ε fo due to the fields seen during coherent oscillations,

A and D complex constants, ν y vertical betatron tune, νres spin resonance tune

WE MEASURED DEPENDENCE ON • dipole strength

• distance to 1st order spin resonance

• beam’s size

• beam’s momentum spread

• frequency sweep range Δf for deuterons

25

RF-DIPOLE SPIN RESONANCE STRENGTH PROTONS

RF Dipole Voltage Study November 2005

0

2

4

6

0 1 2 3

ε FS (x

10 -4

)

Vrms (kV)

νx = 3.575νy = 3.525fres= 906.5 kHzΔf = 8 kHzΔt = 4 ms

1 kV r.m.s. corresponds to ∫B·dl ~ 0.2 T·mm r.m.s.

LINEAR DEPENDENCE on DIPOLE STRENGTH

26

BEAM SIZE STUDY PROTONS November 2005

M.A. Leonova et al., Phys. Rev. ST-AB 9, 051001 (2006)

• Used Fast Quadrupole to increase beam’s size.

• Measured beam’s vertical size for different currents in the Fast Quad.

11.4

11.8

12.2

12.6

13

0 1 2 3 4 5

ε FS /

ε Bdl

ΔyFWHM (mm)

εFS / εBdl = 12.1 ± 0.1

27

VERTICAL BETATRON TUNE STUDY PROTONS November 2005

M.A. Leonova et al., Phys. Rev. ST-AB 9, 051001 (2006)

Fit to a hyperbola -

= +ν ν

εε

FS

Bdl y res

BA gives:

νres = 3.6060 ± 0.0005 (calculated νres = 3.605) A = 0.9 ± 0.9 B = 1.01 ± 0.06

10

100

3.52 3.56 3.6 3.64

ε FS /

ε Bdl

νy

Vdipole> 1 kV

Vdipole< 1 kV

28

RF-DIPOLE & SOLENOID SPIN RESONANCE STRENGTH DEUTERONS

SPIN RESONANCE SEARCH

RF Dipole May 2006

A.D. Krisch et al, Phys Rev ST-AB 10, 071001 (2007)

-0.5

0

0.5

916.9 917.0

frf (kHz)

e-cooling ON

-0.5

0

0.5

(+1, +1)(1/3, -1)(-2/3, 0)

P V

e-cooling OFF

= 916 960 10 Hz = 42 2 Hz

++

__

fr w

= 916 992 10 Hz = 23 2 Hz

++

__

fr w

RF Solenoid May 2007

V.S. Morozov et al, Phys. Rev. Lett. 100, 054801 (2008)

-0.5

0

0.5

(+1, +1)(-1/3, -1)(-2/3, 0)(-1, +1)

916.9 917.0 917.1frf (kHz)

e-cooling ON for 25 s

c)

-0.5

0

0.5e-cooling ON for 15 sP V

b)

-0.5

0

0.5 a)e-cooling OFF = 916 988 10 Hz

= 86 2 Hz+

+_

_fr w

= 917 010 10 Hz = 41 1 Hz

_+

+_

fr w

= 916 990 10 Hz = 29 1 Hz

+_+_

fr w

29

RF FREQUENCY RANGE Δf & BEAM Δp/p DEUTERONS

RF Solenoid May 2007

Submitted to PRL

εFS / εBdl = 1.02 ± 0.05

“BNL” factor of 2 confirmed

RF Dipole May 2006

A.D. Krisch et al., Phys. Rev. ST-AB 10, 071001 (2007)

εFS / εBdl = 0.15 ± 0.01

~ 7 × too small ⇒ problem with (1+Gγ) ??

0.1

1

SOLENOID, IUCF DIPOLE, COSYDIPOLE, COSY, MAY 06, cooling OFFDIPOLE, COSY, MAY 06, cooling ONSOLENOID, COSY, MAY 07, cooling OFFSOLENOID, COSY, MAY 07, cooling ON

ε FS /

ε Bdl

Δf (kHz)

0.3

0.3 310.1

30

VERTICAL BETATRON TUNE STUDY DEUTERONS

RF Solenoid May 2007

Submitted to PRL

No dependence on νy ⇒ No coherent oscillations

εFS / εBdl = 1.02 ± 0.05

RF Dipole May 2006

A.D. Krisch et al., Phys. Rev. ST-AB 10, 071001 (2007)

green medium-dash line – fit to asymmetric hyperbola

black small-dash line –

Kondratenko’s calculation

0.1

1

3.6 3.7 3.8

DIPOLE, MAY 06, cooling OFFSOLENOID, MAY 07, cooling OFFSOLENOID, MAY 07, cooling ONSOLENOID, MAY 07, cooling ONON RESONANCE

νy

3

0.3

νs = ν

y - 4

ε FS /

ε Bdl

31

STRENGTH of RF SPIN RESONANCES

0.1

1

10

100

0.1 1 10

a (p, dipole, COSY)b (p, dipole, COSY)c (p, dipole, COSY)d (p, dipole, COSY)e (p, dipole, IUCF)f (p, dipole, IUCF)g (p, dipole, IUCF)h (p, dipole, IUCF)i (p, dipole, IUCF)j (p, dipole, IUCF)k (p, solenoid, IUCF)l (p, solenoid, IUCF)m (d, dipole, COSY)n (d, dipole, COSY)o (d, solenoid, IUCF)p (e, dipole, MIT)

ε FS /

ε Bdl

Δf (kHz)

Dec.04 (d, dipole, COSY)

Nov.05 (p, dipole, COSY)May 06 (d, dipole, COSY)

May 07 (d, solenoid, COSY)

RF Solenoid RF Dipole

(1 )12 2

+= ∫π

εBdl rmse G B dlp OK

(1 )12 2

+ γ= ∫π

εBdl rmse G B dlp NO

NO SIMPLE FORM