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