Stored Polarized Atomic Hydrogen
for Møller Polarimetry
V.G. Luppov
University of Michigan Spin Physics Center
December 7, 2002
OUTLINE
1. Electron – spin – polarized atomic hydrogen stabilization
1.1 Principle
1.2 Michigan prototype apparatus
2. Target Thickness
2.1 Magnetic compression
2.2 Confinement time
2.3 Atomic hydrogen decay
2.4 Achievable density and thickness
2.5 Atomic hydrogen density monitoring
3. Target electron spin polarization
3.1 Polarization of incoming atomic hydrogen
3.2 Atoms with “wrong” spin admixture
3.3 Polarization “self-cleaning” mechanism
3.4 Depolarization processes
3.5 Polarization reversal
4. Residual gas backgrounds
4.1 Helium background
4.2 Accelerator residual gas background
5. Conclusions
1
Schematic Hyperfine Energy Level Diagram of
Hydrogen Atom in Magnetic Field
17 mK
E(K)
1  
2   +  
Electron spin “up”
(Low Field Seekers-LFS)
10.8K at 8T
68 mK
B(T)
Electron spin “down”
3  
(High Field Seekers-HFS)
51 mK
51 mK
 - electron spin,
      
 - proton spin
For instance, for a magnetic field of 8 T and the atomic hydrogen
temperature of 300 mK, the ratio of electron spins - down to spinsup is exp(2BB/kT)= 3.61015.
In order to stabilize atomic hydrogen several essential
requirements have to be met:
- atoms must be made (by dissociating H2 );
- the electron spins must be polarized, so that atoms interact via the 3u+
potential;
- the spin polarization must be maintained;
- the atomic hydrogen must be confined to a cell and the surface
recombination must be suppressed.
2
Potential Energy of Low Field Seekers ( 1> and 2> ) and High
Field Seekers ( 3> and 4> ) Along the Solenoid Axis.
Storage Cell Displayed Relative to the Solenoid Field Profile
3
Schematic Diagram of the Michigan Prototype Jet Target
20 cm
__________
4
The probability that the electron spin-up atoms
enter the Stabilization Cell
p = e-B/kT
Probability
where  - Bohr magneton (9.2710-24 J/T);
B - magnetic field;
K - Boltzmann constant (1.3810-23 J/K)
T - temperature (T  300 mK)
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
1.00E-09
1.00E-10
0
1
2
3
4
5
6
Magnetic Field (T)
5
7
8
9
10
Magnetic Compression
Axial stored polarized atomic hydrogen density distribution:
n(z) = n(B0)exp[-(B0-Bz(z))/kT]
Density Distribution in Magnetic Field
1.00E+00
Density (arb.units)
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
8
6
4
Magnetic Field (T)
6
2
0
The axial longitudinal solenoid magnetic field decay can be approximated
by Bz(z) = B0(1-z2/z02) (z0=14 cm):
Magnetic Field (T)
Solenoid Field Profile
9
8
7
6
5
4
3
2
1
0
0
2
4
6
8
10
12
14
16
18
Distance from Solenoid Center (cm)
Stored Atomic Hydrogen Density Profile
Density (arb. units)
1
0.8
0.6
0.4
0.2
0
0
2
4
6
8
10
12
14
Distance from Solenoid Center (cm)
7
16
18
Confinement Time
dn/dt = – n/es, where es = esoeB/kT
eso = 4Veff/KvavA (~ 50 ms)
Veff - cell volume (for diameter D=4 cm, effective length
L=19 cm, Veff=239 cm3)
K - Clausing flow conductance fact
(Our cell K=(15(L/D)+12(L/D)2)/(20+38(L/D)+12(L/D)2); K=19)
vav - average atomic velocity
(for T=300 mk vav=(2/√π)√2kT/m=80 m/sec)
A – cell cross section (12.6 cm2).
Confinement Time (sec)
Confinement Time
1.00E+09
1.00E+07
1.00E+05
1.00E+03
1.00E+01
1.00E-01
0
2
4
6
8
Magnetic Field (T)
For 8 Tesla magnetic field es = 3x106 sec: an ideal trap
8
10
Atomic Hydrogen Decay
Rate equations for hyperfine3 and 4 states in case:
- there are no1 and 2 states;
- low density (< 1017 H/cm3) to ignore volume recombination
{H + H +H  H2 + H}
dn4/dt = 4/Veff - 2 K44 n42 – K43 n4 n3 – G43 (n4 + n3)( n4 – n3) - n4/es ,
dn3/dt = 3/Veff – K43 n4 n3 + G43 (n4 + n3)( n4 – n3) – n3/es ,
where ni - atomic hydrogen i state density
i - atomic hydrogen i state feed rate,
Veff - effective volume,
Kij - two-body recombination rate constants (occurring
principally on the surface), {H + H +He  H2 + He}
G43 - two-body magnetic dipole-dipole nuclear relaxation rate
constant, {3  4 }
es - escaping time from the magnetic trap,
________________________________________________________________________
If n3 + n4  n and n3 = n4 = n/2, then:
dn4/dt = 4/Veff - 2 K44 n42 – K43 n4 n3 – G43 (n4 + n3)( n4 – n3) - n4/es ,
+
dn3/dt = 3/Veff – K43 n4 n3 + G43 (n4 + n3)( n4 – n3) – n3/es
_____________________________________________________________
dn/dt = /Veff - Kseff n2 – n/es
where  = 3 + 4 - atomic hydrogen feed rate
Kseff =1/2 (K43 + K44)
9
Two-Body Recombination Rate Constants
K43 =2.510-8 (A/V) 2 exp(2b/kT) T1/2 B-2
K44 = 3 K43
Kseff =1/2 (K43 + K44) = 510-8 (A/V) 2 exp(2a/kT) T1/2 B-2
where A - storage cell surface area,
V - storage cell effective volume,
 - thermal deBroglie wavelength
(=(h2/2kTM)1/2=1.7410-7 T-1/2)
a - H adsorption energy on He surface (a  1 K)
10
Density (atoms/cm3)
Stored Atomic Hydrogen Density vs Magnetic
Field for Different H Feed Rates (T=0.3 K)
1x10^15
atoms/sec
5x10^15
atoms/sec
1x10^16
atoms/sec
1.00E+17
1.00E+16
1.00E+15
1.00E+14
1.00E+13
1.00E+12
1.00E+11
1.00E+10
0
2
4
6
8
10
Solenoid Magnetic Field (T)
Thickness
(atoms/cm2)
Stored Atomic Hydrogen Thickness vs Magnetic
Field for Different H Feed Rates (T=0.3 K)
1.00E+18
1.00E+17
1.00E+16
1.00E+15
1.00E+14
1.00E+13
1.00E+12
1.00E+11
1.00E+10
1x10^15
atoms/sec
5x10^15
atoms/sec
1x10^16
atoms/sec
0
2
4
6
8
10
Solenoid Magnetic Field (T)
11
Stored Atomic Hydrogen Density vs
Temperature (B =8 T)
3
Density (atoms/cm )
1.00E+17
1.00E+16
1x10^15
atoms/sec
1.00E+15
5x10^15
atoms/sec
1x10^16
atoms/sec
1.00E+14
M.Mertig et al,
Rev.Sc.In. 62 (1),
1991
1.00E+13
0
0.1
0.2
0.3
0.4
Temperature (K)
12
0.5
Atomic Hydrogen Density Monitoring
Either a capacitive pressure gauge (Matthey, A.P.M., Walraven, J.T.M., and Silvera,
I.F., Phys. Rev.Lett. 46, 668 (1981),
or a bolometer monitor (Mertig, M., Luppov, V.G., Roser, T., and Vuaridel B.,
Rev.Sci. Instrum., 62(1), 251 (1991)) could be used for continues atomic hydrogen
density measurements.
13
Target Electron-Spin- Polarization
1  
17 mK
E(K)
2   +  
Electron spin “up”
(Low Field Seekers-LFS)
10.8K at 8 T
68 mK
B(T)
Electron spin “down”
3  
(High Field Seekers-HFS)
51
 - electron spin,
51 mK
mK
      
 - proton spin
 = tan , where  = 1/2arctan(a/[h(e + p )B]
a = 9.4210-25 [J] - hyperfine coupling constant,
e = 2.801010 [T-1s-1] – electron gyromagnetic ratio,
p = 4.26107 [T-1s-1] – proton gyromagnetic ratio.
For the mixed state 4> a fraction of atoms with “wrong”
electron–spin–up direction is tan2 .
14
Target Electron-Spin- Polarization
Fraction of Electron Spinup
Electron Spin-up Fraction vs. Magnetic Field
1.00E-03
1.00E-04
1.00E-05
1.00E-06
0
2
4
6
8
10
Magnetic Field (T)
Density (arb.units)
Density Distribution in Magnetic Field
1.00E+00
1.00E-01
1.00E-02
1.00E-03
1.00E-04
1.00E-05
1.00E-06
1.00E-07
1.00E-08
8
6
4
Magnetic Field (T)
15
2
0
Polarization “Self-Cleaning” Mechanism
eso = 4Veff/KvavA (~ 50 ms)
Veff - cell volume (for diameter D=4 cm, effective length
L=19 cm, Veff=239 cm3)
K - Clausing flow conductance fact
(Our cell K=(15(L/D)+12(L/D)2)/(20+38(L/D)+12(L/D)2); K=19)
vav - average atomic velocity
(for T=300 mk vav=(2/√π)√2kT/m=80 m/sec)
A – cell cross section (12.6 cm2).
16
Depolarization Processes
dn2/dt =ξK333n33 + G32n32– n2/es0,
where
ξ = 0.91 – a fraction of {3 + 3 + 3  H2 + 2}
(1- ξ) → {3 + 3 + 3  H2 + 3}
K333 - three-body recombination rate constant
(K333≈9·10-39 cm6/sec),
G32 – electronic relaxation rate constant
(G32 = 1.1·10-15exp(-1.35B/T) cm3/sec)
es0 = 0.05 sec
3
Density (atoms/cm )
Stored Electron-Spin-Up ([2>) Atomic Hydrogen Density vs
Magnetic Field for Different H Feed Rates (T=0.3 K)
1x10^15 ato ms/sec
5x10^15 ato ms/sec
1x10^16 ato ms/sec
1.00E+11
1.00E+10
1.00E+09
1.00E+08
1.00E+07
1.00E+06
0
2
4
6
8
Magnetic Field (T)
17
10
3
Density (atoms/cm )
Stored Electron-Spin-Up ([2>) Atomic Hydrogen Density vs
Magnetic Field for Different H Feed Rates (T=0.3 K)
1x10^15 ato ms/sec
5x10^15 ato ms/sec
1x10^16 ato ms/sec
1.00E+11
1.00E+10
1.00E+09
1.00E+08
1.00E+07
1.00E+06
0
2
4
6
8
10
Magnetic Field (T)
3
Density (atoms/cm )
Stored Atomic Hydrogen Density vs Magnetic
Field for Different H Feed Rates (T=0.3 K)
1x10^15 atoms/sec
5x10^15 atoms/sec
1x10^16 atoms/sec
1.00E+17
1.00E+16
1.00E+15
1.00E+14
1.00E+13
1.00E+12
1.00E+11
1.00E+10
0
2
4
6
8
Magnetic Field (T)
18
10
Polarization Reversal
● To reverse the stored atomic hydrogen longitudinal polarization the
magnetic field orientation has to be changed.
● For this purpose, the solenoid magnetic field should be first turned off,
and then turned back on with the opposite polarity.
● Then the storage cell should be refilled with atomic hydrogen.
● The total procedure should not take longer than 1.5 hours.
Schematic Diagram of the Michigan Prototype Jet Target
19
Residual Gas Backgrounds
● Helium Background
Pressure (Torr)
Vapor Pressure of Liquid He4
1.60E-05
1.00E-04
1.00E-08
1.00E-12
1.00E-16
1.00E-20
1.00E-24
1.00E-28
1.00E-32
2.80E-04
2.70E-07
3.40E-10
8.10E-16
4.20E-32
0
0.1
0.2
0.3
0.4
0.5
0.6
Temperature (K)
● The superfluid film flows from the coldest towards the warmest
surfaces until it evaporates.
● A special “film-burner” technique can be used to keep pressure,
measured at 300 K, as low as 810-7 Torr.
● This pressure corresponds to helium density of n300K = P/kT = 2.41010
atoms/cm-3 at 300 K, or n0.3K = n300K300K/0.3K = 81011 atoms/cm-3
at 300 mK, or 1.61012 electrons/cm3, which is about 0.02% of the
atomic hydrogen electron density (1016 electrons/cm3).
● This helium pressure could be significantly decreased by means of
differential pumping.
● Accelerator Residual Gas Background (by EAC)
● At JLab, the accelerator residual gas pressure at room temperature is
about 1·10-5 Torr. It mainly consists of N2 and water.
● The corresponding electron density is 3·1012 electrons/cm3 , or about
0.03% of the electron density of the atomic hydrogen.
● It should be mentioned that the residual gas pressure near
the target would be significantly lower due to cryopumping.
20
.
Conclusions
● The considerations above show that stored, longitudinally electron-spinpolarized atomic hydrogen can be used as a pure, 100% polarized gas target.
● A thickness of at least 1·1017 H/cm2 can be reached with a target diameter
of 4 cm and a length of 18 cm along the beam.
Possible Problems with the Electron Beam
The following possible problems have not yet been evaluated:
● Atomic hydrogen ionization and excitation by the beam.
● Heating of the copper storage cell by the beam 500 MHz RF.
21