V.G. Luppov
University of Michigan
June 9, 2003
Storage of Polarized Atomic Hydrogen
OUTLINE
1. Introduction2. Electron-spin-polarized atomic hydrogen storage
2.1 Principle2.2 Michigan apparatus
3. Target thickness4. Target electron spin polarization5. Unpolarized Gas Backgrounds:
5.1 Metastable H 2s state5.2 Helium Background5.3 Accelerator Residual Gas Background5.4 H2 Background Due to Recombination Processes
6. Possible layout for Møller Polarimetry7. Conclusions
51 mK
17 mK
4⟩ = − ↓⇑⟩ + ε ↑⇓⟩
2⟩ = ↑⇓⟩ + ε ↓⇑⟩
1⟩ = ↑⇑⟩
3⟩ = ↓⇓⟩
10.8K at 8T
68 mK
Schematic Hyperfine Energy Level Diagram of Hydrogen Atom in Magnetic Field
↑ - electron spin, ⇑ - proton spin
In order to stabilize atomic hydrogen:
- atoms must be made (by dissociating H2 );- the electron spins must be polarized;- the spin polarization must be maintained;- the atomic hydrogen must be confined to a cell; - the hydrogen surface recombination must be suppressed.
For atomic hydrogen at B = 8 T and T = 300 mK, ratio electron spins-down to spins-up is exp(2µBB/kT)= 3.6⋅1015
Electron spin “down”
(High Field Seekers-HFS)
Electron spin “up”
(Low Field Seekers-LFS)E(K)
B(T)
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
Hout ( 300 mK)
Mixing Chamber (300 mK) Coated with Superfluid He4 Film
Hin ( 30K)
Schematic Diagram of the Michigan Target
__________20 cm
8 Tesla Solenoid
Still (~ 900 mK)
Dissociator
Mixing Chamber (300 mK)
H2 Inlet
H
The probability that the electron spin-up atoms enter the Stabilization Cell
p = e-µB/kT
1.00E-101.00E-091.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+00
0 1 2 3 4 5 6 7 8 9 10
Magnetic Field (T)
Prob
abilit
y
where µ - 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).
Confinement Time
dn/dt = – n/τes, where τes = τesoeµB/kT
For storage cell with diameter of 4 cm, effective lentgh of 19 cm,
and for n = 1016 atoms/cm3, T = 300 mk and B=0
τeso ~ 4 sec
For 8 Tesla magnetic field τconf= 2x108 sec: an ideal trap
Confinement Time
1.00E+00
1.00E+02
1.00E+04
1.00E+06
1.00E+08
1.00E+10
0 2 4 6 8 10
Magnetic Field (T)
Conf
inem
ent T
ime
(sec
)
Stored Atomic Hydrogen Density vs Magnetic Field for Different H Feed Rates (T=0.3 K)
1.00E+12
1.00E+13
1.00E+14
1.00E+15
1.00E+16
1.00E+17
0 2 4 6 8 10
Solenoid Magnetic Field (T)
Den
sity
(a
tom
s/cm
3 ) 1x10^16atoms/sec5x10^15atoms/sec1x10^15atoms/sec
Stored Atomic Hydrogen Thickness vs Magnetic Field for Different H Feed Rates (T=0.3 K)
1.00E+13
1.00E+14
1.00E+15
1.00E+16
1.00E+17
1.00E+18
0 2 4 6 8 10
Solenoid Magnetic Field (T)
Thic
knes
s (a
tom
s/cm
2 )
1x10^16atoms/sec5x10^15atoms/sec1x10^15atoms/sec
Stored Atomic Hydrogen Density vs Temperature (B =8 T)
1.00E+13
1.00E+14
1.00E+15
1.00E+16
1.00E+17
0 0.1 0.2 0.3 0.4 0.5
Temperature (K)
Den
sity
(ato
ms/
cm3 ) 1x10^16atoms/sec
5x10^15atoms/sec
1x10^15atoms/sec
M.Mertig et al,Rev.Sc.In. 62(1), 1991
Atomic Hydrogen Density MonitoringEither 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 continuous atomic hydrogen density measurements.
Target Electron-Spin- Polarization
↑ - electron spin, ⇑ - proton spin
For the mixed state |4> the fraction of electron–spin–up atoms is tan2 θ,
where θ = 1/2⋅arctan(a/[h(γe + γp )B],a = 9.42⋅10-25 [J] - hyperfine coupling constant,γe = ge·µB/ħ = 2.80⋅1010 [T-1s-1] = electron gyromagnetic ratio,γp = gn·µn/ħ = 4.26⋅107 [T-1s-1] = proton gyromagnetic ratio.
51 mK
17 mK
4⟩ = − ↓⇑⟩ + ε ↑⇓⟩
1⟩ = ↑⇑⟩
3⟩ = ↓⇓⟩
10.8K at 8T
Electron spin “down”
(High Field Seekers-HFS)
Electron spin “up”
(Low Field Seekers-LFS)E(K)
B(T)
2⟩ = ↑⇓⟩ + ε ↓⇑⟩
68 mK
Electron Spin-up Fraction vs. Magnetic Field
1.00E-06
1.00E-05
1.00E-04
1.00E-03
0 2 4 6 8 10
Magnetic Field (T)
Frac
tion
of E
lect
ron
Spin
-up
Density Distribution in 8 T Solenoid's Magnetic Field
n(z) = n(B0)exp[-µ(B0-Bz(z))/kT]
1.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+00
02468
Magnetic Field (T)
Den
sity
(arb
.uni
ts)
Polarization “Self-Cleaning” Mechanism
Escape time for gradB = 0τ esc ~ 4 sec
As soon as low field seekers enter grad B they will be pushed out.
Hout ( 300 mK)
Mixing Chamber
Hin ( 30K)
Depolarization Processes (3> → 2> )dn2/dt =ξK333n3
3 + G32n32– n2/τes0,
where K333 - three-body recombination rate constant (K333≈9·10-39 cm6/sec),
ξ = 0.91 – a fraction of {3> + 3> + 3> → H2 + 2>}
(1- ξ) → {3> + 3> + 3> → H2 + 3>}
G32 – electronic relaxation rate constant (G32 = 1.1·10-15exp(-1.35B/T) cm3/sec)
τes0 = 4 sec
For B = 8 T, T=300 mK and (n3 + n4) ↓ = 1016 atoms/cm3 :
n2↑ = 4·109 atoms/cm3
Metastable 2S StatePermitted Transitions Between Different H Energy Levels and Life Times
2S and 2P States in Magnetic Field
τ = 1.56·10-8 sec
τ = 0.54·10-8 sec
τ = 16·10-8 sec
τ = 0.16·10-8 sec
∞τ =
WeakField
Strong Field
B=0
2S1/2
2P1/2
2P3/2
LFS
HFS
Metastable 2S1/2 states with different electron spins from the dissociator will be separated by the magnetic field gradient when they enter the storage cell.
Gas Backgrounds● Helium Background
Typical He pressure of ~ 10-6 Torr corresponds to~ 2.4⋅1010 atoms/cm3 or ~ 4.8⋅1010 electrons/cm3 at T = 300 K or ~ 7.6⋅1011 atoms/cm3 or ~ 1.5⋅1012 electrons/cm3 at T = 300 mK.
It gives about 0.02% unpolarized electrons density background for stored densityof 1016 electrons/cm3.
● Accelerator Residual Gas Background (by EAC)
Typical Jlab residual gas (H2O and N2) pressure of ~ 10-5 Torr corresponds to~ 2.4⋅1011 moleculers/cm3 or ~ 3⋅1012 electrons/cm3 at T = 300 K.It gives about 0.03% unpolarized electrons density background for stored density of 1016 electrons/cm3.
● H2 Background Due to Recombination Processes
For stored H density of 1016 atoms/cm3 molecular hydrogen density in the cell is about 2⋅1010 H2/cm3.
Radiation Heat Load (Qrad) to the Storage Cell
A surface emits thermal radiation according to the Stefan-Boltzmann equation:W = σ·e ·A ·T4 ,
where σ = 5.67·10-12 Watt · cm-2 ·T-4, e = total emissivity (~0.1 for copper), A = area, T = temperature.
Rather complex: T=300 K or 80 K for different parts.For the proposed geometry
Qrad ~ 1mW << 20 mW = dilution fridge cooling power at 300 mK.
Jefferson Lab Hall A Møller Polarimeter Layout
Possible H Target Layout
Conclusions
● The considerations above show that 100% longitudinally electron-spin-polarized
atomic hydrogen can be stored and used as a pure 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 19 cm along the beam.
● The polarized atomic hydrogen storage technique is well established, broadly studied,
and very reliable.
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