jin huang mit for target group discussion. may 07 epr/pumping chamber pol. table updates may 03...
TRANSCRIPT
EPR updates& Preliminary Pol. Gradient
for He-3 Cell BradyUpdate 5, May 07
Jin HuangMIT
For target group discussion
Jin Huang <[email protected]> 2
May 07 EPR/Pumping
Chamber Pol. Table Updates
May 03 First Gradient Model Fitting
May 05 Review & Update
on Gradient
Target Analysis Meeting
Three Parts Study
Jin Huang <[email protected]> 4
EPR analysis◦ New code was developed to cross check◦ Taking advantage of up2date temperature &
density model by Yi’, Chiranjib, etc.◦ Built in uncertainty analysis
NMR analysis◦ New code was developed to cross check◦ Improved the consistency between spin up/down◦ Improved fitting precision◦ Studied systematic effect of NMR fitting
Target Analysis Meeting
From last week Review of pumping chamber pol. table
Jin Huang <[email protected]> 5
Difference was largely understood Thanks to inputs from Chiranjib
◦ The previous EPR results was designed to be updated with new density/temperature model
The core part of EPR analysis consist to 0.1% (also understood)
Majority difference come from density/temperature. In the previous EPR analysis,◦ Pumping chamber temp. used <2 RTDs>
New model corrected that with 10~20C offset -> few percent difference in density -> EPR pol.
◦ Online density distribution molded used New model also improved
Target Analysis Meeting
EPR Results Update
Jin Huang <[email protected]> 6Target Analysis Meeting
Updated EPR comparison plot
Brady
Maureen Astral(2x Higher NMR gain)
Chiranjib’s point was mistakenly drawn lower in last talk: Code bugs truncated his numbers to integers in the last plot.
2.6% sys. error bar
Jin Huang <[email protected]> 7
Comparing to the one, that asymmetry analysis teams used.
Target Analysis Meeting
Pumping chamber polarization table (Same as last week)
New results
Elog 299
New/Elog 299
Compare raw NMR Fitting
Jin Huang <[email protected]> 8
The pumping chamber table ready? Systematic Errors
◦ 1.8% (density) , from Yi Zhang◦ 1.7% (kappa0, world data)
Extrapolation tested @ our temperature◦ 0.5% (kappa0, ΔT~2C (+) 3C) ◦ 0.8% Fitting
Max shift in <Pol.> by changing NMR fitting function◦ 0.4% Density fluctuations◦ => 2.7% for polarization in pumping chamber
To be scaled down 5~10% from the pol. gradient for target chamberThen polarization table should be ready.
Target Analysis Meeting
Polarization table
Jin Huang <[email protected]> 10
Pumping chamber polarization table close to final Target chamber polarization through gradient
calculation Important time scales
◦ Pol. Transfer ~ 1.6 hour (Elog 616, pp. 9)◦ Depolarization @ 220C ~ 14 hour (Halog 244782)◦ Beam Depolarization @ 13uA ~ 35~45hour (this talk)◦ Spin flip Depol / 20min ~ 62 hour (assuming 0.54%
loss) Polarization difference between two chambers
~= (1/TDepolarization )/(1/TPol. Transfer ) ~ 10%!!?? (Rel.)◦ More precise formula: Elog 616, Eq. (2b)
Target Analysis Meeting
Overview of Pol. GradiantFirst Test
Jin Huang <[email protected]> 11
Yi’ has been focusing on Cell Astral with an analytical method. Meanwhile, we have developed a “global fit” method and tested
with cell Brady◦ Model assumptions: simple two chamber model, Elog 616, Eq. (1a-b)
◦ Parameter assumptions Pol. Transfer D: Calculated w/ J. Singh’s notes, further discussed in Elog 616, pp.
9 Γ t = Γp from high temperature spin down of cell Astral (next slides)
np/nt from density model Spin flip loss ~ 0.54% Full Alkali polarization (99%) : negligible effect with ~5% change
◦ Direct solve the above equation and min-Chi2 fit with all selected data No further assumption needed with built-in error calculation
Target Analysis Meeting
Overview of Approach
pppttpt
ppppSEtpp
PPPPPDdt
dP
PPPPPPDdt
dP
BeamFlipSpin
FlipSpin alkali
First Test
Jin Huang <[email protected]> 12
Γ t & Γp describe intrinsic depolarization◦ He-3 direct coupling◦ Wall effect
◦ Assuming Γ t = Γp
Only(?) data ◦ Astral 220C hot spin down◦ Assuming 0.54% spin flip loss
This test is before start of experiment. flip loss Not well measured.
◦ 1/Spin down time = 1/Γ p+spin flip loss ?? Assuming alkali density is low!
◦ -> Γ p=20 hour for Astral
Apply to cell Brady◦ From UVA, cold lifetime:
Brady/Astral = 36h/49h◦ Extrapolate to high T
◦ -> Γ p=14.7 hour for Brady
Alternative approach◦ Including Γ t = Γp in the following global
fitting -> 14.3 hour +-3% (stat.)
Target Analysis Meeting
More on Γ t & Γp
Time (h)
NM
R (
mV
)
Astral 220CDecay Time (Raw)~ 15.08 +- 0.09 h
Bigbite Turned on
(updated May 03)
(updated May 03)
First Test
Jin Huang <[email protected]> 13
Spin up curve◦ Cell: Brady◦ Spin: Trans –◦ Production Temp.◦ Field Sweep
Calibration of pol.◦ NMR Cross calib same
day◦ Freq sweep -> Field
sweep -> Freq sweep◦ Freq sweep Calibrate to
EPR using Gaussian Conv. Fitting
Target Analysis Meeting
Data Selection 1/3Spin up curve
Pumping Chamber Pol. (Fit)
Target Chamber Pol. (Fit)
Data (Halog 255483)Gaussian Conv.
Fitting
Chi2/n(data) = 10.14/7
Naive Exp. Fit
(updated May 03)
First Test
Jin Huang <[email protected]> 14
Initial part of spin flip session 291
Consistent condition to spin up◦ 2 day after the spin up
Start from almost top polarization
Gaussian Conv. Fitting◦ Raw fit produce obvious too
large error bar
Target Analysis Meeting
Data Selection 2/3Production spin flip session 291
Data (Spin Flip 291)
Pumping Chamber Pol. (Fit)
Target Chamber Pol. (Fit)
Chi2/n = 52.37/31
First Test
Jin Huang <[email protected]> 15
First Test
2nd part of spin flip 291 Consistent condition to
spin up◦ 3 day after the spin up
Start from a beam down Go to near equilibrium Gaussian Conv. Fitting
◦ Raw fit produce obvious too large error bar
Target Analysis Meeting
Data Selection 3/3Production spin flip session 291
Data (Spin Flip 291)
Pumping Chamber Pol. (Fit)
Target Chamber Pol. (Fit) Chi2/n = 69.58/51
Jin Huang <[email protected]> 16
First Test
Γbeam = 36 hour +- 3% (stat.) (updated May 03) W/o beam/spin flips : Pt/Pp = 92% (updated May 03)
W/ beam/spin flips : Pt/Pp = 88% (updated May 03) Systematic uncertainty
◦ Major part: Pol. Transfer D (model calculation, not sure yet) intrinsic depol. Γ t , Γp (data+extrapolation, not sure yet) A useful
measurement: two NMR field sweeps w/ NMR signal from both chamber 1st NMR in laser on equilibrium: direct access polarization diff. Laser off, then wait or (preferred) keep monitoring polarization for >2 hours 2nd NMR in laser off equilibrium: rel. calibration of NMR signal between chambers
◦ Minor part: Beam depol. (~50% error depending on match in condition of
spin up curve and spin flip data) -> 1.5% uncertainty on Pt/Pp
spin flip loss (tiny part, well measured, small uncertainty on Pt/Pp)
Target Analysis Meeting
Results & Uncertainties
Jin Huang <[email protected]> 17
First Test
Free up two more parameters in the fitting◦ Intrinsic depolarization factor Γ t = Γp (assume “=“)
◦ Polarization of alkali metal /or/ Pol. calibration constant of spin up curve Change in condition will change calibration constant
The fit shows◦ Γ t = Γp = 14.3 h, very similar to the extrapolation study
◦ Pol. calibration constant is consistent to 1% ◦ Alkali polarization = 98+-2% (stat.)
The resulting polarization ratio change Pt/Pp < 0.5%
Target Analysis Meeting
Further global studies (updated May 03)
Jin Huang <[email protected]> 18
May 05: Review of assumptions•Inspect assumptions on
• Diffusion parameter• Cell life time
•New global fit
Target Analysis Meeting
Jin Huang <[email protected]> 19
Polarization difference between two chambers, (More precise formula: Elog 616, Eq. (2b))~= (1/TDepolarization )/(1/TPol. Transfer ) = (Γ t + Γ beam + Γ SpinFlip )/D
Dominant factors are Γ t and D◦ D : Pol. Transfer ~ 1.6 hour (Elog 616, pp. 9)◦ Γ t :Depolarization @ 220C ~ 14 hour(new analysis this talk)
◦ Beam Depolarization @ 13uA ~ 35~45hour (this talk)◦ Spin flip Depol / 20min ~ 62 hour (assuming 0.54% loss)
These parameter are re-exameed in following slides
Target Analysis Meeting
Important Factors
Jin Huang <[email protected]> 20
Reference of the model◦ X. Zheng’s thesis, the gas diffusion model◦ Notes of J. Singh, a good summary
Assumptions and my comments◦ Based on empirical gas diffusion model, OK◦ Derived from He-4 diffusion model, OK◦ No pol. loss in transfer tube, ?◦ Temperature gradient is constant , OK◦ Transfer tube entrance and exit temperature =
each chamber temperature , small effect◦ Diffusion in both chamber is fast , OK ∝ area/NHe3
◦ no macroscopic gas flow, eg. convection , OK
Target Analysis Meeting
Diffusion factor D
Jin Huang <[email protected]> 21
Yi’ analyzed uncertainty within this formula ~1.7h for Cell Brady Looking for reproducing duke measurement
with this formula
Target Analysis Meeting
Anatomy of the model results
KT
TnD
L
A
ND
m
tt
tt
tt
pc
1
000
1
Total He-3 in the chamber
Transfer tube geometry
condition of diffusion meas.
• Scale with temperature in transfer tube• Calculated with T @ entrance and exit• The hotter the faster
Some factor related to
temperature distribution
Jin Huang <[email protected]> 22
Previously assumed:◦ Γ t = Γp ◦ measured in 220C hot spin down◦ Both have problem
Γ t not equal to Γp ◦ Target chamber and pumping chamber temperature
differ significantly◦ Tt ~ 50-70C, not that far from UVA measurement◦ Tp ~ 260C, highest of used targets in beam
A new assumption would be◦ Γ t ~ UVA number, x2 of what we used -> half of pol diff
◦ Γp need extra study, but not relevant to our analysis
Target Analysis Meeting
Cell Intrinsic Life Time, 1/Γ t
Jin Huang <[email protected]> 23
This study sensitive to ~ Γ t + Γp , rather than Γ t, what we need Also Γp depends on alkali vapor density (slide 30)
Analysis need to be further correctedThe polarization decay rate is sum of following:◦ Pumping chamber intrinsic life time @ 200~210C◦ Target chamber intrinsic life time @ 78C◦ Spin flip loss◦ Residual alkali @ pumping chamber
Previously ignored Can have considerable effects
Target Analysis Meeting
Comments on hot spin down
Jin Huang <[email protected]> 24
Polarization of alkali w/o laser is balance of He-3 spin exchange & alkali depolarization
Palkali/PHe3 described by SE eff. η◦ η is Density dependent, assume same as
following◦ Palkali/PHe3 <25%
Target Analysis Meeting
Comments on hot spin down Polarization of alkali w/o laser
Our T
Phys. Rev. Lett. 80, 2801–2804 (1998)
Jin Huang <[email protected]> 25
@ 210C alkali pressure is not negligible◦ ~13% for K, compare to 260C◦ ~18% for Rb , compare to 260C◦ Spin exchange between He-3 & alkali is mostly
density dependent, scale down by density Temperature dependence is small Phys. Rev. Lett. 80, 2801–2804 (1998)
◦ Spin exchange Time ~ 27 hour Add alkali polarization from last slides
◦ -> Alkali spin destruction time = 27~36 hour◦ Larger effect than that of spin flip◦ Larger effect than cold cell life time
Target Analysis Meeting
Comments on hot spin down Residual alkali @ pumping chamber
Jin Huang <[email protected]> 26
New target chamber life time◦ Based on UVA measurement, 36h◦ Ignore temperature difference
room temperature @ UVA? -> <T> = 56C◦ Corrected with density change using simple model
Γ t ([He3])= Γ t ([He3]Fill) – 744/[He3]Fill] + 744/[He3] ~ 32h
◦ Further corrected with Area/Volume ratio Γ t~ 20h
◦ Follow GEN procedure, average above two Γ t~ 26h with extra uncertainty 6hour (updated May 07)
Use the diffusion model discussed before Assuming AFP loss the same as other cells
◦ Missing AFP loss measurement for Brady◦ Do not change much + minor effect
Target Analysis Meeting
Updated global fits for BradyInputs
Jin Huang <[email protected]> 27
Beam depolarization effect◦ The only factor we needed from this study
Pumping chamber life time, 1/Γp ◦ Global fitting is sensitive to
a combination of ~ Γ t + Γp Spin exchange rate Initial polarization for each data sets
Target Analysis Meeting
Updated global fits for BradyFit for
Jin Huang <[email protected]> 28Target Analysis Meeting
The Fit Chi2/n = 131/89 (updated May 07)
Jin Huang <[email protected]> 29
464/I ± 4%(stat.) ◦ “I” is Beam Current (uA)◦ Not sensitive to Γ t inputs
Can systematically change if use a different periods of spin flip data
Currently using the spin flip data most close to the spin up curve measurement◦ Ensure minimal change in condition
Compare to historical estimations◦ X. Zheng calculation: 622/I◦ GEN measurement w/ EPR: 400+-200/I
Target Analysis Meeting
Fit Result and DiscussionBeam depolarization effect
Jin Huang <[email protected]> 30
Pumping chamber intrinsic life time, 1/Γp ◦ Global fitting is sensitive to
a combination of ~ Γ t + Γp
◦ Best fit: Γp ~ 10hour Significant change suggesting …
Sensitive to alkali vapor density (updated May 07) Γp -> Γp0+X*γSE, X is cell dependent 0.1~1, Babcock, 2006
Large temperature dependence? Possible underestimation of target chamber life time?
Spin exchange rate ~ 4 hour◦ Correlated with assumption that Alkali polarization is
99%. Initial polarization for each data sets
Target Analysis Meeting
Fit Result and DiscussionOther parameters (not used for Pt/Pp)
Jin Huang <[email protected]> 31
Best fit:◦ W/o beam/spin flips : Pt/Pp = 95.5% (updated May 07)
Improved since using larger lifetime @ Target chamber◦ W/ beam/spin flips : Pt/Pp = 90.8% (updated May 07)
◦ Should be better for other cells other cell have wider transfer tube &/ longer lifetime
Systematic Uncertainties◦ Diffusion, D: (1-90.8%) x (6% + model uncert. )~ 0.5~1%◦ Cell life time, Γ t: (1-95.5%)x 30%? ~ 1~1.5%
◦ Beam depolarization: ~ (95.5%-90.8%) x 30% ~ 1.5%◦ Overall ~2~2.5% + model assumptions◦ 4% uncertainty allowed for a 5% polarization table
Uncertainty for pumping chamber Pol ~ 2.7%
Target Analysis Meeting
Form Brady polarization ratioTarget chamber / pumping chamber, Pt/Pp