jin huang mit for target group discussion. may 07 epr/pumping chamber pol. table updates may 03...

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


May 07: Pumping Chamber Pol. Table Updates



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


From last week Review of pumping chamber pol. table


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


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


Comparing to the one, that asymmetry analysis teams used.


Pumping chamber polarization table (Same as last week)

New results

Elog 299

New/Elog 299

Compare raw NMR Fitting


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.


Polarization table


May 03: First tests of the gradient models



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)


Overview of Pol. GradiantFirst Test


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


Overview of Approach

pppttpt

ppppSEtpp

PPPPPDdt

dP

PPPPPPDdt

dP

BeamFlipSpin

FlipSpin alkali

First Test


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.)


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


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


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


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


Data Selection 2/3Production spin flip session 291

Data (Spin Flip 291)


Target Chamber Pol. (Fit)

Chi2/n = 52.37/31

First Test


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


Data Selection 3/3Production spin flip session 291

Data (Spin Flip 291)


Target Chamber Pol. (Fit) Chi2/n = 69.58/51


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)


Results & Uncertainties


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%


Further global studies (updated May 03)


May 05: Review of assumptions•Inspect assumptions on

• Diffusion parameter• Cell life time

•New global fit



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


Important Factors


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


Diffusion factor D


Yi’ analyzed uncertainty within this formula ~1.7h for Cell Brady Looking for reproducing duke measurement

with this formula


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


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


Cell Intrinsic Life Time, 1/Γ t


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


Comments on hot spin down


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%


Comments on hot spin down Polarization of alkali w/o laser

Our T

Phys. Rev. Lett. 80, 2801–2804 (1998)


@ 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


Comments on hot spin down Residual alkali @ pumping chamber


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


Updated global fits for BradyInputs


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


Updated global fits for BradyFit for

Jin Huang <[email protected]> 28Target Analysis Meeting

The Fit Chi2/n = 131/89 (updated May 07)


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


Fit Result and DiscussionBeam depolarization effect


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


Fit Result and DiscussionOther parameters (not used for Pt/Pp)


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%


Form Brady polarization ratioTarget chamber / pumping chamber, Pt/Pp

jin huang mit for target group discussion. may 07 epr/pumping chamber pol. table updates may 03...

Documents

previous epr analysis

chamber model

density epr pol

chamber table ready

asymmetry analysis teams

week review of pumping

epr analysisnew code

polarization tablemay