1. Jin Huang MIT For target group discussion

2. May 07 EPR/Pumping Chamber Pol. Table Updates May 03 First Gradient Model Fitting May 05 Review & Update on Gradient Target Analysis Meeting Jin Huang 2

3. Target Analysis Meeting Jin Huang 3

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 Jin Huang 4

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  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 Jin Huang 5

6. Target Analysis Meeting Jin Huang 6 Brady MaureenAstral (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

7.  Comparing to the one, that asymmetry analysis teams used. Target Analysis Meeting Jin Huang 7 New results Elog 299 New/Elog 299 Compare raw NMR Fitting

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 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 chamber Then polarization table should be ready. Target Analysis Meeting Jin Huang 8

9. Target Analysis Meeting Jin Huang 9

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/T Depolarization )/(1/T Pol. Transfer ) ~ 10%!!?? (Rel.) ◦ More precise formula: Elog 616, Eq. (2b) Target Analysis Meeting Jin Huang 10 First Test

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 = Γ p from high temperature spin down of cell Astral (next slides)  n p /n t 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 Jin Huang 11 First Test

12.  Γ t & Γ p describe intrinsic depolarization ◦ He-3 direct coupling ◦ Wall effect ◦ Assuming Γ t = Γ p  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 = Γ p in the following global fitting -> 14.3 hour +-3% (stat.) Target Analysis Meeting Jin Huang 12 Time (h) NMR (mV) Astral 220C Decay Time (Raw) ~ 15.08 +- 0.09 h Bigbite Turned on (updated May 03) First Test

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 Jin Huang 13 Pumping Chamber Pol. (Fit) Target Chamber Pol. (Fit) Data (Halog 255483) Gaussian Conv. Fitting Data (Halog 255483) Gaussian Conv. Fitting Chi2/n(data) = 10.14/7 Naive Exp. Fit (updated May 03) First Test

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 Jin Huang 14 Data (Spin Flip 291) Pumping Chamber Pol. (Fit) Target Chamber Pol. (Fit) Chi2/n = 52.37/31 First Test

15.  2 nd 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 Jin Huang 15 Data (Spin Flip 291) Pumping Chamber Pol. (Fit) Target Chamber Pol. (Fit) Chi2/n = 69.58/51

16. First Test  Γ beam = 36 hour +- 3% (stat.) (updated May 03)  W/o beam/spin flips : P t /P p = 92% (updated May 03)  W/ beam/spin flips : P t /P p = 88% (updated May 03)  Systematic uncertainty ◦ Major part:  Pol. Transfer D (model calculation, not sure yet)  intrinsic depol. Γ t, Γ p (data+extrapolation, not sure yet) A useful measurement: two NMR field sweeps w/ NMR signal from both chamber  1 st NMR in laser on equilibrium: direct access polarization diff.  Laser off, then wait or (preferred) keep monitoring polarization for >2 hours  2 nd 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 P t /P p  spin flip loss (tiny part, well measured, small uncertainty on P t /P p ) Target Analysis Meeting Jin Huang 16

17. First Test  Free up two more parameters in the fitting ◦ Intrinsic depolarization factor Γ t = Γ p (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 = Γ p = 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 P t /P p < 0.5% Target Analysis Meeting Jin Huang 17

18. Inspect assumptions on Diffusion parameter Cell life time New global fit Target Analysis Meeting Jin Huang 18

19.  Polarization difference between two chambers, ( More precise formula: Elog 616, Eq. (2b) ) ~= (1/T Depolarization )/(1/T Pol. 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 Jin Huang 19

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/N He3 ◦ no macroscopic gas flow, eg. convection, OK Target Analysis Meeting Jin Huang 20

21.  Yi’ analyzed uncertainty within this formula  ~1.7h for Cell Brady  Looking for reproducing duke measurement with this formula Target Analysis Meeting Jin Huang 21 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 Scale with temperature in transfer tube Calculated with T @ entrance and exit The hotter the faster Some factor related to temperature distribution

22.  Previously assumed: ◦ Γ t = Γ p ◦ measured in 220C hot spin down ◦ Both have problem  Γ t not equal to Γ p ◦ 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 ◦ Γ p need extra study, but not relevant to our analysis Target Analysis Meeting Jin Huang 22

23.  This study sensitive to ~ Γ t + Γ p, rather than Γ t, what we need  Also Γ p depends on alkali vapor density (slide 30)  Analysis need to be further corrected The 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 Jin Huang 23

24.  Polarization of alkali w/o laser is balance of He-3 spin exchange & alkali depolarization  P alkali /P He3 described by SE eff. η ◦ η is Density dependent, assume same as following ◦ P alkali /P He3 <25% Target Analysis Meeting Jin Huang 24 Our T Phys. Rev. Lett. 80, 2801–2804 (1998)

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 Jin Huang 25

26.  New target chamber life time ◦ Based on UVA measurement, 36h ◦ Ignore temperature difference  room temperature @ UVA? -> = 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 Jin Huang 26

27.  Beam depolarization effect ◦ The only factor we needed from this study  Pumping chamber life time, 1/Γ p ◦ Global fitting is sensitive to a combination of ~ Γ t + Γ p  Spin exchange rate  Initial polarization for each data sets Target Analysis Meeting Jin Huang 27

28. Target Analysis Meeting Jin Huang 28  Chi2/n = 131/89  (updated May 07)

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 Jin Huang 29

30.  Pumping chamber intrinsic life time, 1/Γ p ◦ Global fitting is sensitive to a combination of ~ Γ t + Γ p ◦ Best fit: Γ p ~ 10hour  Significant change suggesting …  Sensitive to alkali vapor density (updated May 07)  Γ p -> Γ p0 +X*γ SE, 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 Jin Huang 30

31.  Best fit: ◦ W/o beam/spin flips : P t /P p = 95.5% (updated May 07)  Improved since using larger lifetime @ Target chamber ◦ W/ beam/spin flips : P t /P p = 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 Jin Huang 31