1. 1 B-field Uniformity Issues Two Basic Problems Depolarization of n and 3 He due to field gradients –Discussed in Pre-Proposal (2002) –Provided specification on False EDM’s for n and 3 He due to Geometric Phase –Not addressed in Pre-Proposal (2002)

2. 2 Non-uniform B-field and particle velocity give in particle rest frame. –Collisions with walls and other particles gives a random variations in  leads to spin relaxation –Gives relaxation for both T 1 (longitudinal) and T 2 (transverse) relaxation –For our field configurations ( ) and temperatures: –Recall minimum T ~ 100 s, optimum T ~ 30,000 s Field Gradient Depolarization

3. 3 Lots of theory/data for Polarized 3 He –Gamblin and Carver PR 138, 946 (1965) –Schearer and Walters PR 139, 1398 (1965) –Cates, Schaefer, and Happer PRA 37, 2877 (1988) All formulas ~ agree when applied within their limits

4. 4 Cates et al give T 2 :

5. 5 3He @ 0.3K 3He @ 0. 4K Neutron Along z  B/B0 = 10 -3  B/B0 = 2.5x10 -4

6. 6 Uniformity Spec. (based on T 2 )  B/B 0 ~ 1x10 -3 for minimum performance  B/B 0 ~ 2x10 -4 for optimum performance Increasing B 0 reduces T 2 (as 1/B 2 ) Increasing Temp. reduces T 2 (as 1/T 7 )

7. 7 False EDM from Geometric phase Pendlebury et al PRA 70 032102 (04) Lamoreaux and Golub PRA 71 032104 (05) Geometric phase contribution to false EDM’s depends strongly on radial fields perpendicular to B 0 –These result from dB x /dx in our exp. x

8. 8 Geometric phase contributions Gradients and vxE field gives d false Impacts neutron and 3 He Magnetometers ( 199 Hg & 3 He) pick up phase at different rate due to higher velocities –Can be reduced by frequent collisions with buffer gas or phonons if collision rate Then GP doesn’t have time to build up

9. 9 False EDMs from B v = v x E field Radial B-field due to gradient v x E field changes sign with neutron direction 2R BvBv BvBv

10. 10 Form for false EDM d f Pendlebury formula (for simple orbit at v) –Depends on  Thus d f drops with increasing B x –Has a resonant term Somewhat washed out by averaging

11. 11 Corresponds to 0.1  g/cm

12. 12 For 3 He can see resonance vs. T (since ) B 0 =10mg, dB/dx=0.1  g/cm

13. 13 False EDM for 3 He Collisional reduction of d f for 3 He

14. 14 Effect of collisions on 3 He |d f | B 0 =10mg, dB/dx=0.1  g/cm With Collisions

15. 15 Effect of collisions on 3 He |d f | B 0 =10mg, dB/dx=0.1  g/cm Lamoreaux & Golub (rectangular Geometry)

16. 16 d f Bottom Line Without collisional effect on 3 He we are doomed To achieve d n ~ 1x10 -28 e-cm requires

17. 17 dB x /dx Gradients 50 cm 10 cm 7.5 cm x y z

18. 18 Calculations from Riccardo Schmidt Reference design: L = 390cm, R = 69 cm For N = 34 can have - 15 - 10 - 505 15 xcm - 0.002 0 0.004 B x - B 0 B 0 % N loops = 30 N loops = 34 N loops = 40

19. 19 Z = 0, 10, 25 cm Y = 0, 5, 10 cm N = 34

20. 20 Eddy Currents from Dressed Spin when We want B rf >> B 0 (10 mG) so B rf ~ 1 G and  rf /2  near 3 kHz L t W Don’t tell Caltech Freshman

21. 21 Graphite Coating on Cells For L=50cm, W=10cm, t=100nm B rf = 1gauss,  = 2  (3kHz)  Graphite ~ 1x10 -6 ohms-cm –Smallest  I could find Gives ~ 50  W/sheet Note  Cu (4K) ~ 2x10 -11 ohms-cm (10 W!) But, Good News: ~ R 4

22. 22 Summary T 2 limits high fields and is Geom. phase ~ –Can’t simply minimize a gradient at a single point –Antisymmetric gradients (dominant term in cos  field profile) cancel when comparing d n from 2 cells –Largest gradients may (will!) come from magnetic materials inside 4-layer 300K shield or leakage through shield; not from cos  coil Full-scale MC of GP buildup required Lamoreaux / Golub/Schmid