# Presentation: 485316

## B-field Uniformity Issues

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

## 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 T1 (longitudinal) and T2 (transverse) relaxation
For our field configurations (                       ) and temperatures:   
Recall minimum T ~ 100 s, optimum T ~ 30,000 s

- Collisions with walls and other particles gives a random variations in            leads to spin relaxation
- Gives relaxation for both T1 (longitudinal) and T2 (transverse) relaxation
- For our field configurations (                       ) and temperatures:
- Recall minimum T ~ 100 s, optimum T ~ 30,000 s

**Field Gradient Depolarization**

## Field Gradient Depolarization

- Lots of theory/data for Polarized 3He
- 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

## Cates et al give T2:

## Neutron

**3He @ 0.3K**

**3He @ 0. 4K**

**Neutron**

**Along z**
******B/B0 = 10****-3**

******B/B0 = 2.5x10****-4**

## Uniformity Spec.(based on T2)

-  B/B0 ~ 1x10-3 for minimum performance
-  B/B0 ~ 2x10-4 for optimum performance
- Increasing B0 reduces T2 (as 1/B2)
- Increasing Temp. reduces T2 (as 1/T7)

## 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 B0
- These result from dBx/dx in our exp.

## Geometric phase contributions

- Gradients and **v**x**E **field gives dfalse
- Impacts neutron and 3He
- Magnetometers (199Hg & 3He) 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

## False EDMs from  Bv = v x E field

- Radial B-field due to gradient

- v x E field
- changes sign with
- neutron direction

- 2R

**B****v**

**B****v**

## Form for false EDM df

- Pendlebury formula (for simple orbit at v)
- Depends on                Thus df drops with increasing Bx
- Has a resonant term
- Somewhat washed out by averaging

## Corresponds to 0.1 g/cm 

- Corresponds to 0.1 g/cm

## For 3He can see resonance vs. T (since                   )

**B****0****=10mg, dB/dx=0.1********g/cm **

## False EDM for 3He

- Collisional reduction of df for 3He

## Effect of collisions on 3He |df|

**B****0****=10mg, dB/dx=0.1********g/cm **

**With Collisions**

## Effect of collisions on 3He |df|

**B****0****=10mg, dB/dx=0.1********g/cm **

- Lamoreaux & Golub (rectangular Geometry)

## df Bottom Line

- Without collisional effect on 3He we are doomed
- To achieve dn~ 1x10-28 e-cm requires

## dBx/dx Gradients 

**50 cm **

**10 cm **

**10 cm **

**7.5 cm **

**x**

**y**

**z**

## Calculations from Riccardo Schmidt

- Reference design: L = 390cm, R  = 69 cm
- For N = 34 can have

- -

- 15

- -

- 10

- -

- 5

- 0

- 5

- 10

- 15

**x**

**cm**

- -

- 0.002

- 0

- 0.002

- 0.004

***B***

***x***

**-**

***B***

**0**

***B***

**0**

**%**

**N****loops**** = 30**

**N****loops**** = 34**

**N****loops**** = 40**

##   N = 34

**Z = 0, 10, 25 cm**

**Y = 0, 5, 10 cm**

**  ****N = 34**

## 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**

## Graphite Coating on Cells

- For L=50cm, W=10cm, t=100nm
- Brf = 1gauss,  = 2(3kHz)
-  Graphite ~ 1x10-6 ohms-cm
- Smallest  I could find
- Gives <P> ~ 50 W/sheet
- Note Cu (4K) ~ 2x10-11 ohms-cm (10 W!)

**But, Good News:  <P> ~ R****4**

## Summary

- T2 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 dn 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