Electric field calculation for the neutron EDM SNS experiment.

Septimiu Balascuta

Ricardo Alarcon

ASU, 02/07/2008

The requirements for the electric field in the neutron EDM experiment:

• Electric field in the cell > 50 kV/cm• The electric field uniformity should be 0.1%

(optimum requirement) or <1% (the minimum requirement).

• The reverse accuracy <1%• Spark rate: 0.1/year.• Eddy current heating should be < 1 mW.

Summary:

• Electric field uniformity inside measurement cell for three geometries of the cell and electrode.

• The effect of the valve on the electric field uniformity.• The effect of the optical guides on the electric field uniformity. • A method to decrease the power loss (due to eddy currents) in the

film on the surface of the electrodes in the presence of and external RF magnetic field.

The 1st configuration of the electrodes and cell.

All the Lucite walls are insulators and 1.3 cm thick.

High Voltage electrode dimensions: height = 29.8 cm, radius=5 cm

Grounded electrode: height=24.8 cm, radius=2.5 cm

Cell boundaries: 5 cm <X< 12.6 cm, -5.08 cm<Y<5.08 cm, -25 cm<Z<25 cm

Y

X

5.081.3

1.62

1.9

2.5

1.3

6.381.9

5

3.7

5

1.62

1.3

B

A B

C D

High voltage electrode dimensions: Height = 32 cm, Radius=5 cm;

Grounded electrodes: Height 24 cm<H (g) <29 cm, Radius=2.5 cm;

Lateral walls of the cell are conductive and 1.3 cm thick;

Top/bottom walls of the cell are not conductive and 1.3 cm thick.

Cell boundaries: 5 cm <X< 12.6 cm, -5.08 cm<Y<5.08 cm, -25 cm<Z<25 cm

The 2st configuration of the electrodes and cell with conductive lateral walls.

Y

X 5.08

0.72 0.472.5

1.3

6.38

16

5

3.7 5

7.6

7.47

H(g)

1.3

A B

C D

The 3rd configuration of the electrodes and cell with conductive walls.

The radius of the high voltage electrode is varied.

High voltage electrode: Height=11cm +R(HV) where R(HV) is the radius of the High Voltage electrode is increased 5 cm< R(HV)< 5.75 cm.

Grounded electrodes: Height H(g) varied (27.5 cm <H(g)<30 cm) and constant radius equal with 2.8 cm;

Lateral walls of the cell are conductive and 1.3 cm thick;

Top/bottom walls of the cell are insulator: 1.3 cm thick.

Cell boundaries: 5 cm <X< 12.6 cm, -5.08 cm<Y<5.08 cm, -25 cm<Z<25 cm

A B

C D

The effect of the valve on the electric field uniformity.

A. Valve mounted on the ground electrode.

B. Valve mounted on the back wall.

D

D

X

Z

Center valve at

X=8.8 cm,

Y=0 cm, Z=-25 cm

Center valve at:

X=12.6 cm,

Y=0 cm, Z=-7 cm

Z

X

Figure (A, B): The relative electric field close to the sharp edge of the hole along the vertical direction (A) and along the beam direction (OZ) (B). Valve mounted on the grounded electrode.

Figure (C, D): The relative electric field close to the sharp edge of the hole along OX directions (figure C and D). Valve mounted in the back wall.

A B

C D

E0 is the electric field in the center of the cell.

The effect of the optical guides on the electric field uniformity inside the cell (for two models of the guides).

Model A: The lateral optical guides are attached to the external surface of the back and front cell walls.

High Voltage electrode has radius 5.35 cm and height 32.7 cm.

The grounded electrode has the radius 2.8 cm and height 28 cm.

Lateral guides are rectangular sheets: 0.99 cm (close to H.V. electrode) and 0.86 cm thick (close to 0 V electrode). Their dielectric constant wil be named “epsilon”.

The Electric field uniformity close to the back wall was calculated for no optical guides attached (figure A) and for optical guides with dielectric constant 2 and 3.5 (figure B, C).

A B

C

Figure D: The electric field uniformity calculated in the vertical plane through the middle of the cell.

D

Model B: The lateral optical guides (1.3 cm thick) pass through the recess inside the electrodes. The surface of the guides facing the liquid Helium is conductive. The top and bottom guides (1.2 cm thick and Lx=7.6 cm long) are not conductive.

The height of the lateral optical guides is 29.68 cm.

Figure 1B: Making the surface of the Optical Guides (O.G.) not conductive increases the relative electric field variation up to 2%.

1A

1B

Figure (A,B). The relative electric field variation is calculated along directions parallel with the horizontal OX axis on the vertical surface of the back face of the cell) and in the Z=0 vertical plane passing through the middle of the cell. The electric field in the center of the cell (X=8.8 cm, Y=Z=0 cm) E0=52.63 kV/cm for a voltage applied on the High Voltage electrode equal with 400 kV.

AB

A method to decrease the power P loss (due to the eddy currents) in the conductive film on the surface of the electrodes in an external RF

magnetic field.

• The thickness of the conductive film will be about 200 micrometers thick.• “P” depends linearly on the conductivity of the film.• “P” decreases if there are gaps (maxim1 mm wide) in vertical planes

(parallel with XOY) on the surface of the film.

Figure A: The power loss in the (1 mm) film on the surface of the electrodes is plotted versus the conductivity of the film (Sigma_LC) for a film with no gaps, and for a film with 2, 8, 10 and 12 gaps.

Gaps located at Z= ± 5cm, ± 10 cm, ±15 cm, ±20 cm, ±25 cm and ±35 cm along the OZ axis.

B

A

The electric field uniformity calculated near the Z=5 cm gap on the HV electrode (at X=5.0 ) and on the grounded electrode (X=12.6 cm) for a film with no gaps (A) and a film with (eight) gaps 0.5 cm wide (fig. B) 0.2 cm wide (fig. C) and 0.1 cm wide (fig. D).

A B

C D

Conclusion:• A uniformity of the electric field less then 0.1% can be obtained

inside the measurement cells.

• The power loss in the film can be decreased bellow 1 mW by increasing the number of gaps (less then 1 mm wide) in the film or / and decreasing the thickness and the conductivity of the film.

• The electric field uniformity can be less then 0.1% if the lateral optical guides are located inside the recess volume of the electrodes.