1. Magnetic Field Finite-Element Calculations for the Upper Cryostat S. Balascuta, R. Alarcon Arizona State University B. Plaster, B. Filippone, R. Schmid Caltech The nEDM Collaboration 11/02/2007

2. Design Considerations 1.The magnetic field uniformity inside the collection volume has to be  5  10 -4. 2. 3 He spin relaxation time has to be bigger than 10000 seconds inside the collection volume. The loading and transfer time of 3 He from the ABS source to the collection volume is less than 2000 seconds. 3. The loss in the polarization of 3 He from ABS source to measurement cells can be minimized if the field changes adiabatically in any point along the 3 He path.

3. The location of the 3 He magnet and collection volume inside the upper cryostat

4. The geometry of the coils and of the shield inside the upper cryostat. 24 cos(  ) coils (R=20 cm, L=134 cm) Transport solenoid (r=5 cm, L=80 cm) Magnetic shield R=21 cm, L=136 cm, 62 mils thick.

5. The cos  coils x y JJ Coil j’ The position of each “cos  ” coil is given by the angle  J In the presence of the shield the field uniformity along OZ axis decreases but is still big along the OX and OY axis. SJSJ Coil j ’J’J SJSJ ’J’J JJ On circle: A (x j, y j ); On Ellipse: A’ (x j1, y j1 ) A A’ Project back on circle A’ to B (x J2, y J2 ) B K>0

6. The magnetic field distribution inside 24 coils (K) placed inside the shield with two gaps (12 cm wide and 64 cm long) with and without the transport solenoid. Shield: Metglas, 62 mils thick, R=21 cm, L=136 cm long, with two gaps 12 cm wide. Transport solenoid: 80 cm long, center at X c =51.19, Y c =0, Z c =47.73 cm

7. L gap Y Z 32.3cm 68cm OAC 42 cm D 35.7cm The correction of the asymmetry in the OZ direction by adjusting the length and the center of the gap. Shield: Metglas, 62 mils thick, R=21 cm, L=138 cm long, with two gaps 12 cm wide.

8. N=24 + M=8 coils with the same radius (20cm) and length (134 cm) inside shield (R=21 cm, 136 cm long) with two gaps (12 cm wide, 60.6 cm long) X Y K 12 cm 3 He N=24 coils with current I 1 =14.7 mA. M=8 coils with current I 8 ( I 2 =I 8 +I 1 ) Transport solenoid (80 cm long, R= 5 cm), with a current I s =45.3 mA. For the N=24 (+M=8) coils, the optimum K= -0.03 with I 2 =I 1 +I 8 =40 mA.

9. The longitudinal (T1) relaxation time for 3 He inside the collection volume of the upper cryostat versus temperature. The volume average total gradients are:

10. Conclusions For the upper cryostat we have considered a system of N=24 coils (with current I 1 ) and M=8 coils (with current I 2 ) coils ( with radius R=20 cm and length L=134 cm). The M=8 coils overlap some of the N=24 coils. The magnetic shield (R=21 cm, L=136 cm) has two gaps (12 cm wide, and 60.6 cm long). In the presence of the transport solenoid (with a current 45.3 mA) the field inside the collection volume is asymmetric along OX and OZ. To eliminate the asymmetry along the OZ axis, the length of the two gaps is decreased to 60.6 cm and the Z coordinate of their center is moved to +2 cm. For the optimum currents I 8 =25 mA and I 1 =14.7 mA through the M=8 coils and N=24 coils (with K=-0.03) the relaxation times T 1 and T 2 are bigger than 5·10 4 seconds (if the temperature in the collection volume is T<0.5 K).