1. Cos θ Coil and Magnetic Shielding Progress B. Filippone and B. Plaster Caltech December 3, 2004

2. What’s Been Done ? Last collaboration meeting –MATHEMATICA model of cos θ coil developed –Transverse shielding factors and DC permeability curves measured for various ferromagnetic shields at 300K and 77K ¼-scale prototype cos θ coil constructed - BP –Mapped inside a tri-axial square (8’ x 8’) Helmholtz coil system Prototype Cryoperm and µ-metal shields acquired from Amuneal – BP –Cos θ coil mapped inside shields at 300K Model of cos θ coil coupled to a ferromagnetic shield developed – BF –Studied impact of mirror currents on field uniformity and gradients –Implications for false EDM signal due to Berry’s phase

3. Cos θ Coil Basics Nominal full-scale geometry: r = 35cm; ℓ = 300cm Prototype geometry: r = 8.75cm; ℓ = 87.5cm 20 equally spaced (along x-axis) rectangular wire loops Nominal design permits little access to center of coil

4. Cos θ Coil Basics As discussed last meeting, possible solution is to construct the coil with circular end-cap openings Calculations indicated that field uniformity was actually better with radii of end-cap openings equal to coil radius than with no end-cap openings

5. Prototype Cos θ Coil 24-gauge magnet wire wrapped around Al support frame (required significant precision machining)

6. Coil Mapping Results Field mapped with single-axis fluxgate magnetometer –Field of ~1.6 Gauss with ~2 A current –Earth’s field attenuated to ≤ 5 mGauss with the tri-axial Helmholtz coil system B x field profile along the z-axis (coil axis) fiducial volume

7. Coil Mapping Results Field mapped with single-axis fluxgate magnetometer –Field of ~1.6 Gauss with ~2 A current –Earth’s field attenuated to ≤ 5 mGauss with the tri-axial Helmholtz coil system B x field profile along the z-axis (coil axis) fiducial volume

8. Coil Mapping Results Field mapped with single-axis fluxgate magnetometer –Field of ~1.6 Gauss with ~2 A current –Earth’s field attenuated to ≤ 5 mGauss with the tri-axial Helmholtz coil system B x field profile along the y-axis (“vertical” axis) fiducial volume

9. Coil Mapping Results Field mapped with single-axis fluxgate magnetometer –Field of ~1.6 Gauss with ~2 A current –Earth’s field attenuated to ≤ 5 mGauss with the tri-axial Helmholtz coil system B x field profile along the x-axis (“horizontal” axis) fiducial volume

10. Prototype Magnetic Shields Cryoperm µ-metal Toroidal coils wound around each shield for AC demagnetization purposes Shield dimensions (identical): r = 9.33cm, ℓ = 91.44cm, t = 60 mils Solenoid also used for AC demagnetization purposes

11. AC Demagnetization Procedure Shield + cos θ coil configuration mounted inside tri-axial square Helmholtz coil system Cos θ coil energized to operating DC current AC fields from the solenoid and toroidal coils applied and ramped down in magnitude over 30 minute time span (each in succession) –Hope was to completely demagnetize the shields and force them onto their “anhysteresis” curves by superposing the AC fields on the DC bias field Permeability along the anhysteresis curve is higher than along the normal B vs. H curve (“ideal permeability” on anhysteresis curve) –Khriplovich and Lamoreaux (p. 39): “… performing the demagnetization with the internal fields applied achieves the equilibrium magnetization immediately… “

12. Shield+Coil Mapping Results Field mapped with single-axis fluxgate magnetometer –Field ~doubled due to mirror currents (as naively expected) B x field profile along the z-axis (coil axis) Mirror currents appear to improve the field uniformity along the z-axis Brad F. …

13. Shield+Coil Mapping Results Field mapped with single-axis fluxgate magnetometer –Field ~doubled due to mirror currents (as naively expected) B x field profile along the x-axis (“horizontal” axis) Mirror currents appear to have little effect on uniformity along the x-axis Asymmetric behavior; probably not completely demagnetized

14. Shield+Coil Mapping Results Field mapped with single-axis fluxgate magnetometer –Field ~doubled due to mirror currents (as naively expected) B x field profile along the y-axis (“vertical” axis) Asymmetric behavior; probably not completely demagnetized

15. AC Demagnetization Issues Asymmetric behavior along the x- and y-axes most likely due to the fact that the shields were not completely demagnetized –“Magnetically hard regions” may exist along the welds or elsewhere Complete demagnetization will probably require higher currents (currently limited to 5 A) and lower frequencies –Desirable to go to < 1 Hz (or thinner shields!) –Were able to drive more current with RLC circuit tuning 60 Hz

16. Near Term Plans Significant hardware projects underway at Caltech to begin cryogenic tests of the cos θ coil + shield configuration –Vertical support platform to mount a dewar inside tri-axial square Helmholtz coil system –Precision x-y table mounted vertically above dewar with stepping motors for 3-D motion (essentially building automated cryogenic mapping system) Also intend to construct prototype-sized Metglas shield Poised to make significant progress on hardware efforts outlined in 2005-2006 R&D proposal once $$$$ comes through