Magnetic shielding calculations

and alsoPetr Volegov

Andrei Matlashov Michelle Espy

LANL, P-21, SQUID team

Igor Savukov

Requirements for shielding

•To reduce the gradients and field variation that can shorten helium coherence time•To minimize noise in the SQUID gradiometer•To avoid instabilities in SQUID operation

Gradients are shielded differently than uniform field! SQUID gradiometers are not sensitive to uniform component

SQUID detector

SQUID pickup loopsHelium cell

Large gradiometer

Extremely Sensitive, Very Long Baseline Planar SQUID GradiometerR. Cantor and J. A. Hall, STAR Cryoelectronics, Santa Fe, NM USAA. N. Matlachov and P. L. Volegov, Los Alamos National Laboratory, Los Alamos, NM USAWe have developed an extremely sensitive, low-Tc first-order planar gradiometer with a very long baseline of 9 cm. The thin-film gradiometric pickup loop consists of two series-configured 3 cm x 6 cm pickup loops with center-to-center spacing of 9 cm fabricated on a 150 mm Si wafer. The pickup loop is connected to the input circuit of a separate dc SQUID chip using superconducting wire bonds. The measured magnetic field sensitivity of the gradiometer referred to one pickup loop is 0.105 nT/0, and the intrinsic noise of the dc SQUID coupled to the thin-film pickup loop typically is 3 µ0/Hz½. This results in a magnetic field noise of 0.3 fT/Hz½ and a magnetic field gradient noise of 0.033 fT/cm-Hz½. Measurements were carried out in our magnetic shielded room.

Ambient noise in a lab

Rev. Sci. Instr. 71, 1529 (2000)

100 pT/Hz1/2 at 3 Hz

For nEDM experimentWe need 0.1 fT/Hz^1/2So shielding factor1 million is required

Drawing of the nEDM shield

Estimates of Johnson noise

Table compiled by Brad Filippone

Estimates based on the theory of Ref.[1] foran infinite cylinder

0.28

0.24

3.7

435.0,3

2 0 GR

tkTGB

[1] S.-K. Lee and M. V. Romalis, arXiv:0709.2543v1

A factor of 2 difference?

Transverse shielding factor by mu-metal

1])/(1[ 212

122112 SSDDSSS

14])/(1[ 132

124114 SDDSS

11 D

dS

51012.2D001.0d

952.0/ 12 DD

418014 S

Shielding by a singleInfinite cylindrical shell

Shielding by two shells

Shielding by 4 shells

Axial shielding factor will be much smaller and much more uncertain

Transverse shielding by SC cylinder

]/84.1exp[ az

3.92 m

2a

a=0.62 m

In the center, reduction is by 350 times

However, we need to consider proximityof the SC cylinder to mu-metal and that the equation assumes a semi-infinite cylinder

So the shielding factor can be about 100

Overall factor fill be about 4x10^5

Axial shielding factor by mu-metal

14]/1[ 13

124114 SLLSS

510001.0d

12014 S

)3/1

2(

211 aa

KSS T

I checked numerically that for two shells with L= 4m and spacing 5 cm, by adding the 2nd shell, the shielding factor only doubled in agreement with the analytical prediction. Thus, for 4 layers, the expected shielding factor will be only 120

4L

1]/1[ 121 LLS

This equation contains unknown parametersso instead we can do numerical calculations. For a cylinder with L=4 m, S1=30. For 4 mu-metal cylinders, as in nEDM shield design

The condition when shielding factors are only added, not multiplied,

T. J. Sumner, J. M. Pendlebury, and K. F. Smith, J. Phys. D: Appl. Phys. 20, 1095 (1987)

Axial shielding with a superconducting cylinder

Superconducting cylinder

Mu-metal shield

Solenoid

Additional axial shielding by the superconductor is 1000 times, and overall axial shielding becomes 1.2e5

Analytical shielding factor:Exp(-3.832 z/R)~10^4

Superconducting endcaps?

]/832.3exp[ az]/84.1exp[ az

Superconducting cylinder, axial-component shielding

Superconducting cylinder, transverse-field shielding

Hi-mu cylinder, axial-component shielding ]/405.2exp[ azHi-mu cylinder, transverse-field shielding ]/832.3exp[ az

1. J. R. Claycomb and J. H. Miller, Jr., IEEE Trans. on Magnetics 42, 1694 (2006)2. K. H. Carpenter, IEEE Trans. On Appl. Supercond. 6, 142 (1996)

It was shown in [2] that the equation is the same for the hole, but instead of the cylinder radius the hole radius needs to be used.

The above analytical expressions were derived in Ref.[1]

Therefore, shielding can be dramatically improved by adding endcaps on the SC cylinder

This might require consideration of boundary conditions. However, since we have ferromagnetic shell just outside the cosine coil, magnetic lines will be closed through this shell and not much will be reflected by superconducting endcaps. Nevertheless, one has to check it!

aa

End cap

a

Cosine coil vs solenoidCosine coilmetglass

cellsNoise from metglass 0.2 fTWhat about non-uniformity?What about instabilities?

Superconducting shieldsolenoid

cellsWe can “freeze” the field in the superconducting cylinder whichis expected to be very stable?Noise level can be lower

Electrodes

Superconducting shield

Electrodes

Conclusions• Aluminum support structure produces noise 1.8 fT/Hz^1/2, but it will be reduced by superconducting shield

• Noise from inner metglass layer is acceptable, 0.2 fT/Hz^1/2?• SQUID gradiometer noise is 0.3 fT/Hz^1/2 at 4K, but at 0.5K… • External laboratory noise level at 3Hz is about 100 pT/Hz^1/2• Required shielding is about 1e6• For a given shield, transverse shielding 4e5 and axial 1.2e5• Extra noise reduction by gradiometer, about 10-100• Overall shielding is satisfactory, although some improvement

can be achieved: endcaps, spacing, thicker mu-metal• Perhaps, 3D simulations are needed?• Some redesign of the shield?