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Submitted on 1 Jan 1978
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ON BALANCING SUPERCONDUCTING GRADIOMETRIC MAGNETOMETERS
K. Aittoniemi, P.J. Karp, T. Katila, M. Kuusela, T. Varpula
To cite this version:
K. Aittoniemi, P.J. Karp, T. Katila, M. Kuusela, T. Varpula. ON BALANCING SUPERCON-
DUCTING GRADIOMETRIC MAGNETOMETERS. Journal de Physique Colloques, 1978, 39 (C6),
pp.C6-1223-C6-1225. �10.1051/jphyscol:19786541�. �jpa-00218029�
JOURNAL DE PHYSIQUE Colloque C6, suppl61nent au no 8, Tome 39, aoat 1978, page C6-1223
OK BALANCING SUPERCONDUCTING GRADIOMETRIC MAGNETOMETERS
Aittoniemi K., Karp, P.J.*, Katila T., Kuusela M.L., and Varpula T.
D e p a r t ) n e n t o f T e c h n i d Physics, Helsinki University o f Technology, SF
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02150 Espoo 15, FinlandRLsum6.- Nous d6crivons un systEme d'bquilibrage de gradiomEtres supraconducteurs et un 6quipement pour mesurer l'bquilibrage en laboratoire avec une pr6cision de l'ordre du ppm.
Abstract.- A system for balancing superconducting gradiometric magnetometers and equipment for ppm- level testing of the balance in a laboratory are described.
In measuring local magnetic fields gradiome- tric SQUID magnetometers arethemost sensitive instrw ments at low frequencies. Since the gradients of external disturbing magnetic fields are much lower than the absolute values of these fields, a good balance of the superconducting sensing coils impro- ves the signal-to-noise ratio.
After manufacture the responses of the super- conducting gradiometer coils may deviate as much as 1% from each other. Zimmerman and Frederick / 1 / used adjustable superconducting vanes for compensation of axial and radial balancing errors in the magnetometer coils. Another system has been reported, where fixed superconducting obstacles were used for compensation, but the axial balance could in addition be continu- ously adjusted with the aid of a movable supercon- ducting ring placed near the center of one of the gradient coils 121. An alternative solution is the use of adjustable miniature gradiometers coupled in series with the main coils /3,4/.
In the following we will describe a system which utilizes both fixed and movable superconducting rings for balancing. The rings are placed in three orthogonal directions close to the corresponding sensing loops. Figure 1 illustrates the construction of an asymmetric first order gradiometer. The coarse balance is obtained using fixed rings. The sizes of these rings are chosen according to the results shown in figures 2 and 3 . Due to practical limita- tions the procedure must occasionally be repeated before an unbalance of the order of 100 ppm is rea- ched. The fine balance is obtained using movable rings as shown in figure 1.
*; Present address : LET1
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Commissariat 21 1'Energie Atomique, 85 X, 38041 Grenoble Cedex, France.BALANCE ADJUSTMENTS
SCREW TAPS
Nb-RING FOR AXIAL BALANCE
UPPER FLUX TRANS- FORMER COIL
Nb-RINGS FOR RADIAL BALANCE
SUPPORT
SQUID SUPPORT
\ -
/ , l-~-~~RF~L.~ TRANS-
Fig. 1 : An asymmetric first order magnetic gradio- meter. The equipment for balancing consists of three
orthogonal movable superconducting rings. The fixed rings used for coarse balance are not shown in the figure
.
The curves shown in figures 2 and 3 are calculated as follows : since the magnetic flux in- side the superconducting ring is constant, any change
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786541
10-6
0 0.5 1 .O 1.5
a / r,
Fig. 2 : The effect of a superconducting ring, coaxial with the sensing loop of the gradiometer, on the axial balance of the magnetometer. The ra- dial thickness of the ring is assumed to be small.
Two values for the ratio of the height h to the radius of the sensing loop rl are depicted :- h/rl = 0.05,
- --
h/rl = 0.02. In practice one must allow about 10% error for Ae.F i g . 3 : The change in radial imbalance of the gra-
diometer, caused by a superconducting ring positioned as shown in the figure. When the ring is moved to the other side of the plane of the gradiometer loop, the sign of Ae changes.
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h/rl = 0.05,---
h/rl = 0.02, d/rl = 0.8.of the external flux A@ex at the site of the ring
,2
(located in the origin, cf figure 2) builds up a shielding clirrent wfiich in turn produces a vector potential &(r,z)
where r and z are cylindrical coordinates and r2 is the radius of the rinp. The magnetic flux penetra- ting the gradiometer loop
A@loop
can be calculated fromA@loop = $1 &(r,~) .dl (2)
where 1 is a closed path a l o n ~ the wire of the loop.
The change of the balance Ae can be expressed simply
where rl is the radius of the gradiometer loop, Ells
is the mutual inductance and L p is the self-induc- tance of the ring. The last approximation is valid only for the coaxial case where a is the distance between coaxial loops. For calculations of A(r,z) in the coaxial case tables for semi-infinite circu- lar current sheets can be used 151.
The first test was performed inside a coil system in a laboratory. A volume of 2 x 2 ~ 2 m3 was sur- rounded by modified Helmholtz-coils producing three orthogonal fields. The inhomogeneity of the field within the volume of the gradiometer was %
lo-' .
Itwas also possible to produce first and second gra- dient. Alternating fields up to %
lo-'
or frequen- cies up to several kHz could be used.As an example we consider the balancing of one of the radial directions of the first order gradiometer of figure 1. The magnetic field around the origin of the gradiometer can be expressed as a series :
We denote S1 and -S2 the projections of the sensing loops in the x-direction
.
When an AC field is applied, the output amplitude of the magnetometer iswhere the axis of the gradiometer is parallel to the z-axis and the distance between the gradiometer
coils is 2L. The upper signs of equation (5) are valid for the first (arbitrary) measurement position.
The lower signs apply after rotating the magnetometer by 180° around the z-axis. The method of rotation in- creases the accuracy. In our coil system,.where the inhomogeneity is about lo-', an unbalancing at ppm level can be detected.
Another advantage of the use of large scale laboratory coils is the possibility of testing the frequency dependence of the balance. lletallic ?arts in the magnetometers are unavoidable and they might significantly change the balance at line frequencies and higher.
The most accurate test of the gradiometric balance close to DC is the response during rotation in the earth's magnetic field. The response due to the magnetic field gradient present at the measure- ment site can be distinghuished from the response due to the unbalancing, because their angular de- pendences are different. Best results were, however, obtained at sites far from magnetic anomalies.
References
/I/ Zimmerman, J.E. and Frederick, N.V., Appl, Phys, Letters
2
(1971) 16/2/ Saarinen, M., Karp, P.J.., Katila, T,E., and Siltanen, P., Cardiovasc. Res.
8
(1974) 820 131 Opfer, J.E., Yeo, Y.K., Pierce, J I M , andRorden, L.H., IEEE Trans. Magn..
9
(1974) 536 141 Brenner, D., Williamson, S.J. and Kaufman, L.,Proceedings of LT 14, Krusius M. and Vuori'o M., Eds., p. 226, vol. 4, (North Holland, Amsterdam
1975)
/5/ Alexander, N.B. and Downing, A.C., Report ORNL- 2828 (1959)
