US 3193734 A
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July 5, 1955 c. F. HEMPSTEAD ETAL 3,193,734
SUPERCONDUCTING FLUX CONCENTRTOR 2 Sheets-Sheet 1 Filed March 22, 1962 Cf HEMPSTEAD /Nx/E/vToRs K B KIM atl A T TORNEV July 6, 1.955 c. F.'HEMPsTEAD ETAL 3,193,734
SUPERCONDUCTING FLUX CONCENTRATOR Filed March 22, 1962 y 2 Sheets-Sheet 2 FIG' 4 F/G. 4A
/NVENTORS C. F HEMPSTEAD BV KB. /f/M www A TTOR/VE V United States Patent() 3,193,734 SUPERCONDUCTING FLUX CNCENTRATR Charles F. Hempstead, Millington, and Young B. Kim,
N ew Providence, N l assignors to Bell Telephone Laboratories, Incorporated, New York, NX., a corporation of New York Filed Mar. 22, 1962, Ser. No. 181,762 9 Claims. '(Cl. 317-158) This invention relates to magnetic circuits and more particularly to magnetic iiux concentrators utilizing superconducting coils.
The need for very high magnetic tields has increased greatly in the past several years as a result of the rapid progress in many areas of physical research. Generally speaking, these high magnetic fields have, until recent years, been achieved in one of twoways; The rst, the so-called brute torce method, provides sustained magnetic fields at the cost of large and elaborate electromagnets and correspondingly large power and cooling apparatus. rlhe secondmethod provides short-duration pulsed 4magnetic fields with less elaborate magnetic coils but at the cost of shortened coil life. The iirst method is generally undesirable due to the prohibitive cost of the equipment, whereas the second method may be undesirable due to the short time duration of the magnetic iield.
lthough the use of superconductors in the construc-y tion or" electromagnets has been known for half a century, it has only been relativelyrecently that work in this eld was begun in earnest. This upsurge is, to a large degree, attributable to recent discoveries and improvements in wire which retain their superconductivity at useful current densities in the presence of magnetic fields in the order of ltltlkilogauss and greater. As used herein, the term superconducting Wire is understood to refer to wire formed of a material displaying zero resistivity to a current owing therein at temperatures below a point referred to as the superconducting transition temperature. The attractiveness of magnets such as solenoidal coils wound of rsupercondu'cting wire resides in the fact that such structures require nopower to sustain the magnetic iield once it is established. Thus it is now possible, through the use of superconducting wire, to produce large magnetic elds that can be sustained indefinitely with relatively small and inexpensive associated equipment.
Such magnets, however, still require means for establishing the initial current and for regulating it once it is established. Heretofore this requirement has necessitated current conducting elements between the 10W temperature superconducting coil and the high temperature power supply. As a result, heat is introduced into the low temperature environment surrounding the superconductingT magnet both by resistive heating of, and by heat conduction through, the current conductinff elements. This, in turn, necessitates additional refrigeration in order that the necessary low temperature be maintained.
lt is therefore an object of the present invention to provide sustained high magnetic fields with superconducting coils requiring no external current source.
it is another object of the present invention to provide sustained high magnetic fields by concentrating the flux derived from relatively low magnetic elds.y
The above objects are accomplished, in accordance with ythe principles oi the present invention, through the use of shorted superconducting coils. It is well `known that an electric current can be established in a closed conducting loop by induction. This law, iirst observed by Faraday, states that an (electromotive force) is set up in a circuit when the magnetic iiux linking `the circuit is changed in any manner. The magnitude of the is yproportional to the time rate ot change of linx-linkages with the circuit.
If the :Klux-linkages through a shorted coil are increased while it is in its normal conducting state, a current is induced in the coil. However, since circuit resistance gives rise to power dissipation, the induced current eventually dies out. It the coil is then cooled to a point below its superconducting transition point and the means by which the initial llux was established removed, another current is induced; however, since there are no longer any circuit losses, this second induced current is sustained, According to Lenzs law the direction of the induced is such that any current it produces tends to oppose the change of ilux that produces it. The sustained current therefore causes the total flux linkages through the coil to remain substantially constant in both number and direction.
Although the total flux is conserved, the flux distribution can be varied. ln accordance with the principles oi the present invention, the conserved iiux is distributed throughout a smaller volume by utilizing certain Lcoil geometries so that a higher ux density is achieved.
In order that the invention may be clearly understood and readily carried into eiiect it will now be described with reference, by way of example, to the accompanying drawings in which:
FIG. l is aperspective view of one embodiment of the present invention utilizing two solenoidal superconducting Coils; t
FlG. 2 is a perspective view, partially broken away, of another embodiment of the present invention utilizing a single multilayer solenoidal coil;
FlG. 3 is a graphical representation of the flux distribution in the embodiment of FIG. 2;
FIG. 4 is a view, partially in cross-section, of still another embodiment of the present invention utilizing a coil of pancake geometry; y f
FIG. 4A is a cross-sectional view of a superconducting wire having an outer coatingof normal conducting substance useful in practicing the present invention; and
FIG. 5 is across-sectional view showing the pancake coil of FIG. 4 in a test setup.
Referring more 'speciiically to the drawings, there is shown in the perspective Viewof FiG. l one embodiment useful in explaining the principles' of the present invention. FIG. l shows two single-layer solenoidal coils 1 and 2. Coilk l has a length I1 and radius r1 and is wound of superconducting wire with nlturns per unit length. Coil 2 has a length l2, radius r2, and is Wound of superconducting wire with n2 turns per unit length, rThe ends, 3-3 of the winding of coil 1 are connected to ends 4 4', respectively, of coil 2'also by means of superconducting wire. Such wire can be formed of Nb-Zr, Nb3Sn or any of the other superconducting materials known in the art.
ln the course of the following analysis, it will be assumed that the lengths of coils 1 and 2 are long enough, With respect to theirdiameters, that any magnetic fields produced within the coi/ls is substantially uniform. This assumption is verified by practice and results in an error ot only a iew percent. y Y K While coil 1 is at a temperature above its superconducting transition temperature, a uniform external magnetic lfiel-d H0 is established through it in a direction parallel to its axis. As a result of the establishment of field H0 a current is induced in coil 1. However, this current quickly decays due to :the resist-ance of the Winding, .which is in its normal conducting state.
With H0 still applied, coils 1 and 2 and the connecting Wires, are cooled-to a temperature below their superconducting transition point by suitable refrigerating means not shown. The external magnetic iield H0 is ythen removed.
Thefilux linkage A1. in
coil 1 Vis given by the equation arsarsa The current i, induced in coil 1 when H0 is removed, which current also ilows through coil 2, has la magnitude given by HZIlL/lgl.
Substituting for z' and )(1,
ViniW/zHo H 7 2 (Verwarm The flux concentration factor ,B is defined as the ratio of H2 to H0 and is equal to Vrnmz V17L12+V2n22 L* "a1 l@ a2 712 V1 "i From Equation 8, it is seen that as long as n2 is greater than n1, a flux concentration factor greater than unity can be achieved. For example, if r11/n2 equals 3A0 and V2/V1 equals lAOO, in the circuit of FIG. 1, the flux concentration factor equals five.
FIG. 2 yis a partially broken away perspective illustrat-ion of another embodiment of the present invention comprising a single multilayer solenoidal coil 20 wound of superconducting wire. Coil 20 has an outer radius a2, an inner radius al, and a length b. The two ends 21 and 21' of coil 20 are shorted together by means of a superconducting element 22 so that -when coil 20 is cooled below its superconducting transition temperature, it denes a single current loop whose resistance is zero.
The operation of lthe flux concentrator of FIG. 2 can be explained if it is again assumed that the length b of coil 2() is quite long compared to its diameter and the winding has a substantially uniform turn density. Initially la uniform external magnetic field H0 is established parallel to the 4axis of coil 2() in the direction shown while coil 20 is in its normal conducting state. The field H0 is uniform throughout coil 2() from the axis to the outer radius. An initial current is induced in coil 2() which produces a field tending to yoppose H0, This current, however, decays rapidly, due to circuit resistance. Coil 20 is then cooled to its superconducting state and the external field H0 removed. A new current z' is induced in coil 20 which produces a magnetic field H1 tending to conserve the total ilux linkages A0 through the coil. The lt-otal ilux linkages A0 can be calculated as follows:
The flux linkages with a turn at a distance r from th axis of coil 20 is given by Denning m as the number of turns per unit length along the axis of coil 20 and n as the number of layers of wire per unit length in the radial direction, the total ilux linktages through the coil is In general, the electromotive force induced in a closed loop is given by oa E.l\/l.F.--t-R For a shorted coil in its superconducting state, however, R=O. Therefore,
`=0 and constant Although the total flux linkages A0 must remain constant after H0 is removed, the distribution of the flux need not be uniform. In the multilayer solenoidal coil 20, the flux ydensi-ty due to the induced current z' is maximum in the center and decreases line-arly from the inner radius a1 to the outer radius a2. At point A, in the mid-region of coil 20, the resulting flux density can be calculated with the aid of the graph of FIG. 3.
In FlG. 3, the radius of coil 20 is plotted along the abscissa and the flux density along the ordinate. The dashed curve 31 represents the initial uniform flux density H0 within coil 2t). The solid curve 32 shows the approximate distribution of flux density resulting from the induced current z'. In practice, the sloping portion of curve 32 will depart from perfect linearity to the extent that the above-mentioned assumptions depart from reality.
The final flux density Hm as seen from curve 32 can be written as By utilizing the expressions of Equation 11 and integrating, the total flux Ar linking a single turn at an arbitrary radius r is Equation 12, when integrated once again over the entire coil, yields an expression for the total flux linkages )r1 due to current z'.
b H :"m 1era) (eenzaam) 13) Therefore, with a coil having a length that is quite long compared to its diameter, it is seen that a maximum ux concentration factor of two is obtained as the inner radius approaches zero.
If a solenoidal coil such as coil 2t) of FIG. 2 has a length b that is not long compared to its diameter, the flux concentration factor can be greater than the value calculated from Equation 14. This is due to the fact that the lines of magnetic flux diverge near the ends of the coil; and whereas this eifect can be neglected in the case of a long coil, it must be considered in a complete analysis of a shorter coil.
'coil having an inner radiusy approaching zero and a length to outside `diameter ratio of approximately .05.
In accordance with the principles of the present invention, the magnitude of the flux density can be further increased by the subsequent reapplication of the uniform external field in a direction opposite to the first direction, while the coil is still in its superconducting state. The additional current induced in the coil as a result of this reapplication of an external field establishes an additional magnetic field component tending to oppose the new change in iiux. The additional magnetic field component thereby established is therefore in the same direction as the previously established field.
Referring once again to FIG. 2, after H1, the field due to superconducting current, has been established, a new uniform external magnetic field Ho is applied along the axis of coil 20 as shown. The total current i is caused to increase as a result, until the total linx linkages through coil 20 equals the original flux x0 plus the new iiux linkages. At a point A Within the coil the resulting iiux density is equal to H1 plus the new flux density I13H0 minus the external field flux density H. The total iiux at point A, designated H1', is therefore given by the The same principle applies equaly well to the embodiment of FIG. 1. In that embodiment the new external field H0 would be applied only to coil 1 in a direction opposite H0 and the new flux in coil 2 would become equal to ,BH0-|H. f
It is obvious that the new external field H0 can be used as a tine adjustment means for the fiux concen- States Patent No. 3,124,455 yissued March 10, 1964, was
utilized. In this embodiment, which is of the so-called pancake geometry, the wire, having a diameter of approximately .025 inch, waswound on a stainless steel form 4i?. There were 39 layers of winding consisting of 191/2 turns per layer. Each layer was separated by a .001 inch wrapper of stainless steel. The inside diameter of the coil 41 was .25 inch, the outside diameter was 2.276 inches and the length was .5l inch. As in the case of the previous embodiment, the ends 42 and 43 of the coil were shorted together.
FIG. 5 is a simplified cross-sectional View of the coil of FIG. 4 installed in a typical test setup. Coil 40 is shown suspended in the air gap of a magnet having a controllable magnetic field. For reasons of clarity the suspension means for coil 40 have not been shown. Likewise, only the pole pieces 50 and 51 of the magnet have been illustrated. Coil 40 is oriented near the center of the air gap with its axis perpendicular to the faces of pole pieces 50 and 51. Surrounding coil 40 is a Dewar liask 53. A uniform magnetic field of 6.8 kilogauss was established through coil 4) while it was in its normal conducting state. apoint below the critical temperature of the NbaSn wire byadding liquid helium 52 to the iask and the eld was removed. The magnetic liux density wasrneasured at The temperature was then reduced tok point P in the center of coil 40`and found to be approximately 15 kilogauss and the resultant ux concentration factor approximately 2.2.
. As mentioned above, the present invention can be practiced by utilizing any of the superconducting wire known in the art. The operation of the invention is enhanced, however, by utilizing wire having a core of superconducting ma-terial and an outer layer of normal or nonsuperconducting material. A cross-sectional view of such Wire is shown in FIG. 4A wherein the superconducting core is designated by numeral 44 andthe normal conducting outside coating is designated by numeral 45. Typical of this type wire is the NbBSn Wire disclosed in the abovementioned copending application of E. Buehler and J. E. Kunzler and the metallically insulated wire disclosed in the copending application of T. H. Geballe, Serial No. 52,409, filed August 29, 1960, now United States Patent No. 3,109,963 issued November 5, 1963.
As described in the last-mentioned copending application of T. H. Geballe, by utilizing superconducting wire having an outer layer of nonsuperconducting material of low resistivity, the stability of operation is improved. In case of a temporary excursion above the superconducting transition point, the current in the superconducting core of this wire is transferred to the nonsuperconducting outer layer. Once the superconductivity of the core is reestablished, the reverse process takes place and the current is coupled back into the superconducting core. In the meantime, some energy will have been lost due to resistive heating, depending upon the length of time the device was above the `superconducting transition point. The amount of energy loss, however, is quite small for short excursions above the superconducting transition point.
In all cases it is understood that the above-described circuits represent only a limited number of embodiments of the present invention. Many other embodiments including those utilizing different coil geometries and core materials can be constructed by those skilled in the art without departing from the spirit and scope of the present invention.
What is claimed is: n
1. A flux concentrator comprising, a lirst coil of superconducting wire having nl turns per unit length wound in the form of a cylinder having a volume V1, a second coil of superconducting wire having n2 turns per unit length Wound in the form of a cylinder having a volume V2, where n1 n2 and means for connecting the first and second ends of said first coil to the first and second ends of said second coil respectively, external means for establishing a constant magnetic yfield component along the axis of said first coil while said coil is in its normal conducting state, means for establishing a substantially uniform magnetic fieldv through said coil parallel to the axis thereof, said externally applied eld being established while said coil is in its knormal conducting state, means for changing said coil to its superconducting state, and means for subsequently removing said externally applied field.
6. The flux concentrator according to claim 5 wherein said superconducting Wire is Nb-Zr.
7. The ux concentrator according to claim 5 wherein said superconducting wire is NbsSn.
8. The flux concentrator according to claim 5 wherein said superconducting Wire has an outer coating of a normal conducting substance.
9. The method of concentrating the ux of a magnetic eld comprising the steps of, applying an external uniform magnetic eld through a shorted multilayer coil Wound of superconducting Wire in a direction substantially parallel to the axis of said coil while said wire is in its normal conducting state, cooling said Wire to a temperature below its superconducting transition temperature,
external uniform magnetic tield parallel to the axis of said coil in a direction opposite that of said irst applied magnetic ield.
OTHER REFERENCES McFee: Application of Superconductivity to the Generation and Distribution of Electric Power, Electrical Engineering, February 1962, pages 122-429.
LARAMIE E. ASKIN, Primary Examiner.
removing said external eld, and applying a controllable 15 JOHN F, BURNS, Examiner.