Superconducting devices by optimization of the superconductor's local critical current

Abstract

The present invention relates to a method and an apparatus for producing superconducting devices and to superconducting devices. The method comprises determining one or more regions of reduced critical current density in the superconducting device and modifying the critical current density in the one or more regions of reduced critical current density, so as to increase the overall critical current or to decrease the overall AC losses of the superconducting device. The modifying comprises modifying the amount and/or distribution of the superconducting material in the one or more regions of reduced critical current density; and/or modifying the chemical composition of the superconducting material in the one or more regions of reduced critical current density; and/or decreasing the cooling temperature in the one or more regions of reduced critical current density. A superconducting device formed according to such method can also be provided.

Claims

1. A superconducting device including: a superconducting material having one or more local regions, in which a different amount of the superconducting material is used in the one or more local regions as compared to the other regions of the superconducting device; and at least one superconducting cable, layer, or filament having a distribution of the superconducting material that varies along a length of the superconducting cable, layer or filament, wherein the superconducting cable, layer or filament has: at least one region of decreasing width and/or thickness in which the width and/or thickness of the superconducting cable, layer, or filament decreases gradually; and at least one region of increasing width and/or thickness in which the width and/or thickness of the superconducting cable, layer, or filament increases gradually.

2. The superconducting device according to claim 1, wherein the superconducting device comprises a superconducting coil and the one or more local regions comprise the innermost turn or turns of the coil; or the superconducting device comprises a single layer solenoid and the one or more local regions comprise the regions located at the ends of the solenoid when viewed in the direction along the solenoid's axis; or the superconducting device comprises a single layer toroid and the one or more local regions comprise the regions located closest to the centroid of the toroid in each turn of the toroid; or the superconducting device comprises a multilayer solenoid and the one or more local regions comprise the regions located at the ends of the solenoid when viewed in a direction along the solenoid's axis and/or the turn or turns closest to the solenoid's axis; or the superconducting device comprises a multilayer toroid and the one or more local regions comprise the regions located closest to the centroid of the toroid in each turn of the toroid and/or the inner toroid layers; or the superconducting device comprises a striated superconducting tape and the one or more local regions comprise the central filament or filaments of the striated tape; or the superconducting device comprises a stacked superconducting device comprising a plurality of superconducting layers, each superconducting layer having a plurality of filaments, and the one or more local regions comprise the central filament or filaments of each superconducting layer of the stacked superconducting device.

3. The superconducting device according to claim 1, wherein said superconducting cable, layer, or filament has a variable cross-sectional area and/or a variable material composition along a lengthwise direction of the cable, layer, or filament; and/or the superconducting device comprises a plurality of individual superconducting cables, layers, or filaments, and wherein at least two superconducting cables, layers, or filaments have different cross-sectional areas and/or different material compositions.

4. The superconducting device according to claim 1, wherein the superconducting device comprises a plurality of turns of the at least one superconducting cable or layer, wherein the density of the windings of the at least one superconducting cable or layer in the one or more local regions of the superconducting device is lower than the density of the windings in the other regions of the superconducting device.

5. The superconducting device according to claim 1, wherein the superconducting cable is striated superconducting tape comprising a plurality of filaments, wherein: the widths and/or the thicknesses and/or the material composition of at least two of the filaments are different; and/or the width and/or thickness and/or the material composition of at least one filament varies along the lengthwise direction of the tape.

6. The superconducting device according to claim 1, wherein the superconducting device comprises a plurality of superconducting layers, each layer having a plurality of filaments, wherein: at least one layer comprises filaments having different width and/or thickness and/or chemical compositions; and/or the filaments of at least two of the layers have different widths and/or thicknesses and/or chemical compositions.

7. The superconducting device according to claim 1, wherein the superconducting device further comprises a plurality of heat sinks arranged in or in the vicinity of said one or more local regions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) These and other aspects will now be described in detail with reference to the following drawings:

(2) FIG. 1 shows a conventional rectangular tape having a uniform cross-section used for winding high temperature superconducting (HTS) coils;

(3) FIG. 2 shows a conventional coil assembled from a rectangular HTS tape, wherein FIG. 2A is a perspective view of the coil, FIG. 2B shows schematically the coil's cross-section in a plane including the coil's axis 122, FIG. 2C shows schematically half the cross-section and FIG. 2D shows an abstraction of the coil (for conceptual purposes);

(4) FIG. 3 shows an M-shaped superconducting tape for winding M-shaped superconducting coils;

(5) FIG. 4 shows a tiling pattern for cutting tapes for M-shaped coils from a rectangular tape;

(6) FIG. 5 shows various M-shaped tapes and their characteristic points, wherein FIG. 5A shows an embodiment of an M-shaped tape and FIG. 5B shows a different embodiment of an M-shaped tape;

(7) FIG. 6 shows an M-shaped superconducting coil assembled from a superconducting M-shaped tape, wherein FIG. 6A is a perspective view of the M-shaped coil, FIG. 6B shows the coil's cross-section in a plane including the coil's axis 182, FIG. 6C shows half the cross-section and FIG. 6d shows an abstraction of such a coil (for conceptual purposes);

(8) FIG. 7 shows various superconducting coils assembled from tapes having varying widths, wherein FIG. 7A shows a single M-shaped coil, FIG. 7B shows a single bow-tie shaped coil, FIG. 7C shows a back to back array of M-shaped coils, FIG. 7D shows a front to front array of M-shaped coils. and FIG. 7E shows an array of bow-tie shaped coils;

(9) FIG. 8 shows a conventional single layer superconducting solenoid in FIG. 8A and an optimized single layer superconducting solenoid in FIG. 8B;

(10) FIG. 9 shows a cross-sectional model of a single layer toroid in FIG. 9A, a conventional single layer superconducting toroid in FIG. 9B and an optimized single layer superconducting toroid in FIG. 9C;

(11) FIG. 10 shows a conventional multilayer superconducting solenoid in FIG. 10A and an optimized multilayer superconducting solenoid in FIG. 10B;

(12) FIG. 11 shows a conventional multilayer superconducting toroid in FIG. 11A and two exemplary optimized multilayer superconducting toroids in FIG. 11B and FIG. 11C;

(13) FIG. 12 shows a conventional striated superconducting tape in FIG. 12A and three exemplary optimized striated superconducting tapes in FIGS. 12B to 12D;

(14) FIG. 13 shows a conventional superconducting tape having a superconducting layer with uniform thickness in FIG. 13A and an optimized superconducting tape having a superconducting layer with varying thickness FIG. 13B;

(15) FIG. 14 shows the magnetic field orientation dependence of the critical current I.sub.c of tapes doped with different concentrations of Zr;

(16) FIG. 15 shows a coil made from a superconducting tape exhibiting a non-uniform doping, wherein FIG. 15A shows the streamlines in the tapes of a circular coil and FIG. 15B shows a blueprint for using a superconducting tape with a variable doping;

(17) FIG. 16 shows a stack of striated superconducting tapes having filaments of different widths;

(18) FIG. 17 shows a lift factor as a function of the applied magnetic field in Tesla for different temperatures, wherein FIG. 17A shows the lift factor for the case of an applied magnetic field that is parallel to the ab plane of the superconducting film and FIG. 17B shows the lift factor for the case of an applied magnetic field that is parallel to the c axis of the superconducting film;

(19) FIG. 18 shows superconducting coils (conventional and optimized);

(20) FIG. 19 shows the magnetic field of a conventional superconducting coil in FIG. 19A and of an optimized superconducting coil in FIG. 19B;

(21) FIG. 20 shows the normalized current density in a conventional superconducting coil in FIG. 20A and in two exemplary optimized superconducting coils in FIG. 20B and FIG. 20C);

(22) FIG. 21 shows simulation results for a non-optimized striated tape in FIG. 21A and FIG. 21C and for an optimized striated tape FIG. 21B and FIG. 21D;

(23) FIG. 22 shows the magnetic field in a non-optimized coil in FIG. 22A and in an optimized coil in FIG. 22B;

(24) FIG. 23 shows the dependency of AC losses on (I/I.sub.c);

(25) FIG. 24 shows the dependency of the magnetization AC loss on the critical current density.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENT

(26) Throughout the drawings, the same reference signs are used for the same or similar elements. It should be understood that even though embodiments are separately described, single features thereof may be combined to additional embodiments.

(27) Coils Assembled from Superconducting Tapes

(28) In manufacturing superconducting devices such as magnetic coils, solenoids, toroids, etc., the superconducting cable from which the devices are assembled may be formed in the shape of a thin tape. For example, the thin tape may be composed of a mono- or multi-filament composite superconductor including individual superconducting filaments which extend along substantially the length of the multi-filament composite conductor (i.e. along the lengthwise direction). The filament(s) may be surrounded by a matrix-forming material, which is not a superconducting material. The superconducting filaments and the matrix-forming material may be encased in an insulating layer. Other superconducting tapes or wires are also known in the art and may be used in the examples of the invention.

(29) FIG. 1 shows schematically a conventional rectangular superconducting tape 10 having a uniform cross-section used for winding high temperature superconducting (HTS) coils, such as pancake or double-pancake type of coils. For a better understanding the tape is not shown to scale. Typical dimensions of the tape are width H=12 mm and length L about 18 m for a tight 50 turn coil with a 5 cm inner radius. The thickness of the tape ranges from about 50 to 100 micrometers including a superconducting layer of about 1 to 10 micrometers in thickness. Other dimensions are also possible.

(30) FIG. 2 is a schematic representation of a conventional coil 12 assembled from a rectangular HTS tape with uniform width, wherein FIG. 2A is a perspective view of the coil, FIG. 2B shows schematically the coil's cross-section in a plane including the coil's axis 122, FIG. 2C shows schematically half the cross-section and FIG. 2D shows an abstraction of the coil (for conceptual purposes). R1 denotes the inner radius of the coil and cg denotes the coil gap (i.e. the gap between the turns).

(31) In an example of the invention, a coil may be assembled from a tape having a variable cross-section (i.e. a variable cross-sectional area). The shape of the tape may be for example an M-shape. FIG. 3 shows the basic shape of an M-shaped tape 14 that may be used for winding M-shaped coils. As shown in FIG. 3, the width of the M-shaped tape 14 reduces gradually in a lengthwise direction of the tape between a first predetermined point P1 and a second predetermined point P2 and increases gradually between the second predetermined point and a third predetermined point P3.

(32) A tape of such shape may be directly manufactured without any cutting involved. Alternatively, M-shaped tiles may be cut from an original rectangular superconducting tape, preferably in a way that no superconducting material is discarded.

(33) FIG. 4 shows an exemplary tiling pattern 16 that may be used to cut tapes for M-shaped coils from a rectangular superconducting tape. The overall length L and the width H of the (uncut) rectangular tape may be the same or similar to those of the rectangular tape shown in FIG. 1. The tape may be further specified by two additional parameters d and h1, wherein d denotes the distance in lengthwise direction from the first predetermined point P1 to the second predetermined point P2 and h1 denotes the width of the tape at point P2 (i.e. at the apex of the M-shape). Parameters d and h1 may be determined considering the specific application and may depend on several factors such as the current and the inner radius of the coil among others.

(34) FIG. 5 shows in more detail two possible M-shaped tapes for coil winding and their characteristic points. The tapes may be cut from a rectangular tape, such that no superconducting material is wasted. The M-shaped tape shown in FIG. 5A is similar to the M-shaped tape shown in FIG. 3. In this tape the points (0,h1) and (d,h1) are connected by a straight line. Similarly, the line linking points (d,h1) and (L,h1) is a straight line. However, the lines linking points (0,h1) and (d,h1) and points (d,h1) and (L,h1), respectively, do not necessarily have to be straight lines. For a material conservation to take place, it is only necessary that the line linking points (0,h1) and (d,h1) is an odd function centered in point (d/2,H/2) and that the line linking points (d,h1) and (L,h1) is an odd function centered in point (L-d/2,H/2). An example of such tape is shown in FIG. 5B.

(35) FIG. 6 shows schematically an M-shaped coil 18 assembled from an M-shaped tape, wherein FIG. 6A is a perspective view of the M-shaped coil, FIG. 6B shows the coil's cross-section in a plane including the coil's axis 182, FIG. 6C shows half the cross-section and FIG. 6D shows an abstraction of such a coil (for conceptual purposes). In FIG. 6 R1 denotes the inner radius of the coil and cg the coil gap (i.e., the gap between the turns).

(36) Other coil designs, for which there may be a comparatively low waste of superconducting material are also possible.

(37) FIG. 7 shows various exemplary coils 18 assembled from superconducting tapes having varying width in a lengthwise direction. For simplicity only the abstract shape of the coil is shown. Further, to aid visualization the parameter d is not presented. FIG. 7A shows a single M-shaped coil and FIG. 7B shows a single bow-tie shaped coil. The bow-tie shaped coil may be realized without wasting superconducting material by, for example, winding a single M-shaped coil and rearranging the windings by gently pushing from below (i.e. from the side opposite to the M-shaped cut). FIG. 7C shows a back to back array of M-shaped coils, FIG. 7D shows a front to front array of M-shaped coils and FIG. 7E shows an array of bow-tie shaped coils. Larger arrays can be produced by using both bow-tie and M-shaped coils in different orientations.

(38) Depending on the application, the superconducting tape may be cut or formed in a more-complex shape, for example including a plurality of regions of increasing width and a plurality of regions of decreasing width.

(39) The above design principles may be extended to single and multi-layer solenoids and toriods wound from superconducting tapes.

(40) Single Layer Solenoids

(41) FIG. 8 shows schematically an axisymmetric model of a single layer solenoid 20 having a symmetry axis 210, wherein FIG. 8A shows a conventional single layer solenoid and FIG. 8B shows a single layer solenoid according to an example of the invention. The conventional solenoid is assembled from a rectangular tape 10 of uniform width. The solenoid shown in FIG. 8B is assembled from an M-shaped tape 14 having variable width, with a wider region 14a being used in the outer (end) turns of the solenoid and a narrower region 14b being used in the central turns. In the example shown in FIG. 8B, each rectangular tape has a constant thickness along the longitudinal direction (i.e. along the lengthwise direction of the tape). However, it is possible to use rectangular tapes with a variable thickness along the longitudinal direction.

(42) Single Layer Toroids

(43) FIG. 9 shows schematically a single layer toroid 30. For ease of explanation, a cross-sectional model (see FIG. 9A) is used. Here, a cut plane perpendicular to the toroid's symmetry axis and passing through its centroid 302 is used. FIG. 9B shows a conventional single layer toroid and FIG. 9C shows a single layer toroid according to an example of the invention. The number of depicted turns is used for illustrative purposes only and does not necessarily correspond to the actual number of turns used in a single layer toroid. The conventional single layer toroid is assembled from a rectangular tape 10 of constant width. The single layer toroid according to an example of the invention uses a rectangular tape 14 with a variable width, where wider sections 14a of the tape are used close to the centroid 302 of the toroid and narrower sections 14b are used in the regions far from the centroid 302 of the toroid. In this example, the tape has a constant thickness along the longitudinal direction (i.e. along the lengthwise direction of the tape). However, it is possible to use rectangular tapes with a variable thickness along the longitudinal direction.

(44) Multi-Layer Solenoids

(45) FIG. 10 shows an axisymmetric model of a multilayer solenoid 40 having a symmetry axis 410, wherein FIG. 10A shows a conventional multilayer solenoid and FIG. 10B shows a multilayer solenoid according to an example of the present invention. The conventional multilayer solenoid shown in FIG. 1 OA uses rectangular tapes 10 of uniform width, all tapes having the same width. The multilayer solenoid shown in FIG. 10B uses tapes of a variable width, said tapes being wider 14a in the top and bottom (i.e. end) parts of the solenoid and narrower 14b in the central part. Additionally the innermost and the outermost layers may have wider turns. In the example shown in FIG. 10B, a different or the same number of tapes per layer (with or without constant spacing among tapes in each layer) may be used. Further, tapes with a variable thickness along the longitudinal direction (i.e. along the lengthwise direction of the tape) may be used.

(46) Multi-Layer Toroids

(47) FIG. 11 shows a multilayer toroid 50 having a centroid 502. Here, a cut plane perpendicular to the toroid's symmetry axis and passing through its centroid 502 is used. FIG. 11A shows a conventional multilayer toroid, FIG. 11B shows a multilayer toroid according to one example of the invention, and FIG. 11C shows a multilayer toroid according to another example of the invention. In order to aid the visual representation, the number of tapes displayed does not correspond to the actually used number.

(48) The conventional multilayer toroid as illustrated in FIG. 11A comprises a plurality of layers, each layer constituted by rectangular tapes 10 having the same, constant width. Further the widths of the tapes in all layers are the same. In the multilayer toroid shown in FIG. 11B tapes of variable width are used, so that wider regions 14a are used in the innermost layer, while narrower regions 14b are used in the following layers and finally, wider regions 14c are used in the outermost layers. In the multilayer toroid shown in FIG. 11C several layers of tapes of variable width are employed, with the outer layers being constituted by narrower regions 14d of the tapes and the inner layers being constituted by wider regions 14e of the tapes. In the examples shown in FIGS. 11B and 11C, each tape has a substantially constant thickness along the longitudinal direction (i.e. along the lengthwise direction of the tape). However, it is possible to use rectangular tapes with a variable thickness. Further, a different or the same number of tapes per layer (with or without constant spacing among tapes in each layer) may be used.

(49) Superconducting Striated Tapes

(50) As is known in the art, superconducting tapes may be striated to reduce the AC losses of the superconducting devices (such as coils, solenoids or cables among others) assembled from such tapes when exposed to AC fields. The striation process creates small grooves in the surface of the tape, hence breaking the superconducting layer. However, the tape remains mechanically connected, retaining most of its mechanical stability. Conventionally, the striation is carried out constructing filaments of the same, uniform width.

(51) FIG. 12 shows a top view of an exemplary striated superconducting tape 60 constituted by a plurality of filaments 602. FIG. 12A shows a conventional striated superconducting tape constituted by filaments 602 of the same, constant width. For a striated tape with filaments 602 of uniform width the filaments in the center of the tape experience higher AC losses than the filaments close to the tape's edge. Therefore, it is proposed to use filaments of different widths with wider filaments in the edges of the tape. This will increase the loss in the edge filaments, but will also reduce the losses in the central filaments, hence reducing the overall AC losses.

(52) FIGS. 12B to 12D show exemplary striated tapes with filaments 602a and 602b having different widths. In all examples, the superconducting tape is striated by forming a plurality of grooves (shown as thin lines) by a laser. In the example shown in FIG. 12B, each of the filaments has a constant width and thickness along the lengthwise direction of the tape, with the outermost filaments 602a having greater width than the innermost filaments 602b. For simplicity, width optimization of only the outermost filament is presented here, but the priciple is similar when considering optimizing the width of several filaments.

(53) Depending on the intended application, it is possible to have different electromagnetic environments in the same device (consider for instance the innermost and the outermost turns of coils, or the turns at the ends of solenoids and the ones in the central regions) leading to more than one region of reduced critical current density and/or of increased magnetic field. In such cases, it is possible to design a striation pattern in such a way that the AC losses are reduced as much as possible in the overall superconducting device.

(54) Generally, the optimal width of the external (outermost) filament is related to the amplitude of the magnetic field applied. In the case presented above (see FIG. 12B), for an externally applied field with amplitude of 10 mT, the losses can be minimized by using an outermost filament which is 850 m wide. For a field with amplitude of 15 mT, the optimal width of the external filaments would be 610 m. Therefore, in cases where the amplitude of the externaly applied magnetic field changes along the tape's length, the width of the outermost filament can be changed accordingly.

(55) FIG. 12C shows an exemplary layout (not to scale) for the filaments in a tape exposed to a non-uniform magnetic field such that it has a lower amplitude at the tape's central region. In this example, the width of the outermost filament 602c is not constant but varies along the lengthwise direction of the tape.

(56) FIG. 12D shows another exemplary striation pattern (not to scale) of a superconducting tape with filaments of varying width designed so that the magnetization loss is reduced in a plurality of regions of the superconducting tape.

(57) In the examples shown in FIGS. 12C and 12D, the width of at least one individual filament (for example the outermost filament) 602c varies along the lengthwise direction (i.e. the direction along the length of the tape). Further, filaments of different widths are used (with the innermost filaments generally having lower width than the outermost filaments). The laws of variation of the width of each filament along a lengthwise direction depend generally on the applied magnetic field. As illustrated in FIG. 12D, the laws of variation of the width along the lengthwise direction of the tape may be different for the different filaments. Accordingly, the widths of the filaments may vary both along the lengthwise and the transverse (width) direction of the tape (i.e. the direction perpendicular to the longitudinal direction of the tape).

(58) A common characteristic of the designs described above is the redistribution of the superconducting material, so that the overall critical current is increased and/or the AC losses of the superconducting device are reduced. For example, in the case of devices to which a transport current is applied, more superconducting material is allocated in the region(s) which experience(s) the highest reduction in critical current density. For instance, in the case of an inductive coil in a self-field, this means that more material is allocated in the central region of said coil, for example by varying the width of the superconducting tape from which the coil is assembled. In case of striated tapes or stacks of them, the superconducting material is redistributed so that the reduction of losses in some filaments and/or parts of them is higher than the increase of losses in some other filaments and/or parts of them, leading to an overall reduction of the AC losses of the superconducting device. The material may be redistributed for example by varying the width of the filaments constituting the superconducting device in a transverse and/or lengthwise direction of the tape.

(59) Another method for designing superconducting devices is to vary the thickness of the superconducting (for example HTS) layer along the length of the superconducting tape. For example, a larger amount of superconducting material may be deposited in the part of the tape that will need it the most.

(60) In a conventional superconductor (e.g. a superconducting tape) produced by conventional Ion Beam Assisted Deposition (IBAD) process, the fabrication of the superconductor involves a deposition of a superconducting layer (e.g. HTS layer) on top of a substrate. The HTS layer can be grown in different thicknesses. Typically, layers of 1 micrometer in thickness are formed in most superconductors. Thicker layers can be grown at the expense of a longer deposition times, while thinner layers can be formed by reducing the deposition time.

(61) FIG. 13 shows a perspective view of a superconducting tape 70, for example a superconducting tape for winding a circular coil. The conventional superconducting tape shown in FIG. 13A has a superconducting layer with a constant thickness. The superconducting tape according to an example of the invention shown in FIG. 13B has a superconducting layer 71 having a variable thickness, with an M-shaped pattern being formed across the thickness of the superconducting layer. In other words, the superconducting layer according to this example exhibits a variable thickness, with the thickness at the central portion 70a of the tape being lower than the thickness at the edge portions 70b of the tape. The superconducting layer 71 may be formed for example by an IBAD process or a rolling-assisted biaxially textured substrate (RABiTS) process among other processes.

(62) By forming a superconducting layer having a variable thickness as shown in FIG. 13B, a superconducting tape, for example, for winding a coil may be produced. Of course, the same design principle can be employed for producing tapes having a variable thickness for use in other superconducting devices, such as other coil designs (racetrack, saddle, etc.), solenoids, toroids, etc. Further, the thickness of the layer may vary according to a different pattern, depending on the specific design and application.

(63) It is of course possible to vary both the width and the thickness of the superconductor layer.

(64) Alternatively or in addition to varying the amount of superconducting material, for example by varying the cross-sectional area of a superconducting layer, superconducting cable or superconducting filament, the composition of the superconducting material can be spatially varied. For example, the composition of the HTS layer tape can be modified to affect the local critical current density J.sub.c(B) characteristic. Various techniques for modifying the composition of the superconducting layer may be employed, including for example the techniques disclosed in the publication N. D. Khatri et al. Pre fabricated nanorods in RE-Ba-Cu-O superconductors SUST 26, 8 doi:10.1088/0953-2048/26/8/085022 and the references cited therein.

(65) FIG. 14 shows the magnetic field orientation dependence of the critical current I.sub.c of rectangular tapes made of (RE)BCO superconducting material (RE stands for rare earth such as Y, Ga, Sm, etc.) doped with different concentrations of Zr, produced by Super Power Inc. The angle (in degrees) is measured with respect to the superconducting tape's surface. As shown in FIG. 14, there is a tradeoff between the regions of peak performance. Thus, a given concentration of Zr (in this case Zr 0.15) allows for a larger critical current I.sub.c when the field is applied at an angle close to 0 deg, but the same concentration reduces the critical current I.sub.c at angles close to 90 deg.

(66) According to an example of the invention, non-uniform doping can be used to optimize superconducting devices. For instance, coils can be optimized, so that the regions that experience magnetic field with largely different orientations employ tapes with doped HTS layers optimized for the particular angle of the applied field. FIG. 15 illustrates an example of a superconducting coil exhibiting non-uniform doping. The axis of the coil (not shown) is at the left of each image. FIG. 15A shows the streamlines in the tapes of a circular coil and FIG. 15B shows a blueprint for using a superconducting tape with a variable doping, which is optimized for parallel and for perpendicular fields in such coil. In FIG. 15B the solid pattern shows a region 72 with a doping that allows a higher critical current under parallel magnetic field. In the doping example of FIG. 14, this corresponds to the doping labelled Zr 0. In a similar fashion, the dashed region 74 has a doping that allows a higher critical current under perpendicular magnetic field. In the doping example of FIG. 14, this corresponds to the doping labeled Zr 0.15.

(67) Stacked Tape Magnets

(68) Use of filaments having different widths and/or thicknesses as well as tapes with varying doping concentration can be advantageous for pulsed field magnetization of stacks of tapes. In such applications, filaments of different widths, tapes with superconducting layers of varying widths and/or thicknesses and/or tapes with varying doping concentration may reduce the hysteretic losses related to the pulsed fields applied to the stack. The principle behind this is the same as described above for the case of a striated tape.

(69) FIG. 16 shows a stack 80 of superconducting tapes 810, 820, 830 with filaments 802 of different widths, the lines showing the regions (e.g. grooves) that have been striated with a laser. As described above, the width of the filaments 802 is selected so as to reduce the overall AC magnetization loss. Of course, in order to reduce the overall AC magnetization loss, it is also possible to use two further alternative or complementary strategies: use of tapes with superconducting layers of varying thicknesses and/or use of tapes with varying doping concentrations.

(70) Superconducting Devices with Locally Variable Temperature

(71) In addition or alternatively to the above approaches based on locally increasing or decreasing the amount of the superconducting material and/or locally varying the composition of the superconducting material, the overall critical current may be enhanced thermally, i.e. by using local temperature variation to increase the local critical current density of superconducting devices.

(72) Generally, for lower operating temperatures the critical current I.sub.c of a superconductor (for example a superconducting tape) is enhanced by a so called lift factor (l.sub.f). The lift factor l.sub.f at a given temperature T for a superconducting material whose critical temperature is above 77K can be defined as:
l.sub.f=I.sub.c(T)/I.sub.c(77K)

(73) Similar expressions for lift factors can be obtained for other superconducting materials with lower critical temperature by considering a different reference temperature.

(74) FIG. 17 shows the lift factor as a function of the applied magnetic field in Tesla for different temperatures (65K, 50K, 40K, 30K and 20K) for high temperature superconducting coated conductors as reported on http://www.superpower-inc.com. FIG. 17A shows the lift factor for the case of an applied magnetic field that is parallel to the ab plane of the superconducting film (i.e. parallel to the tape's surface) and FIG. 17B shows the lift factor for the case of an applied magnetic field that is parallel to the c axis of the superconducting film (i.e. perpendicular to the tape's surface). As seen from FIG. 17, it is possible to perform a simple linear interpolation between the points connecting the lift factor at 77K and at 65K, which yields:
l.sub.f(T)=0.125T+10.625.

(75) Hence for a temperature of 76 K, a lift factor of 1.125 may be obtained. Similar results can be obtained for the case of an externally applied field.

(76) As seen from above, a small variation in the cooling temperature yields a relatively large lift factor. This fact can be advantageously exploited in the design of superconducting devices. In an example, the cooling system may be configured such that it provides an enhancement of the critical current density in the regions where for example the magnetic field produces a reduction. For example, it is possible to design a coil in such a way that heat sinks are located in the vicinity of the inner turns, so that the small difference in cooling compensates for the higher magnetic field. For example, if the regions where the magnetic field produces a reduction are cooled to 76 K, a lift factor of 1.125 is obtained. Taking into account that the loss is at least proportional to 1/I.sub.c.sup.2, a reduction in AC losses of 21% is expected in regions of the device that otherwise would be at 77K.

(77) The same principle can be applied to other superconducting devices (such as for example solenoids, toroids, stacked-tape magnets, etc.) and to other superconducting materials. By placing the heat sinks at or in the vicinity of the regions of reduced critical current density of such devices, these regions will experience a higher temperature reduction, therefore achieving an overall larger critical current density and a consequent reduction of the AC losses.

(78) Round Conductors

(79) The above examples deal with superconductors in the form of tapes and with superconducting devices produced from such tapes. However, the principle of the compensation of the local critical current I.sub.c reduction due to the magnetic field by a local variation of the amount or composition of superconducting material or by a local variation of the temperature may be applied to other types of superconductors, for example to round conductors or wires. In this way, large magnets assembled from such conductors can be optimized to reduce their mass and volume and/or to increase their critical current and/or to reduce their AC losses.

(80) FIG. 18 shows an exemplary superconducting coil 90 assembled from a round superconductor wire 910, wherein a conventional coil A is shown on the left and an optimized coil B according to an example of the invention on the right. Further shown in FIG. 18 is the magnetic flux density in the superconducting coil (upper half plane of axisymmetric representation). The labels next to the contour lines are the corresponding values (in Tesla) of the amplitude of the magnetic flux density.

(81) The windings of the conventional coil exhibit uniform cross-sections, i.e. wires of the same caliber are used. In the optimized coil B wires of two different calibers 910a and 910b are used. Both configurations produce the same magnetic field in the coil's axis. However, the optimized coil requires less superconducting material. Alternatively, it is possible to design the coil such that with the same amount of superconducting material a larger field is produced.

(82) By using wires of different calibers (diameters), instead of a wire with a single caliber for winding superconducting coils, it is possible to increase both the coil's critical current I.sub.c and the magnetic field while using the same amount of superconducting material. Further, it is also possible to match the critical current I.sub.c and the central magnetic field using less superconducting material. Still further, higher magnetic fields for the same mass and volume would be provided by denser packing in the region with thinner wire. The same applies to other types of superconducting devices, such as solenoids, toroids, etc.

(83) Below are simulation results obtained for various optimized superconducting devices.

EXAMPLE 1

(84) In a first example, a conventional double pancake coil made of 50 turns of superconducting tapes with inner radius of 5 cm was optimized by varying the local critical current. The coil was optimized by using a pair of M-shaped coils in a front to front array arrangement. The table below summarized the parameters of the original (conventional) coil and the optimized coil.

(85) TABLE-US-00001 Optimized coil using front-to-front Original (Conventional) coil M-shape coils arrangement I.sub.C(DC) = 65.11 A, I.sub.C(DC) = 79.24 A, central |B| = 0.118 T central |B| = 0.141 T I.sub.C(AC) = 71 A I.sub.C(AC) = 85 A AC losses at 71 A ---> 0.3047 AC losses at 71 A ---> 0.2202 J/cycle J/cycle AC losses at 77.12 A ---> 0.3013 J/cycle AC losses at 85 A ---> 0.4419 J/cycle

(86) FIG. 19 shows the magnetic field (in Tesla) for the original coils (FIG. 19A) constituting the double pancake coil and the M-shaped coils (FIG. 19B) at their respective critical currents I.sub.c(DC). Both configurations use the same amount of superconducting (HTS) tape. The overall critical current for the original coils is I=65.11 A, whereas the overall critical current for the optimized coils using M-shaped coils the overall critical current is I=79.24 A.

(87) FIG. 20 shows the normalized current density (J/J.sub.c(B)) in the tapes of the original, non-optimized coils (FIG. 20A) and the optimized M-shaped coils (FIGS. 20B and 20C) at peak value. The coil arrays shown in FIGS. 20A and 20B have a transport current of 71 A at 50 Hz. FIG. 20C shows the normalized current density (J/J.sub.c(B)) for the M-shaped coil with a transport current of 85 A at 50 Hz. The axis of the coil (not shown) is at the left of each the image. The solid black domains represent regions 184 of the turns in the coil where the current density has reached its critical value. The dashed domains represent regions 186 of the turns in the coil where the current density has not reached its critical value.

(88) By optimizing the spatial distribution of the amount of superconducting material, as in the above example, it is possible to achieve about 20% increase of coil's critical current I.sub.c for both DC and AC using the same amount of superconducting tape. Further, it is possible to achieve about 19% increase in the magnetic field in the coil's center using the same amount of superconducting tape, about 28% reduction of AC losses at the current transport of 71 A using the same amount of HTS tape and about 7-8% increase of current and field at matched AC losses using the same amount of HTS tape. Thus, AC losses, critical current and central magnetic field could also be matched using less superconducting tape.

EXAMPLE 2

(89) In a second example, a striated tape having 10 filaments was optimized. FIG. 21 shows simulation results for a non-optimized 4 mm wide tape having 10 filaments of equal width (FIGS. 21A and 21C) and for an optimized 4 mm wide tape having 10 filaments with a wider outer filament (FIGS. 21B and 21D).

(90) FIG. 21A to 21B[[a-b]] show the magnetic flux lines at peak value across the tape. A perpendicular magnetic flux density of 10 mT at 50 Hz is applied to both tapes. It is easy to note that in the optimized tape (FIG. 21B), the magnetic flux density in the gaps is lower than in the non-optimized tape (FIG. 21A). As discussed in detail above, this effect allows for reduced AC losses in the overall tape. Thus in the non-optimized tape the AC losses at 10 mT and 50 Hz are about 106.5 J/cycle, whereas in the case of optimized tape the AC losses at 10 mT and 50 Hz are about 97.6 J/cycle. Accordingly, in the optimized tape shown in FIG. 21B, it is possible to achieve about 8% reduction of AC losses for an applied magnetic flux density of 10 mT at 50 Hz using the same amount of HTS tape (4 mm wide) and same number of filaments (10).

(91) FIG. 21C to 21D [[c-d]] show the local cumulative AC losses over one cycle (perpendicularly applied field with amplitude of 10 mT at 50 Hz) for both a tape with filaments of uniform width (FIG. 21C) and for a tape with a wider outer filament (FIG. 21D). In both cases, the regions with the highest losses are the edges of the filaments. However, it is easy to note that the lossy region in the vicinity of the gaps is larger for the non-optimized tape than for the optimized one.

EXAMPLE 3

(92) As explained above, reduction of the critical current density Jc, due for example to the magnetic field, may be compensated with superconducting material or temperature optimization. In an example, a larger amount of superconducting material may be allocated in the regions where Jc is lower and this may be compensated by allowing a smaller amount of superconducting material in the region where Jc is higher. Alternatively or in addition, heat sinks may be located where Jc is lower. These techniques can also be used for round wires.

(93) In a third example, a coil is mass-optimized by using round wires having two different calibers. FIG. 22 shows simulation results of the magnetic field (in Tesla) of an original coil (FIG. 22A) and optimized coil (FIG. 22B) at their respective critical currents I.sub.c(DC). In both cases the coil is made of NbTi and has a 5 cm inner radius and 160 turns.

(94) The original coil is formed by a wire having constant diameter of 0.99 mm having cross-sectional area of 123.14 mm.sup.2. In this case, the critical current I.sub.c(DC) is 1016.4 A. The optimized coil is made of wires having two different wire diameters: a first wire diameter of 0.99 mm (80 turns) and a second wire diameter of 0.808 mm (80 turns). The conductors' cross-sectional area is 102.62 mm.sup.2. The critical current (DC) is 1012.7 A. Thus, the optimized coil uses 16.7% less material.

(95) Thus, by using just two different wire diameters, large magnets can be optimized to reduce mass and volume.

(96) Improvements for devices using wires of different calibers may also include: Increase of both coil's Ic and magnetic field using the same amount of superconducting material; Matched Ic and central magnetic field using less superconducting material; Higher magnetic fields for the same mass and volume would be provided by denser packing in the region with thinner wire.

(97) The proposed use of superconductors for various superconducting devices (such as coils, solenoids, toroids, cables, stack-like devices, etc.) with spatially varying amount and/or composition of superconducting material and/or with spatially varying temperature allows a significant performance increase in comparison to conventional designs. There are many specific applications for the proposed design when, for example, applied to coil winding including but not limited to magnets, coils, dipoles, quadrupoles, superconducting magnetic energy storage systems, current limiters, magnetic resonance devices (NMR, MRI, EPR, EMR, ESR and ICR), racetrack coils for generators and motors, coils for transformers, saddle-shape coils for accelerators, levitation and propulsion coils for magnetic levitated vehicles, magnetic separation devices, coils for split magnets, magnet coils for magnetization of permanent magnets and superconductors, magnet coils for characterization of samples, magnet coils for plasma confinement, coils for cyclotron, coils or coils-solenoid arrays for vector magnets, coils for magneto-optical systems, magnet coils for plasma diversion as in spacecraft communication systems, coils for magnetic propulsion of satellites (control of Hall effect thrusters). Similar applications exist for solenoid, toroid magnets, cables and stack-like devices. The invention is, however, not limited to the above examples: in principle any device employing superconductors may benefit from the invention.

(98) Above, various embodiments of the invention have been described. The invention may, however, be embodied in many different forms and should not be construed as limited to the exemplary embodiments describe above. For example, various features described in connection with different exemplary embodiments may be combined, unless otherwise indicated herein or otherwise clearly contradicted by context. Further, in the drawings, the size of individual elements and regions may be exaggerated for clarity. In addition, the number of turns, layers and/or filaments constituting the superconducting device may not correspond to the real number of turns, layers and/or filaments used.

LIST OF REFERENCE NUMERALS

(99) 10 rectangular superconducting tape 12 superconducting coil assembled from a rectangular superconducting tape 122 axis of the coil 14 M-shaped superconducting tape 14a-e areas of the M-shaped superconducting tape 16 tiling pattern 18 M-shaped superconducting coil 182 axis of the coil 184 areas of the coil where the current density has reached its critical value 186 areas of the coil where the current density is below its critical value 20 single layer superconducting solenoid 210 symmetry axis of a single layer superconducting solenoid 30 single layer superconducting toroid 302 centroid of the single layer superconducting toroid 40 multi-layer superconducting solenoid 410 symmetry axis of a multi-layer superconducting solenoid 50 multi-layer superconducting toroid 502 centroid of the multi-layer superconducting toroid 60 striated superconducting tape 602, 602a-c filament 70 superconducting tape having a superconducting layer of variable thickness along the lengthwise direction 70a part/area of the superconducting tape 70 where the superconducting layer is thin 70b part/area of the superconducting tape 70 where the superconducting layer is thick 71 superconducting layer of variable thickness along the lengthwise direction 72 area having doping optimized for a parallel magnetic field 74 area having doping optimized for a perpendicular magnetic field 80 stack of superconducting tapes 802 filaments 810-830 striated tapes 90 superconducting coil assembled from round superconductors 910 round superconductor wire 910a,b round superconducting wires having different calibers