Low loss superconductor cable

Abstract

A superconductor cable 602 comprises a plurality of filaments 602A-Cextending between opposite ends of the cable and electrically insulated from one another along their lengths. The filaments are arra

Description

Field of the Invention 5 The present invention relates to multi-filament superconductor cables, particularly multifilament high temperature superconductor (HTS) cables. Background 10 Superconducting materials are typically divided into “high temperature superconductors” (HTS) and “low temperature superconductors” (LTS). LTS materials, such as Nb and NbTi, are metals or metal alloys whose superconductivity can be described by BCS theory. All low temperature superconductors have a self-field critical temperature (the temperature above which the material cannot be superconducting, even in zero magnetic LD 15 field) below about 30 K. By contrast, the behaviour of HTS material is not described by C\l BCS theory, and such materials may have critical temperatures above about 30 K (though it should be noted that it is the physical differences in composition and superconducting operation, rather than the critical temperature, which define HTS and LTS materials). The most commonly used HTS are “cuprate superconductors” -20 ceramics based on cuprates (compounds containing a copper oxide group), such as BSCCO (Bismuth strontium calcium copper oxide), or ReBCO (Rare-earth barium copper oxide, where Re is a rare earth element, commonly Y or Gd). Other HTS materials include iron pnictides (e.g. FeAs and FeSe) and magnesium diboride (MgB2). 25 ReBCO superconductors are typically manufactured as tapes approximately 100 microns thick and with a width of between 2mm and 12mm. The structure of a typical tape is illustrated in Figure 1 and includes a substrate 101 (typically an electropolished nickel-molybdenum alloy, e.g., Hastelloy™ approximately 50 microns thick), on which is deposited a series of buffer layers known as the buffer stack 102, of approximate 30 thickness 0.2 microns. An epitaxial ReBCO-HTS layer 103 overlays the buffer stack, and is typically 1 micron thick. A 1-2 micron silver layer 104 is deposited on the HTS layer, and a copper stabilizer layer 105 is deposited on and often completely encapsulates the tape. The silver layer 104 and copper stabilizer layer 105 are deposited on the sides of the tape 100 and the substrate 101 too (not illustrated in Figure 1 for clarity), so that 35 these layers extend continuously around the perimeter of the tape 100, thereby allowing an electrical connection to be made to the ReBCO-HTS layer 103 from either face of the tape 100. These layers 104, 105 may therefore also be referred to as “cladding”. The silver layer 104 makes a low resistivity electrical interface to the ReBCO layer 103, whilst the copper layer 105 enables external connections to be made to the tape (e.g. by 5 soldering) and provides a parallel conductive path for electrical stabilisation. 10 15 25 30 35 “Exfoliated” HTS tape can be manufactured, which lacks a substrate and buffer stack, but typically has a “surrounding coating” of silver. Tape which has a substrate will be referred to as “substrated” HTS tape. An HTS cable comprises one or more HTS tapes, which are connected along their length via conductive material (normally copper). The HTS tapes may be stacked (i.e. arranged such that the HTS layers are parallel), or they may have some other arrangement of tapes, which may vary along the length of the cable. When describing coils in this document, the following terms will be used: • “HTS cable” - a cable comprising one or more HTS tapes. In this definition, a single HTS tape is an HTS cable. • “turn” (or “winding”) - a section of HTS cable within a coil which encloses the inside of the coil (i.e. which can be modelled as a complete loop). • “arc” - a continuous length of the coil which is less than the whole field coil • “critical current” - the current at which the HTS would become normal, for a given temperature and external magnetic field. HTS is considered “become normal” at a characteristic point of the superconducting transition, where the tape generates a critical electric field of Eo volts per metre. The choice of Eo is to some extent arbitrary, but is usually taken to be 10 or 100 microvolts per metre. • “critical temperature” - the temperature, Tc, at which the HTS would become normal, at a given magnetic field and current (strictly, the term “critical temperature” is formally defined for zero magnetic field, but the term is used more generally herein for convenience). • “peak critical temperature” - the temperature at which the HTS would become normal given no external magnetic field, and negligible current. • “generation temperature” (or “current-sharing temperature”) - the temperature at which the HTS material generates heat because it is unable to fully carry the current flowing through it. Typical generation temperatures of around 35 K are found for ReBCO material in an HTS field coil in which the current is around 80% of the critical current (lc) and the magnetic field strength is around 20 T. A superconducting magnet is formed by arranging HTS cables (or individual HTS tapes) into coils, either by winding the HTS cables or by providing sections of the coil made from HTS cables and joining them together. HTS coils come in three broad classes: • Insulated, having electrically insulating material between the turns (so that current can flow only in a “spiral path” through the HTS cables, i.e. around the turns). • Non-insulated, where the turns are connected radially, as well as along the cables (e.g. by connecting the copper stabilising layers of the HTS cables). • Partially insulated, where the turns are connected radially with a controlled resistance, either by the use of materials with a high resistance (e.g. compared to copper), or by providing intermittent insulation between the coils. Non-insulated coils can also be considered as the low-resistance case of partially insulated coils. Partially insulated field coils are described in WO2019150123, for example. Wound coils, as shown in Figure 2, are manufactured by wrapping an HTS cable 201 around a former 202 in a continuous spiral. Sectional coils, as shown schematically in Figure 3, are composed of several sections 301, each of which may contain several cables or preformed busbars 311 and will form an arc of the overall coil. The sections are connected by joints 302 to form the complete coil. While the turns of the coils in figures 2 and 3 are shown spaced apart for clarity, there will generally be material connecting the turns of the coil, e.g. they may be consolidated by potting with a suitable material such as an epoxy. Figure 4 shows an HTS tape 400 (in this case a ReBCO tape), illustrating an x,y,z orthogonal coordinate system which will be used in this document. The y axis is along the length of the tape (i.e. in the direction of the current when the tape is in use), the x axis is across the width of the tape, the z axis is through the thickness of the tape (i.e. normal to the plane of the tape). Figure 5 shows a cross section of an exemplary HTS tape in the x / z plane. The tape is shown in simplified form with an HTS layer 501, a copper cladding 502, and a substrate 503. The crystal structure of ReBCO has three orthogonal principal axes, referred to in the art as a, b, and c. In Figure 5 the a / b plane of the ReBCO layer 501 is shown as a single line 510, perpendicular to the c-axis 520. The critical current of the tape (as well as the generation temperature) depends on the ReBCO crystal thickness and quality, temperature and the magnitude of an external magnetic field, and the orientation of the magnetic field with respect to the c-axis. Typically, when the applied magnetic field vector lies in the a / b plane 510 the critical current is considerably higher than when the applied magnetic field vector is aligned along the c-axis 520, with a smooth variation between these two extremes. In practice, there may be more than one angle at which critical current shows a peak, variation with temperature and magnetic field, and / or variation within the a / b plane but, in a simple analysis, we can consider a tape with a single dominant peak that defines the optimum orientation of the applied magnetic (B) field that gives maximum critical current. ReBCO tapes are normally manufactured so that the c-axis is as close to perpendicular to the plane of the tape as possible (i.e.to be parallel to the z-axis), such that the critical current is maximised when an applied magnetic field is parallel to the plane of the tape. Direct current (DC) power losses in a superconducting material are generally negligible as the DC resistance of the superconducting state is zero. However, power losses are still possible when a superconducting material experiences time-varying magnetic fields or time-varying electric fields. These losses are sometimes referred to as “AC losses” but, as they can be caused by any dynamic or transient changes in magnetic or electric fields, they are referred to herein as “time-varying field losses”. Such losses are a significant issue for superconducting materials because they generate heat, which may raise the temperature of the superconducting material above its current-sharing temperature. Above the current-sharing temperature, current is forced to flow from superconducting regions of the material into neighbouring normal conductive material. Resistive heating of the normal conductive material may then cause hotspots in a superconducting magnet where the temperature increases dramatically. In such cases, the magnet needs to be rapidly warmed or “quenched” to avoid damage. Even small amounts of power generated by time-varying field losses may therefore be unacceptable for superconductor-based magnets. A number of mechanisms may contribute to time-varying field losses within a superconducting material. One type of time-varying field loss is termed “hysteresis loss”, which may occur when variations in the transport current flowing through the superconducting material, or changes in an applied magnetic field, induce a voltage which drives current loops (screening currents) in the superconducting material. Another type of time-varying field loss is termed “coupling loss”, which occurs when changing magnetic fields induce a voltage between two superconducting elements that drives current through a resistive interface or join between the two elements. Hysteretic losses depend on the area of superconducting material that can carry current loops. Since a typical HTS tape has a width of several millimetres, and a consequentially large area, hysteretic losses are a significant factor in HTS tapes experiencing a rapidly changing electric or magnetic field, such as when ramping up an HTS field coil. Using narrower pieces of HTS tape trivially reduces the cross-sectional area but reduces the tape’s current carrying capacity. A coil wound from narrower tape cannot generate as strong a magnetic field. Forming an equivalent strength magnet typically requires joining multiple coils via resistive interfaces, which increases coupling losses. A piece of HTS tape can be striated along its length to create multiple filaments connected in parallel with one another, but striated tapes typically have high coupling losses between filaments. Cables can also be twisted or created by winding HTS tapes helically around a core, which reduces the effective area over which currents can be induced by a changing magnetic field. One type of twisted cable is “Conductor on Round Core” (CORC®) cable. Twisting a cable again limits the current carrying capacity of the cable because unfavourable orientations between the c-axis of the superconducting material and applied magnetic fields are generated. What is needed is a superconducting cable or other current-carrying assembly, particularly a cable made from HTS tapes, that reduces both hysteretic losses and coupling losses (i.e., time-varying field losses) without sacrificing current-carrying capacity. Summary According to a first aspect of the present invention there is provided a superconductor magnet wound from a cable, the cable comprising a plurality of sub-cables extending between opposite ends of the cable and electrically insulated from one another along their lengths. The sub-cables are arranged in parallel with one another to provide respective alternative paths for electric current to flow between the ends of the cable. Each sub-cable includes a superconductor element comprising a stack of high temperature superconductor (HTS) tapes, each tape comprising, each tape comprising HTS material arranged to conduct electrical current along the sub-cable and at least one resistor connected in series with the superconductor element. The HTS tapes in each sub-cable are untwisted and are substantially aligned with a magnetic field generated in use of the superconductor magnet. In use, induced electrical currents that flow between pairs of the sub-cables when the cable is used in an electrical circuit can be suppressed. The magnet is configured such that a current induced to flow through the cable between any two of the sub-cables (i.e. from one sub-cable to another sub-cable within the cable) is required to flow through the resistors of the two sub-cables, i.e. there is no conductive loop or closed path in the cable that comprises the two sub-cables and that does not pass through two or more of the resistors. Thus, coupling currents between the subcables can be suppressed, leading to less heating of the sub-cables and more stable operation of the superconductor elements. For example, screening currents may generally be isolated to each sub-cable individually. Compared to a cable of an equivalent width having a single sub-cable, the total amount of time-varying field losses (i.e. coupling and hysteretic losses) in the superconductor cable of the present disclosure may be reduced by a factor that is equal to, or proportional to, the number of filaments in the cable, e.g. for a certain amount of heating, P (in Watts), the total amount of heating in a multi-sub-cable cable having n sub-cables may be reduced to around P / n. In general, a sub-cable is a conductive pathway that allows electric current to pass from one end of a cable to the other end of the cable. A single power supply may be used to supply electric current to all the sub-cables simultaneously. Each of the sub-cables may be substantially equivalent, such that the electric current divides substantially equally between them. The superconductor material is HTS material. Each sub-cable may comprise at least two resistors connected in series with the superconductor element and arranged at opposite ends of the cable. This arrangement may allow heat to be dissipated from both ends of the cable, thereby reducing (e.g. halving) the cooling power that needs to be supplied to any one end of the cable. Each resistor may be spaced apart from the corresponding superconductor element and electrically connected to the superconductor element by a current lead. This arrangement reduces the thermal load on the superconductor elements and facilitates cooling of the resistors separately from the superconductor elements. To increase the proportion of power dissipated in the resistor, the resistor may have or may be configurable to have a resistance that is significantly greater than a resistance of the current lead. In some implementations, the resistor may have a resistance of from 0.1 to 100 milliohms, or from 1 to 10 milliohms. The current leads may have a cross sectional area that is greater than a cross sectional area of the superconductor element e.g. the current leads may have a diameter that is greater than a diameter of the superconductor element. The superconductor cable may further comprise a cooling mechanism, such as a cryostat, for maintaining a portion of the cable comprising the superconductor material at a temperature below a superconductor transition temperature of the superconductor material whilst one or more of the resistors remains at a temperature above the temperature of the superconductor material. This arrangement has the advantage that at least some coupling currents can be dissipated in the resistors at a higher temperature (using another cooling mechanism, e.g. a liquid nitrogen or water cooling mechanism), rather than at or below the superconductor transition temperature, thereby reducing the heat load on the cooling mechanism used to keep the superconductor material in a superconducting state. For example, the superconductor material may be maintained at a temperature of around 20 K (or below), whilst the resistors are maintained at a temperature of around 77 K (which is attainable with liquid nitrogen cooling), or room temperature, e.g. 300 K (or more). Each superconductor element may be untwisted, such that it does not follow a spiral or helical path within the cable (although the cable itself may bend or it may be wound around an axis, e.g. to form a coil). For example, where the superconductor material is arranged in a layer, the orientation of the layer may remain substantially constant with respect to other parts of the cable, e.g. when cross sections through the cable are taken at any two points along its length, a vector normal to the layer in a first of the cross sections may be substantially parallel to a vector normal to the layer in a second of the cross sections. Having the superconductor elements untwisted means that the superconductor elements may have a constant (or nearly constant) orientation with respect to a magnetic field. In particular, in use, each superconductor element may be arranged such that one or more principal crystal axes of the superconductor material may have orientations with respect to a magnetic field that remain at least approximately constant (i.e. differ by less than a predetermined absolute or relative amount) along the length of the superconductor element. For example, the superconductor elements may be wound into a coil (e.g. a solenoid or pancake coil) such that a principal crystal axis of the superconductor material is oriented perpendicular to the windings, e.g. where the windings are about an axis of the coil, the principal crystal axis may be oriented radially with respect to the coil axis. In the case of the superconductor material being ReBCO, such orientations may allow the field vector of the magnetic field generated by the coil to lie (at least predominantly) in the a / b plane of the superconductor material to obtain an optimal (or near optimal) maximum critical current. By contrast, for superconductor cables in which the sub-cables are twisted (about one another and / or individually twisted), the orientation of the superconductor material varies along the length of the cable, which may reduce the critical current of the superconductor material as a result of the material’s anisotropic critical current dependence on the angle between the principal crystal axis and the magnetic field. Thus, the superconductor material in the present superconductor cable may be operated at higher currents compared to superconductor material in cables in which the sub-cables are twisted. In some other implementations, the superconductor elements may be twisted about one another, or individually twisted about themselves, to further reduce losses. The superconductor elements may have any twist pitch length appropriate for the materials used, e.g. the twist pitch length may be from 2 to 10 times a width of the elongate elements in a direction transverse to their length. The twist pitch length refers to a length measured along the cable (i.e. longitudinally with respect to the cable) over which the sub-cables make a complete revolution about each another, i.e. the distance over which the relative orientations of the sub-cables repeats. For some applications, it may be preferable to have relatively long twist pitch lengths to avoid issues with tightly twisting the superconductor elements, e.g. a twist pitch length greater than 5 times, or greater than 10 times, or greater than 100 times, a width of the elongate elements in a direction 5 transverse to their length. In some examples, the twist pitch length may be in a range from 10 to 1000, from 50 to 100, or from 500 or 1000 times the widths of the elongate elements. Such cables may be easier to manufacture and / or have less strain compared to more tightly twisted cables. In addition, the superconductor elements may be twisted about one another for only a fraction (e.g. less than 10%, less than 20% or less than 10 50%) of the twist pitch length, such that the superconductor elements may have a constant orientation with respect to an applied magnetic field for the remainder of the twist pitch length, i.e. the superconductor elements may be untwisted about one another for more than 90%, more than 80% or more than 50% of their length. 15 25 The sub-cables may be electrically insulated from one another along their lengths by electrical insulator material (such as a polyimide film, epoxy resin or a suitable potting or encapsulation compound) provided between the sub-cables. One or more (e.g. each) of the sub-cables may comprise a diode configured to allow current to flow preferentially through the sub-cable in one direction only. Each diode limits a “backflow” of current through the sub-cable, further reducing the magnitude of coupling currents flowing between the sub-cables and reducing total power losses due to such currents in the cable. For implementations in which two or more of the subcables comprise diodes, the direction in which current flows preferentially through the diodes is preferably the same for each of the sub-cables. Each superconductor element may comprise a respective one or more superconductor tapes or superconductor wires arranged in series or parallel, e.g. each superconductor element may be part of a separate tape or wire. The superconductor tapes may be 30 arranged in a stack, for example. The superconductor element may itself be referred to as a superconductor cable or sub-cable. As one example, each of the superconductor elements may form at least a portion of one or more windings of a superconductor coil. For example, the coil may be formed by 35 winding the superconductor elements about an axis. As noted above, the superconductor elements are untwisted about one another, which may allow, for example, the superconductor material (particularly HTS material) to be aligned with respect to a magnetic field generated by the coil (e.g. a solenoidal magnetic field) to optimise the critical current of the superconductor material and / or limit the amount of 5 hysteresis loss (which may be produced by magnetic field components perpendicular to the ab-plane in ReBCO, for example). 10 15 One or more (e.g. each) of the resistors may be a variable resistor. The variable resistor(s) may be used to adjust the resistance of the filament(s) to control the magnitude of coupling currents that can flow between them. For example, the resistance of each of the sub-cables may be increased to decrease the magnitude of coupling currents as the current through the cable is increased. The resistance of each of the subcables may be subsequently decreased once steady-state current flow through the cable has been attained. Alternatively or additionally, the variable resistor(s) may be used to direct electric current preferentially to filaments that are at substantially the same voltage as one another, such that the magnitude of any coupling currents flowing between these sub-cables is small. The variable resistor(s) may also be used to reduce the total current flowing through a sub-cable that is damaged and / or under-performing (e.g. has a lower critical current) and thereby divert current through filaments that are undamaged and / or performing satisfactorily. In some implementations, the resistance of the variable resistor(s) may be adjusted according to a measured parameter of one or more of the sub-cables, e.g. a critical current or temperature. The magnet may comprise a plurality of turns or windings of the cable about an axis. 25 The coil may, for example, be a solenoid or a pancake coil (in which windings or turns of the coil are nested radially). In some implementations, each of the resistors is a variable resistor. The superconductor magnet can further comprise a controller for adjusting the resistance of 30 each of the variable resistors. The controller may be configured to measure respective voltages of and / or currents flowing through the sub-cables and to adjust the resistance of one or more of the variable resistors in response to a voltage and / or current difference measured between two of more of the sub-cables. The superconductor magnet may comprise an adjustable power supply connected across the superconductor magnet, the controller being configured to adjust a voltage applied by the power supply, and / or a current supplied by the power supply, in response to the resistances of the variable resistors being adjusted. For example, the voltage may be increased according to the total resistance of the cable in order to maintain a constant total current flowing through the cable. Also described herein is a method of operating a superconductor magnet according to the first aspect above. The method comprises applying a voltage difference across the cable to drive electrical current therethrough, i.e. from one end of the cable to the other end. The method further comprises adjusting the resistance of one or more of the variable resistors as a function of at least one or more of: time after applying the voltage difference across the cable, the electrical current flowing through the superconductor cable or the electrical current flowing through one or more of the sub-cables, a magnetic field generated by the cable, and / or a voltage difference across the cable or across pairs of sub-cables. Adjusting the resistance of one or more of the variable resistors may comprise decreasing the resistance of the one or more variable resistors after the electrical current flowing through the cable and / or the magnetic field generated by the cable has reached a steady state (e.g. has reached a value that is within a predetermined range of a target value or has reached a state where variations in the value are less than a predetermined fraction of the value).. Adjusting the resistance of one or more of the variable resistors may comprise adjusting the resistance of the one or more variable resistors to divert current preferentially through one or more of thesub-cables. For example, current may be diverted away from filaments for which coupling losses are significant (e.g. as determined by the voltages of thesub-cables) and through sub-cables for which coupling losses are smaller. Also described herein is a current-carrying assembly comprising a plurality of sub-cables, the sub-cables being electrically connected or connectable in parallel with one another via shared connections at opposite ends of the current-carrying assembly and otherwise being electrically insulated from one another, each sub-cable comprising: a superconductor portion comprising superconductor material; and a resistance in series with the superconductor portion; whereby an induced electrical current that flows, or would flow, between sub-cables via the connections when the sub-cables experience a time-varying electromagnetic field in use flows through at least one resistance of a subcable. 5 Optionally, the superconductor portion comprises at least one tape or flat wire, and the respective superconductor portions of the sub-cables are arranged adjacent each other such that respective planes of the or each tape of each sub-cable are substantially parallel or aligned with each other at each point along a length of the current-carrying 10 assembly. In other words, the tapes are parallel when viewed in cross-section through any given plane perpendicular to a tangent of the current-carrying arrangement at that point. 15 Brief description of the drawings Figure 1 is a schematic representation of an HTS tape; Figure 2 is a schematic representation of a wound HTS coil; Figure 3 is a schematic representation of a sectional HTS coil; Figure 4 is a diagram showing a coordinate system for describing ReBCO tape; Figure 5 is a transverse cross section of a ReBCO tape, showing the principal axes of the ReBCO crystal; Figure 6 is a schematic circuit diagram showing an embodiment of the present invention; Figure 7 is a schematic circuit diagram showing another embodiment of the present invention; and 25 Figure 8 is a schematic cross section view of a plurality of superconductor elements arranged in a cable. Description of Embodiments 30 Embodiments of the present invention reduce hysteretic losses in a superconductor cable by arranging superconductor material as a plurality of filaments (sub-cables). This arrangement reduces the available area of the superconductor material within which screening currents can form compared to a full width cable. Coupling currents between the filaments are suppressed by electrically insulating the filaments from one another 35 along their length. The filaments are electrically connected in parallel with one another 10 15 and loop currents (with associated losses) may still occur between pairs of filaments via their shared connections. These loop currents are suppressed by introducing a resistor into each filament, such that any losses occur substantially only in the resistor. 25 30 Overall, embodiments of the present invention significantly reduce coupling between filaments and isolate screening currents to occur within (narrow) filaments rather than across a full width cable. Reducing time-varying field losses in this way may allow other (potentially disadvantageous) ways of reducing this type of loss, such as twisting of the filaments, to be avoided. Embodiments of the present invention therefore reduce or avoid the trade-off between hysteretic losses and coupling currents in existing multifilament superconductor cables. The present approach is particularly suitable for HTS superconductor materials in the form of tapes (or flat wires) since the tapes can be aligned with a magnetic field direction generated by a field coil wound from the cable to minimise reductions in critical current caused by unfavourable orientations. Figure 6 shows a circuit comprising a superconductor cable 602 having a plurality of filaments 602A-C electrically connected in parallel between the two ends of the cable 602. A power supply is connected across the two ends of the cable 602 to drive electric current through each of the filaments 602A-C. Each filament 602A-C is electrically insulated from the other filaments along its length, such that any electric current flow between filaments, caused by a potential difference between them, necessarily flows through the ends of the of the cable 602, where the filaments are connected, rather than through any intermediate part of the cable 602 located between the ends of the cable 602. Each filament 602A-C may be considered as (or comprising) a sub-cable, and the plurality of filaments or sub-cables together form the cable or, generally, a currentcarrying assembly. The cable 602 illustrated in Figure 6 has three filaments 602A-C, but in general the cable 602 may have any integer number of filaments greater than or equal to two, e.g. 2, 5, 10, 12 or 20 filaments. In some cases, each of the filaments may experience essentially the same rate of change of magnetic field (dB / dt), such that the voltage differences across the cables are expected to be small. In the absence of the resistors, even such small voltage differences may induce large currents to flow between the filaments. However, in the circuit of Figure 6, these currents are limited by the resistors in the filaments, thereby reducing resulting power losses. Each filament comprises a respective plurality of components connected in series, the components comprising (in order, from left to right in the figure) a first resistor 606, a first current lead 608, a superconductor element 610, a second current lead 612 and a second resistor 614. The first and second current leads 608, 612 may comprise normal conductor material, e.g. copper wire, or superconducting material however, in general, any form of electrical conductor may be used, e.g. superconductor wires. The superconductor elements 610 each comprise superconductor material, i.e. HTS material (such as ReBCO) or LTS material, in the form an elongate body, such as a wire or tape. In the superconductor cable 602 of Figure 6, the superconductor elements 610 each comprise a single superconductor tape, although each superconductor element 610 may alternatively comprise a plurality of superconductor tapes connected in parallel or in series with one another (or in some combination of series and parallel arrangements). Each superconductor element 610 may be arranged as a stack of superconductor tapes, for example. The resistors are configured to reduce the magnitude of coupling currents that flow between pairs of the filaments 602A-C as a result of a voltage difference between the filaments 602A-C. An example of such a coupling current is illustrated in Figure 6 by the dashed arrows provided adjacent to two of the filaments 602A-B. The coupling current flows in a closed loop spanning the lengths of the filaments 602A-B and passing through each of the resistors 606, 614 at either end of each of the filaments 602A-B. The inclusion of the resistors 606, 614 in the superconductor cable 602 limits the magnitude of the coupling currents that can flow for a given voltage difference between the filaments 602A-B. The resistance of each resistor 606, 614 is preferably greater than the resistance of each of the current leads 608, 612, such that heating resulting from the coupling current occurs predominantly in the resistors 606, 614, rather than the current leads 608, 612. The resistance of each resistor 606, 614 is also preferably chosen or adjusted so that a supplied current splits substantially equally between the filaments 602A-C. Conveniently, for example, each resistance is substantially equal, all other elements of each filament 602A-C being substantially identical. More generally, the total resistance of each filament 602A-C is substantially the same to achieve an even current split between filaments (although this is not essential). The values of the resistances are chosen at least in part according to a desired power dissipation in use, and may typically be in the range from 0.1 to 100 milliohms, for example. The superconductor elements 610 are placed in a desired arrangement to form a superconducting part 616 of the cable 602. The superconducting part 616 may be arranged as a magnetic field coil wound from adjacent filaments 602A-C, for example. 5 The field coil may be wound in the form of a pancake coil, a solenoid, or any other suitable arrangement Alternatively, each filament 602A-C may be wound into a separate field coil (e.g., a pancake coil) and the field coils arranged adjacent each other to form a composite magnet. 10 15 Where the superconductor elements 610 each comprise one or more substantially flat tapes, they may be arranged adjacent each other such that the tapes are all substantially aligned, lying in substantially the same plane, at each point along the length of the superconducting part 616. The individual tapes, and / or the a / b planes of each tape, can all therefore be substantially aligned with a magnetic field generated by a field coil wound from the cable. For example, in a pancake coil the vectors normal to the tapes can all lie in the plane of the coil or, in a straight solenoid, the vectors normal to the tapes can all be perpendicular to the solenoid’s axis. Additionally, the superconducting part 616 can have a desired width formed by a plurality of filaments 602A-C placed side-by-side. The resulting arrangement will have a current density similar to an equivalent full-width cable but with hysteretic losses reduced by a factor approximately equal to the number of filaments. Embodiments of the present invention therefore provide a cable in which filaments can 25 be substantially untwisted along their length relative to a magnetic field direction This enables the superconductor material in each filament to have a greater critical current and hence to be operated at higher transport currents than in twisted tape cables, enabling the generation of stronger magnetic fields. Simultaneously, time-varying field losses are reduced compared to a non-filamentary cable having the same or an 30 equivalent width such that a cable embodying the present invention can be used in a magnet that is intended to be ramped up or down rapidly, or will otherwise be subjected to changing electromagnetic fields. In use, the superconductor elements 610 are located within a cryogenically cooled region 35 618 such as within a cryostat (although other types of cooling system can be used) that maintains the superconductor material at a temperature below a superconductor transition temperature of the superconductor material (e.g. around 20 K for some HTS materials). The resistors 606, 614 may be located outside of the cryostat or within a higher temperature region of the cryostat to reduce the heat load on the cryostat resulting from the power dissipated within the resistors 606, 614. For example, the resistors 606, 614 may be located in a substantially room temperature region (or at least above 273 K) and cooled with water. In some implementations, some or all of the filaments 602A-C may comprise only a single resistor 606, 614. Alternatively, some or all of the filaments may comprise more than two resistors 606, 614, which advantageously causes heat to be more evenly between the resistors, reducing the cooling power required for each resistor. Figure 7 shows a circuit 700 that is largely the same as the circuit 600 of Figure 6, except that each filament of the superconductor cable 702 comprises a variable resistor 706 and a diode 714 (as opposed to the constant resistance resistors 606, 614). The circuit 700 also comprises a controller 720 that is configured to adjust the resistance of the variable resistors 706 in response to measured currents flowing through each of the filaments and / or measured voltages between or along the filaments. The controller may, for example, be a feedback controller (e.g. a proportional integral derivative, PID, controller). The controller 720 may, in some implementations, adjust the resistance of some or all of the variable resistors 706 to ensure that any voltage differences between or along the filaments remain at values below a predetermined maximum voltage difference. Additionally, the resistances of the variable resistors 706 may be reduced to (or near to) zero when the superconductor cable 702 is not subject to a time-varying magnetic field, e.g. when a field coil is being maintained in a steady state rather than being ramped up or down. The diodes 714 included in the filaments may further reduce coupling currents flowing between the filaments, although including diodes may require higher voltages to be generated by the power supply 604 to drive current through the cable 702. In some cases, diodes may be included in place of one or more of the resistors (e.g. in some cases each of the resistors may be replaced by one or more diodes). The voltage of the power supply 604 may be varied to allow the current flowing through the superconductor cable 602, 702 to be adjusted. For example, the voltage of the power supply 604 may be increased in response to the resistances of the variable resistors 714 being increased. In some cases, the controller 720 may be used to adjust the voltage of the power supply 604 to ensure that the total current flowing through the cable 702 remains constant (i.e. remains within a predefined target range). Figure 8 shows a cross section through a superconductor part 800 of a superconductor cable 602, 702 comprising a plurality of superconductor elements 802. Each superconductor element 802 comprises a supporting structure comprising a channel 804, that may be generally U-shaped, that houses a stack 806 of HTS tapes. The channel 804 may comprise copper and / or aluminium, for example, or another metal or be formed from a suitable material. The HTS tape may be ReBCO tape, for example. In some implementations, the channel 804 may comprise an insulating layer to electrically insulate the stack 806 of HTS tapes from the channel 804 and / or adjacent channels from each other. The depth of the channel 804 and the thickness of the stack 806 may be adjusted depending on the operating current and inductance required. In some examples, the channel 804 may provide a normal conductive path for electrical current in the event of the superconductor material becoming non-superconducting, e.g. in the event of a quench. The superconductor elements 802, with or without a channel 804 or other supporting structure, may be arranged in an array, e.g. a 2 by 6 array of superconductor elements 802 as illustrated in Figure 8, or any other suitable arrangement. The superconductor elements 802 may be spaced apart from one another, with the spaces between the elements filled with an insulator material such as an epoxy resin. The insulator material may additionally provide structural support for the superconductor elements 802. The superconductor cables described above may be wound into a coil to manufacture a superconductor electromagnet. Such electromagnets may be used in many different applications, including superconductor magnetic energy storage (SMES, e.g. for electrical power grid stabilisation), plasma confinement and control such as in a tokamak or stellarator, magnetic resonance imaging (MRI) and / or NMR spectroscopy, hadron therapy, aerospace applications, included in aircraft, unmanned aerial vehicles, satellites, spacecraft, rocket-propelled vehicles and autonomous exploration vehicles.

Claims

1. A superconductor magnet wound from a cable, the cable comprising a plurality of sub-cables extending between opposite ends of the cable and electrically insulated 5 from one another along their lengths, the sub-cables being arranged in parallel with one another to provide respective alternative paths for electric current to flow between the ends of the cable,each sub-cable including a superconductor element comprising a stack of high temperature superconductor (HTS) tapes, each tape comprising HTS material, arranged 10 to conduct electrical current along the sub-cable and at least one resistor connected in series with the superconductor element;wherein the HTS tapes in each sub-cable are untwisted and are substantially aligned with a magnetic field generated in use of the superconductor magnet.LD 15 2. A superconductor magnet according to claim 1, wherein each sub-cableC\l comprises at least two resistors connected in series with the superconductor elementand arranged at opposite ends of the sub-cable.

3. A superconductor magnet according to claim 1 or 2, wherein each resistor is 20 connected in series with the corresponding superconductor element by a current lead extending between the resistor and one end of the superconductor element, the resistor having or being configurable to have a resistance that is greater than a resistance of the current lead.25 4. A superconductor magnet according to any one of the preceding claims, furthercomprising a cooling mechanism for maintaining the superconductor elements of each sub-cable at a temperature below a superconductor transition temperature of the HTS material whilst one or more of the resistors remains at a temperature above said superconductor transition temperature.

305. A superconductor cable according to any one of the preceding claims, wherein the superconductor elements are each elongate elements that extend parallel to one another.14 04 256. A superconductor magnet according to any one of the preceding claims, wherein one or more of the sub-cables comprises a diode.

7. A superconductor magnet according to any one of the preceding claims, wherein 5 one or more of the resistors is a variable resistor.

8. A superconductor magnet according to any one of the preceding claims , further comprising a controller configured to measure respective voltages of and / or currents flowing through the sub-cables and to adjust the resistance of one or more of the variable10 resistors in response to a voltage and / or current difference measured between two of more of the sub-cables.

9. A superconductor magnet according to claim 8, further comprising an adjustable power supply connected across the superconductor magnet, the controller being15 configured to adjust a voltage applied by the power supply, and / or a current supplied by the power supply, in response to the resistances of the variable resistors being adjusted.

10. The superconductor magnet of any one of the preceding claims, wherein each sub-cable is wound into a respective magnetic field coil, the magnetic field coils being20 arranged adjacent to one another and electrically insulated from one another to form the superconductor magnet.

11. The superconductor magnet of any one of the preceding claims wherein the superconductor magnet is a solenoid.25

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