Superconductor strand with plurality of twisted filaments

Abstract

There is presented a strand (252, 2052), wherein the strand is a superconductor strand, comprising a matrix (2060), a plurality of filaments (2056), such as at least 3 or at least 10 or at least 20 filaments, wherein each filament is a superconductor filament, and wherein each filament is encircled by matrix material, wherein each of the filaments comprises a biaxially textured superconductor material, such as a coated conductor, and wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 50 mm. There is furthermore presented a cable and a method.

Description

[0001] SUPERCONDUCTOR STRAND WITH PLURALITY OF TWISTED FILAMENTS

[0002] FIELD OF THE INVENTION

[0003] The present invention relates to a superconductor, and more particularly relates to a superconductor strand with a plurality of individually twisted filaments, and furthermore relates to a method of manufacture and use thereof.

[0004] BACKGROUND OF THE INVENTION

[0005] Superconductor structures may be seen as advantageous since they enable conducting electrical current, such as direct current, without resistive electrical losses. Superconductor structures, such as superconductor strands, are thus being used for several applications, such as power cables, electromagnets, generators and / or transformers. However, superconductor strands may exhibit high energy losses when used in alternating current (AC) applications. Furthermore, superconductor strands - and or superconductor filaments within a superconductor strand - may be affected by magnetic fields in an undesirable manner, both when carrying a DC or AC electrical current. Still further, superconductor strands may be vulnerable to serious damage in case a defect in one or more filaments in the strand occurs, e.g., because such defect might cause resistive heating due to quenching.

[0006] An improved superconductor strand would be desirable, such as a superconductor strand which enables reducing, minimizing, or eliminating losses when used in either direct current (DC) or alternating current (AC) applications, which enables reducing, minimizing, or eliminating an effect from magnetic fields or renders the effect less undesirable, and / or which enables reducing, minimizing, or eliminating a risk of serious damage in case of defects in, and / or quenching of, one or more filaments in the strand would be advantageous.

[0007] SUMMARY OF THE INVENTION

[0008] It may be seen as an object of the present invention to provide an improved superconductor strand, such as a superconductor strand, which enables reducing, minimizing, or eliminating losses when used in either direct current (DC) or alternating current (AC) applications, which enables reducing, minimizing, or eliminating an effect from magnetic fields or renders the effect less undesirable, and / or which enables reducing, minimizing, or eliminating a risk of serious damage in case of defects in, and / or quenching of, one or more filaments in the strand. It is a further object of the present invention to provide an alternative to the prior art. Thus, the above-described object and several other objects are intended to be obtained in a first aspect of the invention by providing a strand, wherein the strand is a superconductor strand, comprising : a. A matrix, b. A plurality of filaments, such as at least 3 or at least 10 or at least 20 filaments, wherein each filament is a superconductor filament, and wherein each filament is encircled by matrix material, wherein each of the filaments comprises a biaxially textured superconductor material, such as a coated conductor, such as an epitaxially grown superconducting layer, such as an anisotropic superconducting layer, such as a second-generation high temperature superconductor, such as a rare-earth barium copper oxide (REBCO) superconducting layer, such as a REBa2CusO7-x superconducting layer, where x =0-0.65, and where RE = Y, Gd, Nd or Eu, and wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 50 mm, such as less than 40 mm, such as less than 30 mm, such as less than 20 mm, such as less than 18 mm, such as less than 16 mm, such as less than 15 mm, such as less than 14 mm, such as less than 12, mm, such as less than 10 mm, such as less than 8 mm, such as less than 5 mm, such as less than 4 mm, such as less than 3 mm, such as less than 2 mm, such as less than 1 mm.

[0009] The invention may be particularly, but not exclusively, advantageous for providing a superconductor strand comprising a plurality of twisted filaments, which enables one or more of the above-mentioned advantages, and / or one or more of reducing, minimizing, or eliminating energy losses when used in alternating current (AC) applications, improving magnetic field stabilization, reducing magnetic field related forces, and / or enabling reducing, minimizing, or eliminating a risk of serious damage in case of defects in one or more filaments in the strand, and / or enabling decreasing the amount of required stabilizing (matrix) material per cross-sectional area of superconductor.

[0010] By providing superconducting elements in the form of filaments, AC losses may be reduced, and magnets may be stabilized, such as described in the peer-reviewed, academic review article "Multifilamentary coated conductors for ultra-high magnetic field applications", Anders Christian Wulff et a / ., Supercond. Sci. TechnoL 34 (2021) 053003, which is hereby incorporated by reference in entirety, and / or in the peer-reviewed, academic article "How filaments can reduce AC losses in HTS coated conductors: a review" by Grilli and Kario, Supercond. Sci. TechnoL 29 (2016) 083002, which is also incorporated by reference in its entirety.

[0011] Another possible advantage of forming superconducting filaments, such as narrow superconducting filaments, is that an effective capping or stabilization of the filament becomes possible, such as where the amount of capping, or stabilizing material, such as the fraction of stabilizing material, on the sides of the filament becomes significant or relatively larger (relative to a width of the filaments), e.g., in comparison to a wide flat tape typically with a width of several mm's, such as 2 to 12 mm (wherein 'width' may in this context be understood as a dimension orthogonal to a longitudinal direction, which is in plane with an interface between a superconducting material and a buffer or substrate, and / or as the largest dimension orthogonal to a longitudinal direction). By increasing the cross-sectional fraction of stabilizer material relative to the corresponding fraction of superconductor layer, a superconducting tape / wire structure, which has more stabilizing material per area of superconducting material may be provided, and may therefore be more tolerant towards quenching, such as local heating, such as local loss of superconducting properties. Adding stabilizing material (such as a material chosen from the group comprising silver, copper, nickel, tin, aluminum, zinc, niobium, phosphor, sulfur, germanium, chrome, molybdenum and / or bismuth), such as silver, or copper, to the first and second side of the superconducting material may increase thermal and electrical stability of the superconducting material (such as composite). Adding stabilizing material on the edges of a standard wide tape does not significantly increase the stabilizer fraction to superconductor material fraction for a wide tape, such as a 4 mm or 12 mm, wide tape. For example: For a narrower tape, such as 70 pm wide and 50 pm thick tape, 1 pm HTS layer, adding 10 pm of stabilizer material on all faces of the tape yields a ratio of stabilizer to HTS layer width of about 40, which is a factor of two (2) higher than that for a 12 mm wide and 50 pm thick tape with the same stabilizer layer thickness.

[0012] A possible advantage of 'torsionally twisting the filaments' is that it obviates any directional dependence of magnetic fields on the filament, such as obviates the critical current angular magnetic field dependence, by averaging out this directional dependence. The critical currents magnetic field angular dependence is understood as common in the art for coated conductors. In addition, twisting reduces any coupling currents between filaments which may occur when subjecting the strand to alternating current, or alternating magnetic fields, or changing the current, or changing a magnetic field. Coupling currents are electrical currents running through the matrix, which is electrically conducting, and thereby electrically connecting filaments. Coupling currents are understood as common in the art and as described in academic review article "Multifilamentary coated conductors for ultra-high magnetic field applications", Anders Christian Wulff et aL, Supercond. Sci. TechnoL 34 (2021) 053003.

[0013] Further, the individual twisting of filaments may improve mechanical flexibility of the filaments, such as reduce the intolerance of in-plane bending of coated conductors, allow the subsequent bending of strands bundled from filaments around smaller radii. The broad distribution of filament orientations means that in-plane bending, which may be detrimental to superconductor performance, may be reduced, cf., e.g., "Structural analysis of REBCO coated conductors and quasi-isotropic strands under bending using continuum shell element" X. Peng and H. Yong, Cryogenics 133 (2023) 103701.

[0014] By torsionally twisting with a short twist pitch the averaging out of the directional dependence on applied magnetic fields may occur on a shorter length. Further, coupling currents occur below a certain critical length, given partly by the frequency of the alternating current (AC), and / or the alternating magnetic field, and / or the perturbation of the current, and / or the perturbation of the magnetic field. Thus, shorter twist pitch allows for less AC-loss at a higher frequency, and / or higher magnetic field stability.

[0015] It may be seen as an insight of the present inventors, that by relying on (narrow or relatively narrow) filaments, it becomes practically feasible to reduce the torsional twist pitch without damaging the superconducting material in said filament. It may further be seen as an insight of the present inventors, that relying on (narrow or relatively narrow) filaments, such as twisted narrow filaments, it becomes practically possible to obtain transposition of said filaments, which has otherwise for coated conductors only been possible using the Roebel cable technology as described in the academic review article "Multifilamentary coated conductors for ultra-high magnetic field applications", Anders Christian Wulff et aL, Supercond. Sci. TechnoL 34 (2021) 053003.

[0016] By 'strand' is understood a multifilament structure, wherein a plurality of filaments, such as a plurality of substantially parallel filaments (such as being on average parallel, such as average directions deviating less than 10°, such as less than 1°, such as allowing that they are non-parallel locally), are arranged and held together in a solid matrix, such as held together, such as bundled together, such as bundled together in a solid matrix. Strand may additionally and / or alternatively be referred to as 'wire' (and strand and wire may be referred to interchangeably within the present application).

[0017] 'Superconductor' is understood as is common in the art, such as describing the capability to be 'superconducting' (e.g., during use), which is understood as is common in the art, such as the capability of an element or a material to conduct electrical current with substantially zero, such as zero, electrical resistance, optionally when cooled below a characteristic transition temperature. 'Superconducting' and 'superconductor' may be referred to interchangeably within the present application. The superconductor (material) may be epitaxially grown superconductor material. 'Matrix' is understood as is common in the art, such as an element in which something (such as the superconductor strands) is enclosed and / or embedded. The matrix may be monolithic (e.g., due to all filaments, such as in a bundle of filaments, being plated at the same time with matrix material, such as being cast with matrix material, such a being soldered together by matrix material, such as being sintered together by matrix material) or may comprise separate regions of matrix material, e.g., due to each filament being plated individual before being arranged in the strand.

[0018] By 'matrix material' is understood a material comprising, such as consisting of, a metallic material, which optionally geometrically connects each filament. An advantage of a matrix material may be thermal and electrical contact between filaments, possibly resulting in thermal stability reducing the risk of a quench, and electrical stability allowing for a shunt of the current. Further, the nature of a matrix will allow neighbouring filaments to share the intermediate thermally and electrically stabilising material, thus reducing the requirement on the volume of stabilising material for each filament. It may be seen as an insight of the present inventors, that relying on (narrow or relatively narrow) filaments, such as twisted narrow filaments, each filament will carry a smaller fraction of the total current carried. Thus, a quench of the superconducting material, due to impurities and / or defects and / or reduced critical current of the superconductor material, will have a smaller impact on the total strand.

[0019] In an embodiment the matrix material is Cu or an alloy of Cu, such as Cu and Zn (Brass) or Cu and Sn (Bronze), or Cu-Sn-Zn or Cu and Ag, or Cu and Ni, or Cu and Cr, or Cu and Al and / or Ti and / or Mg, or a combination thereof. The content of Cu in the alloy is at least 50%.

[0020] In an embodiment the matrix material is Sn or an alloy of Sn, such as an alloy with Ag, In, Ti, Mg, Zn, Cr, Al and / or Nb, or a combination thereof. The content of Sn in the alloy is at least 50%.

[0021] In an embodiment the matrix material may be Ni and its alloys, such as Ni and Cr, such as Ni and Al. In addition, it may also be a matrix material including In, Ti, Mg, Nb, S, P, Mo, Bi, and / or in combination with the above alloys or a combination thereof.

[0022] The matrix material may be comprised of any spatial combination of the above mentioned alloys. A 'filament' is understood as is common in the art, such as an optionally flexible elongated element, such as a solid elongated element. By ’elongated’ may be understood something having a larger dimension in a first direction (such as the direction referred to as the length direction), such as significantly longer, such as 2, 5, 10, 100, 1000, 10000 or 100000 times longer than the dimension in one or both of the other two directions (such as the directions referred to as width and height) orthogonal to the first direction. By ’solid element' may be understood an element comprising a solid phase, such as consisting of a solid phase.

[0023] By 'superconductor filament' may be understood a filament comprising, such as consisting of, coherent biaxially textured superconductor material and, if present, adjoining one or more buffer layers and / or a substrate. The 'superconductor filament' may thus be understood to comprise the biaxially textured superconducting material and optionally further material in the form of one or more buffer layers and / or a substrate if present, or only superconducting material if neither buffer layers(s) nor substrate is present (e.g., in case the one or more buffer layers and the substrate have been removed). The superconductor filament may thus in addition to the superconducting material for example furthermore comprise additional (possibly non-superconducting) material, such as a substrate and / or one or more buffer layers. In one example, a superconductor filament may comprise, such as consist of, superconductor material and one or more adjacent buffer layers and / or a substrate. In the case of a biaxially textured superconducting material where no substrate and no buffer layer is present and / or adjoining, the superconductor filament may in another example comprise, such as consist of, merely the superconducting material.

[0024] In another example, a superconductor filament may comprise, such as consist of, biaxially textured superconductor material and one or more adjoining buffer layer(s) and / or a substrate, where the one or more adjoining buffer layers is biaxially textured and wherein the substrate is optionally biaxially textured, such as a composite comprising a non-textured, such as a non-biaxially textured, substrate, where said non-biaxially textured substrate may be coated with one or more biaxially textured buffer layers.

[0025] By 'plurality of filaments' may be understood a number n of filaments being equal to or larger than 2, such as larger than 2, such as larger than 3, such as larger than 5, such as larger than 10, such as larger than 20, such as larger than 50, such as larger than 100, such as larger than 200, such as larger than 500, such as larger than 1000.

[0026] By 'each filament is encircled by matrix material' may be understood that each filament is encircled, such as completely encircled, such as encircled 360°, around an axis, such as a longitudinal axis of the filament.

[0027] 'Longitudinal (direction)' of an element may generally be understood as is common in the art, such as a lengthwise direction of the element, such as a direction along an axis (which may optionally be locally non-rectilinear), for which the element has the largest length from one end to the other. Additionally, or alternatively, in the context of current carrying elements, a longitudinal direction may be parallel with an average current direction during use (such as a direction of minimum resistivity). A (longitudinal) length may be understood to be the length along a longitudinal direction, such as the total length of a stretched out element. A 'longitudinal axis' is understood to be an axis of the element being parallel with a longitudinal direction.

[0028] 'Biaxially textured' is to be understood as is common in the art, such as a polycrystalline material, such as a material being characterised by a solid body consisting of multiple individual grains, wherein adjacent grains are separated by grain boundaries to form a single solid element and wherein the grains are substantially being aligned with a specific crystallographic orientation in two on each other perpendicular crystallographic directions. The orientational deviation is within less than 20°, such as the misorientation angle is less than 20°, such as deviating less than 20°, in two on each other perpendicular directions. Biaxial texturing may be achieved via epitaxial coating.

[0029] Additionally, or alternatively, to being biaxially textured, the superconductor material, such as the superconductor material of each filament, may be defined as second-generation (2G) High Temperature Superconductor (HTS).

[0030] Additionally, or alternatively, to being biaxially textured, the superconductor material, such as the superconductor material of each filament, may be defined as REBCO.

[0031] Additionally, or alternatively, to being biaxially textured, the superconductor material may be one or more or all of:

[0032] A coated conductor, an epitaxially grown superconducting layer, an anisotropic superconducting layer, a second generation high temperature superconductor, and / or a REBCO superconducting layer.

[0033] 'Superconductor material' is understood as is common in the art, such as describing the capability of the material to be 'superconducting' (e.g., during use), such as wherein 'superconducting material' is understood as is common in the art, such as in the context of 'superconducting' as described above in the preceding paragraph.

[0034] Each superconductor filament may comprise, such as consist of, superconducting material of a coated conductor (CC). 'Coated conductor' is understood as is common in the art, such as a superconductor, which has been manufactured by coating (superconducting) material on a substrate, such as to form a layer of superconductor material obtaining both in-plane and out-of plane texturing of the grains (biaxial alignment or biaxial texturing). The biaxial texturing may be seen as achievable via a coated conductor construction and / or via a coated conductor fabrication method.

[0035] The superconductor material, such as the superconductor material of each filament, may be high-temperature superconducting material.

[0036] 'High-temperature superconducting (HTS)' (or high-Tc) is understood as is common in the art, such as the capability of a material to be superconducting above a temperature of above 30 Kelvin, such above a temperature corresponding to the boiling point of liquid nitrogen, which is approximately 77 Kelvin.

[0037] 'Torsionally twisted' is understood as is common in the art, such as wherein a twist is larger than zero. Twist may be understood as is common in the art, such as described in the article 'Helical and Localised Buckling in Twisted Rods: A Unified Analysis of the Symmetric Case', G. H. M. van der Heijden and J. M. T. Thompson, Nonlinear Dynamics 21 : 71-99, 2000, which is hereby included by reference in entirety. For example, twist may be quantified by formula (39) in the above-mentioned reference by Heijden, et aL, more particularly in section 3 of said reference, which is hereby included by reference. For example, the twist Tw for a given filament or a part of a filament may be given by: wherein T is the (local) torsion TS, and ds is a spatial segment along the length of the filament or part of the filament.

[0038] By 'each of the filaments is torsionally twisted' may be understood that each of the filaments is torsionally twisted individually and / or with one or more other filaments. For example, in one embodiment each filament may be (optionally exclusively) individually twisted around its own axis. In another embodiment, each filament is twisted around its own axis and around another axis, such as a common axis for a plurality of filaments. 'Torsional twist pitch' is to be understood as is common in the art, such as the distance along the length of a twisted filament when the total angle of twist is 360°, such as the distance along a filament or a part of a filament for which a twist (Tw), e.g., as defined above, is 1. Twisting occurs when one end of a filament is held fixed and a torque, or moment of torsion, is applied at the other end of the filament, with the torque vector parallel to the length of the filament. The resulting twist angle is the magnitude of the torque divided by the torsional stiffness. The torsional stiffness being the shear modulus of the filament times the torsional constant, divided by the length of the filament parallel to the torque vector.

[0039] Twisting a filament introduces 'shear stress' within the filaments. The magnitude of the shear stress is maximum at a point in the filament furthest from the axis of twist. Shear stress may lead to a strain of the superconductor material resulting in changes to the critical current and / or the critical temperature of the superconductor. Further, shear stress may introduce defects and / or cracks in the superconductor material of the filaments if above a certain threshold value. This threshold value will depend on the specific properties of the superconductor material, and direction of the shear stress (tensile or compressive). In a specific example a threshold value of tensile shear stress has been observed to be 0.45 %, cf., "Effect of off-axis bending on microstructural and transport properties of coated conductor tape", R. Ries et al 2023 Supercond. Sci. TechnoL 36 014006.

[0040] Twisting a filament without constraining the ends in the longitudinal direction results in helical buckling, such as writhe, such as wrapping. The resulting structure will resemble a wrapping around a real or fictitious former or core. These may differ geometrically from the twisting of filaments due to substantial parts of the tapes being outside the axis of twisting.

[0041] By 'wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than a distance D' it is understood that said twist pitch can be anywhere in the filament. In embodiments the twist pitch is on average less than said distance D, when averaged along the full length of the filament.

[0042] It may be understood that the length along which torsional twist pitch is measured is along the filament axis (which may or may not be parallel with a strand axis).

[0043] Twisting is further described in Fig. 9 and the accompanying text in the peer-reviewed, academic review article "Multifilamentary coated conductors for ultra-high magnetic field applications", Anders Christian Wulff et a / ., Supercond. Sci. TechnoL 34 (2021) 053003, which is hereby incorporated by reference in entirety. The filaments may be twisted individually, in pairs or in bundles including more than two filaments. According to an embodiment, there is presented a strand wherein an aspect ratio of each filament in a cross-sectional plane orthogonal to a longitudinal axis of the filament is equal to or less than 100: 1, such as equal to or less than 75: 1, such as equal to or less than 50: 1, such as equal to or less than 25: 1, such as equal to or less than 20: 1, such as equal to or less than 10: 1, such as equal to or less than 5: 1, such as equal to or less than 2: 1.

[0044] 'Aspect ratio' may be understood as is common in the art, such as the largest ratio t / w or w / t of thickness t (with thickness optionally being measured in a direction orthogonal to a longitudinal direction and orthogonal to an interface between a superconducting coating and substrate) over width w (with width optionally being measured in a direction orthogonal to a longitudinal direction and orthogonal to a thickness direction and / or orthogonal to an interface between superconducting material and substrate material) of the filament. In case there is no substrate, an aspect ratio may be calculated as the ratio t / w of thickness t over width w of the smallest possible circumscribing rectangle.

[0045] It may be an advantage to have a relatively low ratio t / w of width over thickness, for example due to a low ratio rendering the integration of filaments into a superconducting structure simpler. Another possible advantage of a low aspect ratio may be that it facilitates torsionally twisting with a low torsional twist-pitch. Another possible advantage may be that it enables packing filaments tightly in both lateral dimensions (with lateral being orthogonal to longitudinal), which may in turn be beneficial for heat management and for guiding current around defects (e.g., due to current being able to go around a defect in two dimensions).

[0046] According to an embodiment, there is presented a strand wherein for each filament there exists a fictitious closed line in a cross-sectional plane orthogonal to a longitudinal axis of the strand, which line is entirely in matrix material and which line is encircling said filament, such as completely encircling, such as encircling around 360°, and wherein the other filaments within the plurality of filaments are outside of said closed line.

[0047] A possible advantage may be that matrix material is assigned to each filament. This may be beneficial for heat management and / or for having matrix material at each filament for the purposes of shunting.

[0048] In embodiments, the fictitious line may be drawn for each filament so that an area of matrix materials within the fictitious line is at least a factor of 0.1, such as at least a factor of 0.2, such as at least a factor of 0.5, such as at least a factor of 1.0 such as at least a factor of 2, such as at least a factor of 5, such as at least a factor of 10, times the area of the filament within the line. This may be beneficial for having sufficient matrix material at each filament. According to an embodiment, there is presented a strand wherein in a cross-sectional plane orthogonal to a longitudinal axis of the strand, geometrical centres of the filaments are distributed in both dimensions, such as wherein a maximum distance between geometrical centres of filaments in any direction is at least 10 %, such as at least 25 %, such as at least 50 %, such as at least 75 %, such as at least 90 % of a maximum distance between geometrical centres in the orthogonal direction.

[0049] This may be beneficial for enabling distributing matrix material between the filaments in an efficient manner (e.g., where more filaments may be close to the same areas of the matrix). Another possible advantage may be that it enables electrical current to go around a defect in two dimensions, which may in turn reduce a risk of overheating at a defect.

[0050] The 'longitudinal axis of the strand' may be understood as is common in the art, such as being parallel with a current carrying direction, such as an average or integrated current carrying direction, and / or being a direction along which the strand has it largest dimension.

[0051] The longitudinal axis of a filament may be understood as is common in the art, such as being parallel with a current carrying direction, such as an average or integrated current carrying direction, and / or being a direction along which the filament has it largest dimension.

[0052] According to an embodiment, there is presented a strand wherein the matrix comprises copper and / or tin, such as a copper alloy and / or a tin alloy, such as at least 50 % w / w copper and / or such as a least 50 % tin, such as consists of copper or consists of tin.

[0053] An advantage of copper may be that it is has good properties in terms of both heat and current conduction.

[0054] According to an embodiment, there is presented a strand wherein each filament comprises superconducting material, which comprises, such as consists of, rare-earth barium copper oxide. Rare-earth barium copper oxide (which may also be referred to as REBCO), such as REBa2Cu3O7-x, where x =0-0.65, and where RE = Y, Gd, Nd or Eu, may be advantageous for enabling forming a biaxially textured superconductor.

[0055] According to an embodiment, there is presented a strand wherein each filament has, such as in a cross-sectional plane orthogonal to a longitudinal direction of the filament, a largest dimension in a direction being orthogonal to a longitudinal direction of the filament, of less than 1 mm, such as less than 800 pm (micrometer), such as less than 750 pm, such as less than 600 pm, such as less than 500 pm, such as less than 400 pm, such as less than 300 pm, such as less than 250 pm, such as less than 200 pm, such as less than 150 pm, such as less than 100 pm, such as less than 80 pm, such as less than 60 pm, such as less than 50 pm, such as less than 40 pm, such as less than 30 pm, such as less than 25 pm, such as less than 20 pm, such as less than 10 pm.

[0056] An advantage of a relatively small width may be that it enables having multiple filamented superconductors in a superconducting structure, which may go to reduce or minimize the screening field magnitude for each filament and / or hysteresis energy losses (Qh). Another advantage is that mechanical bending, including twisting around the longitudinal axis of the filaments, becomes easier the narrower the filaments are. A possible advantage of twisting may in turn be that it enables transposition (such as transposition) with reduced, minimal or zero in-plane bending relative to in-plane bending for wider filaments (where in-plane bending may in general be disadvantageous, such as degrades the superconducting properties). Another possible advantage is that the fraction of metal capping per individual filament increases and thus increases the thermal stabilization. Another possible advantage is that smaller filaments reduce the amount of Joule heating in case of rupture / breakdown of a single filament.

[0057] A width of a filament may be understood to be a dimension, such as a largest dimension, in a direction orthogonal to a longitudinal direction of each filament and / or a direction being parallel with an interface between superconducting material and substrate material, if any.

[0058] According to an embodiment, there is presented a strand with a plurality of filaments wherein a width, such as a maximum dimension in a direction orthogonal to a longitudinal direction of each filament and optionally furthermore being parallel with an interface between superconducting material and substrate material, of each filament is equal to or more than 1 micrometer, such as equal to or more than 10 micrometer, such as equal to or more than 25 micrometer, such as equal to or more than 50 micrometer, such as equal to or more than 100 micrometer, such as equal to or more than 200 micrometer, such as equal to or more than 500 micrometer. A possible advantage is that this minimum width may be advantageous for overcoming an issue of grain size (of e.g., REBCO with grain sizes of ca. 50 nm) becoming comparable to the width. Another possible advantage may be that it allows dissipation of current into surrounding materials, such as a cupper matrix.

[0059] As mentioned above, a possible advantage of forming narrow superconducting filaments is that an effective capping or stabilization of the filament becomes possible, such as where the amount of capping, or stabilizing material, such as the fraction of stabilizing material, on the sides of the filament becomes significant or relatively larger (relative to a width of the filaments), e.g., in comparison to a wide flat tape typically with a width of several mm's, such as 2 to 12 mm. According to an embodiment, there is presented a strand wherein a length, such as a maximum dimension in a longitudinal direction of each filament, such as along the strand, is equal to or larger than 1 m, such as equal to or larger than 2 m, such as equal to or larger than 3 m, such as equal to or larger than 5 m, such as equal to or larger than 8, such as equal to or larger than 10 m, such as equal to or larger than 100 m, such as equal to or larger than 1 km, such as equal to or larger than 10 km, such as equal to or larger than 100 km, such as equal to or larger than 1000 km.

[0060] The length of each filament may be understood as the largest dimension of the filament. It may be understood, that the length is to be measured along the filament and / or for the configuration of the filament wherein the length is maximum (such as for example the length of a filament would be the length of the rolled out filament rather than a length or diameter of a coil comprising a rolled-up filament). The length may in particular embodiments be 1 m, such as 100 m, such as 1 km, such as 20 km, such as 100 km, such as above 100 km, such as within 1 m-30 km, such as within 1 km-30 km.

[0061] According to an embodiment, there is presented a strand with a plurality of filaments wherein a length, such as a maximum dimension in a longitudinal direction of each filament, of each filament is equal to or less than 1 km, such as equal to or less than 100 m, such as equal to or less than 25 m, such as equal to or less than 10 m.

[0062] A possible advantage of relatively shorter length of filament sections may be that, e.g., shorter pieces of manufactured coated conductors, such HTS tapes, in e.g. 4 mm width or 12 mm width, and in lengths of, e.g., 100 m can be spliced together. The splicing section can span lengths such as 1-100 cm, such as 10 cm or 50 cm, or several meters, such as 1-10 m, such as 1 m or 5 m. The splicing can be produced industrially by electrodeposition, such as copper plating, such as silver plating, such as tin plating, or soldering, such as Sn soldering. The filaments can be mechanically twisted into a transposing matrix and then, e.g., copper plated, or soldered, to adhere to the filaments. The longer the splicing section, the lower the electrical resistance across the splicing, or joint. This solution solves the problem for joining superconducting (SC), such as HTS, tapes where the tapes are typically soldered together only in local short sections at tape ends. Using shorter pieces from SC, such as coated conductors, such as HTS, such as REBCO, manufacturing possibly enables complete, or partial, overlapping of joining sections over, e.g., several meters meaning that joints will no longer constitute a so-called weak point. Using shorter production pieces from the HTS manufacturing simplifies the coated conductor production and allows a larger superconductor performance span because the multifilaments can be transposed along the entire length of a superconducting wire, or cable, with a variation in the individual filament quality, such as superconductor performance, as long as individual filaments with low, mid and high performance (e.g. Icor Tc) are distributed evenly, i.e. statistically distributed evenly along the entire wire or cable length.

[0063] This means that the multifilament transposed wire, or cable, can be produced with a generally lower HTS production criteria, and may even benefit from employing HTS tapes from different vendors, such as with a variation in superconducting performance level providing a levelized performance along the entire wire.

[0064] According to an embodiment, there is presented a strand wherein a length, such as a maximum dimension in a longitudinal direction of the strand, such as along the strand, is equal to or larger than 1 m, such as equal to or larger than 2 m, such as equal to or larger than 3 m, such as equal to or larger than 5 m, such as equal to or larger than 8, such as equal to or larger than 10 m, such as equal to or larger than 100 m, such as equal to or larger than 1 km, such as equal to or larger than 10 km, such as equal to or larger than 100 km, such as equal to or larger than 1000 km.

[0065] The length of each strand may be understood as the largest dimension of the strand. It may be understood that the length is to be measured along the strand and / or for the configuration of the strand wherein the length is maximum (such as for example the length of a strand would be the length of the rolled out strand rather than a length or diameter of a coil comprising a rolled-up strand).

[0066] According to an embodiment, there is presented a strand wherein filaments within the strand are partially overlapping longitudinally with respect to each other, such as wherein the strand comprises filaments both having parts at the same longitudinal position of the strand and at different positions of the strand.

[0067] A possible advantage may be that it enables forming a superconductor strand, which is longer than the individual filament. An advantage of the overlap is that it enables passing current from one filament to the next (overlapping) filament in an effective manner.

[0068] By 'partially overlapping' is to be understood that neither filament within an overlapping pair of filaments are completely overlapping the other, such as one filament extending further in one (longitudinal) direction than the other, and the other filament extending further in the opposite (longitudinal) direction, while a portion of each filament spans the same longitudinal region. According to an embodiment, there is presented a strand wherein an engineering current density JE of the strand at a temperature of 77 Kelvin and at zero applied magnetic field is at least 1500 A / cm2, such as at least 2000 A / cm2, such as at least 3000 A / cm2, such as at least 5000 A / cm2, such as at least 10000 A / cm2, such as at least 20000 A / cm2, such as at least 40000 A / cm2, such as at least 70000 A / cm2. According to an embodiment, there is presented a strand wherein an engineering current density JE of the strand at a temperature of 20 Kelvin and in a magnetic field applied along any direction, perpendicular to the strand, is at least 7500 A / cm2, such as at least 10000 A / cm2, such as at least 15000 A / cm2, such as at least 25000 A / cm2, such as at least 50000 A / cm2, such as at least 100000 A / cm2, such as at least 200000 A / cm2, such as at least 350000 A / cm2.

[0069] 'Engineering current density' is understood as is common in the art, such as wherein the engineering current density is defined as the current density for a cross-sectional area of the strand, including superconducting material, matrix and optionally other materials if present, such as core, capping, one or more of substrates, buffer layers or buffer-stacks and stabilizing layers.

[0070] According to an embodiment, there is presented a strand wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 400 filaments pr. square centimetre, such as at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre.

[0071] A large density may be beneficial for having current distributed to a relatively high number of filaments per area, which may in turn be beneficial for reducing consequences (e.g., related to resistive heating and / or loss of current carrying capacity) if one or more individual filaments becomes defect.

[0072] According to an embodiment, there is presented a strand further comprising a core and / or a capping.

[0073] A 'core' may be understood to be a centrally placed optionally metallic (such as copper, stainless steel, gold or silver) element, optionally wherein the one or more superconductor filaments are twisted around the core. An advantage of a core may be that it yields mechanical strength to the resulting superconducting strand. A 'capping' may be understood as a peripherally placed material. An advantage of a capping may be that it yields mechanical and / or thermal protection and / or electrical protecting, such as acting as a shunt, of the superconducting portions of the resulting superconducting strand. Another possible advantage of a capping may be that it yields additional / extra mechanical strength to the resulting superconducting strand. It may also provide extra thermal heat capacity, which may serve to protect against superconductor quenching (see "Multifilamentary coated conductors for ultra-high magnetic field applications", Anders Christian Wulff et a / ., Supercond. Sci. TechnoL 34 (2021) 053003, which is hereby incorporated by reference in entirety).

[0074] According to an embodiment, there is presented a strand, wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 40 mm.

[0075] According to an embodiment, there is presented a strand, wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 4 mm.

[0076] According to an embodiment, there is presented a strand, wherein an aspect ratio of each filament (2056) in a cross-sectional plane orthogonal to a longitudinal axis of the filament is equal to or less than 10: 1, such as equal to or less than 5: 1, such as equal to or less than 2: 1.

[0077] According to an embodiment, there is presented a strand, wherein for each filament there exists a fictitious closed line in a cross-sectional plane orthogonal to a longitudinal axis of the strand, which line is entirely in matrix material and which line is encircling said filament, such as completely encircling, such as encircling around 360°, and wherein the other filaments within the plurality of filaments are outside of said closed line, and wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper.

[0078] According to an embodiment, there is presented a strand, wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre. According to an embodiment, there is presented a strand, wherein for each filament there exists a fictitious closed line in a cross-sectional plane orthogonal to a longitudinal axis of the strand, which line is entirely in matrix material and which line is encircling said filament, such as completely encircling, such as encircling around 360°, and wherein the other filaments within the plurality of filaments are outside of said closed line, wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper, and wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 400 filaments pr. square centimetre, such as at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre.

[0079] According to an embodiment, there is presented a strand, wherein in a cross-sectional plane orthogonal to a longitudinal axis of the strand, geometrical centres of the filaments are distributed in both dimensions, such as wherein a maximum distance between geometrical centres of filaments in any direction is at least 10 %, such as at least 25 %, such as at least 50 %, such as at least 75 %, such as at least 90 %, of a maximum distance between geometrical centres in the orthogonal direction, and wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper.

[0080] According to an embodiment, there is presented a strand, wherein an engineering current density JE of the strand at a temperature of 77 Kelvin and at zero applied magnetic field is at least 40000 A / cm2, such as at least 70000 A / cm2

[0081] According to an embodiment, there is presented a strand, wherein an engineering current density JE of the strand at a temperature of 20 Kelvin and in a magnetic field applied along any direction, perpendicular to the strand, is at least 7500 A / cm2, such as at least 10000 A / cm2, such as at least 15000 A / cm2, such as at least 25000 A / cm2, such as at least 50000 A / cm2, such as at least 100000 A / cm2, such as at least 200000 A / cm2, such as at least 350000 A / cm2. According to an embodiment, there is presented a strand, wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 40 mm, such as less than 30 mm, such as less than 20 mm, such as less than 18 mm, such as less than 16 mm, such as less than 15 mm, such as less than 14 mm, such as less than 12, mm, such as less than 10 mm, such as less than 8 mm, such as less than 5 mm, such as less than 4 mm, such as less than 3 mm, such as less than 2 mm, such as less than 1 mm, and wherein in a cross-sectional plane orthogonal to a longitudinal axis of the strand, geometrical centres of the filaments are distributed in both dimensions, such as wherein a maximum distance between geometrical centres of filaments in any direction is at least 10 %, such as at least 25 %, such as at least 50 %, such as at least 75 %, such as at least 90 %, of a maximum distance between geometrical centres in the orthogonal direction.

[0082] According to an embodiment, there is presented a strand, wherein each of the superconductor filaments comprises, such as consists of, superconductor material and one or more adjacent buffer layers and / or a substrate.

[0083] According to an embodiment, there is presented a strand, wherein each of the superconductor filaments comprises, such as consists of, superconductor material and a substrate.

[0084] According to an embodiment, there is presented a strand, wherein the twist Tw for a given filament or a part of a filament may be given by: wherein t is the (local) torsion ts, and ds is a spatial segment along the length of the filament or part of the filament.

[0085] According to an embodiment, there is presented a strand, wherein torsional twist pitch is the distance along the length of a twisted filament when the total angle of twist is 360°, such as the distance along a filament or a part of a filament for which a twist (Tw), optionally wherein twist Tw is determined according to the preceding paragraph, is 1.

[0086] According to an embodiment, there is presented a strand, wherein each filament is individually twisted . This may be advantageous for enabling and / or facilitating, increasing flexibility with regards to how filaments are arranged, such as with regards to how a first filament is arranged (e.g., in terms of angular and / or translational position) with respect to a second filament, wherein the first filament is the nearest neighbor of the second filament. This may in turn be beneficial for improving the electrical properties of the strand, such as the electrical properties of the (local) part of the strand, such as the part with the first and second filament.

[0087] According to an embodiment, there is presented a strand, wherein the matrix material is comprising, such as consisting of, a metallic material.

[0088] According to an embodiment, there is presented a strand, wherein for one or more cross-sectional planes orthogonal to a longitudinal axis of the strand, such as for cross-sectional planes cross- sectional planes orthogonal to a longitudinal axis of the strand within at least 10 %, such as at least 20 %, such as, such as at least 30 %, such as at least 40 %, such as at least 50 %, such as at least 60 %, such as at least 70 %, such as at least 80 %, such as at least 90 %, of the strand, there exists one or more pairs of filaments within the strand, wherein a first filament within the pair is the nearest neighbor of a second filament within the pair, and wherein a minimum angle between a first line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a first filament within said pair, and a second line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a second filament within said pair, is at least 10° (10 degrees), such as at least 15°, such as at least 20°, such as at least 25°, such as at least 30°, such as at least 35°, such as at least 40°, such as at least 45°, such as at least 50°, such as at least 55°, such as at least 60°, such as at least 65°, such as at least 70°, such as at least 75°, such as at least 80°, such as at least 85°, such as 90°.

[0089] A possible advantage of the minimum angle being at least 10° or at least 35°, is that it enables, or ensures, a level of anisotropy, e.g., so that an applied homogeneous magnetic field may affect the individual filaments within the pair differently, e.g ., in case electrical properties of one filament is reduced to a certain extent due to the applied magnetic field, the electrical properties of the other filament is not reduced or less reduced. This may in turn go to ensure that the electrical properties of at least a subset of filaments are not reduced to the maximum extent. This may alternatively or additionally increase, such as optimized, a robustness towards applied magnetic field, such as wherein the electrical properties of the strand are less dependent on an orientation of an applied magnetic field (such as increasing the isotropy of the strand).

[0090] A possible advantage of the having the angular orientation of the biaxially textured superconductor material of neighboring strands exhibiting a non-zero angle, such as the minimum angle being at least 10° or at least 35°, is that the above mentioned effect (such as the isotropy of the electrical properties of the strand) is increased locally, e.g., allowing splitting up the strand and / or having a part of the strand damaged while retaining the effect in the resulting strand and / or the remaining non-damaged (such as functional) part of the strand.

[0091] By 'a minimum angle' is understood the smallest of the two angles formed between crossing lines (in case there is difference between the angles formed, otherwise the minimum angle will be 90°).

[0092] 'Nearest neighbor' is understood as is common in the art, such as wherein a first filament is the nearest neighbor of a second filament, if a distance between a position of the first filament and the second filament is no larger than a distance between the second filament and any other filament. It is understood that a filament can have a plurality of nearest neighbor filaments (e.g., in case a plurality of first filaments being at the same distance to a second filament, with no other filament being at a shorter distance to the second filament). 'Distance' is in this context to be measured along a straight line within the (or each) cross- sectional plane. A position of each filament to be used for measuring the distance is the geometrical center (within the cross-sectional plane or within each cross-sectional plane) of the biaxially textured superconductor material of the filament. For example, a distance between a first filament and a second filament is the distance measured along a straight line from the geometrical center of the biaxially textured superconductor material of the first filament to the geometrical center of the biaxially textured superconductor material of the second filament.

[0093] By 'an orientation of the biaxially textured superconductor material' may be understood an orientation of a line achieved by fitting (e.g., by regression) a straight line to said superconductor material and / or an orientation of a line achieved by drawing a line between the two points of said superconductor material being farthest apart from each other in said cross-sectional plane. It may be understood, at least within the context of these embodiments relating to a minimum angle between a first and second line, that there exists for each filament (within the pair of filaments), two points of said superconductor material being farthest apart from each other in said cross-sectional plane, which two points are farther apart than any other pair of two points of said superconductor material being farthest apart from each other in said cross-sectional plane.

[0094] According to an embodiment, there is presented a strand, wherein for one or more cross-sectional planes orthogonal to a longitudinal axis of the strand, such as for cross-sectional planes cross- sectional planes orthogonal to a longitudinal axis of the strand within at least 10 %, such as at least 20 %, such as, such as at least 30 %, such as at least 40 %, such as at least 50 %, such as at least 60 %, such as at least 70 %, such as at least 80 %, such as at least 90 %, of the strand, there exists one or more pairs of filaments within the strand, wherein a first filament within the pair is the nearest neighbor of a second filament within the pair, and wherein a minimum angle between a first line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a first filament within said pair, and a second line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a second filament within said pair, is at least 35° (35 degrees), such as at least 40°, such as at least 45°, such as at least 50°, such as at least 55°, such as at least 60°, such as at least 65°, such as at least 70°, such as at least 75°, such as at least 80°, such as at least 85°, such as 90°.

[0095] According to a second aspect of the invention, there is presented a cable comprising a plurality of strands according to the first aspect, such as a. wherein each strand is individually torsionally twisted, b. wherein each strand is wrapped around an axis, such as an axis of the cable and / or an axis outside of the strand, and / or c. wherein the strands within the plurality of strands are transposed with respect to each other.

[0096] A plurality of strands can be arranged together to form a cable.

[0097] According to this aspect there is presented a cable (such as comprising a plurality of strands), such as a power cable (such as a cable capable of transmitting electrical power at at least 10 V, such as at least 100 V, such as at least 1000 V, such as at least 10 kV, and / or transmitting a current of at least 100 Ampere), comprising one or more strands provided according to the first aspect.

[0098] By 'cable' is understood a conducting structure comprising the plurality of strands, such as wherein the strands are twisted around their own axis and / or a common axis. A length of the cable may be at least 0.1 m, such as at least 1 m, such as at least 10 m, such as at least 100 m, such as at least 1000 m. The cable may comprise at least 5 filaments, such as at least 10 filaments, such as at least 100 filaments, such as at least 500 filaments, such as at least 1000 filaments, such as at least 10000 filaments.

[0099] According to alternative further aspects of the invention, there is presented any of a coil, an electrical generator, a transformer, Nuclear Magnetic Resonance (NMR) scanners, Magnetic Resonance Imaging scanners, fusion reactor poloidal or toroidal field magnets, central column solenoid magnets, stellarator magnet coils, toroids, solenoids, accelerator magnets, or race-track coil magnets, comprising one or more strands according to the first aspect, such as wherein the one or more strands are capable of conducting in total an electrical current of 1 A, such as at least 10 A, such as at least 50 A, such as at least 100 A, such as at least 1000 A.

[0100] According to a third aspect of the invention, there is presented a method for manufacturing a strand according to the first aspect, said method comprising : a. Providing the plurality of filaments, such as including : i. Providing a substrate, optionally including one or more buffer layers,

[0101] II. Coating, such as epitaxially coating, said substrate with superconducting material, so as to provide the biaxially textured superconductor material on the substrate, ill. Segmenting, such as segmenting longitudinally, said substrate and the superconductor material so as to form the plurality of filaments, b. Torsionally twisting each filament, c. Providing at least some matrix material so as to encircle each filament with matrix material, wherein providing at least some matrix material optionally takes place before or after arranging the filaments in the strand, and d. Optionally prior to or subsequent to torsionally twisting each filament, arranging the filaments in the strand.

[0102] In embodiments, the method comprises twisting the filaments individually, in pairs or in bundles including more than two filaments. An advantage may be that it enables minimizing energy losses. Additionally, transposing may also be carried out (with twisting and / or transposing being beneficial for reducing energy losses, cf., e.g., the article "How filaments can reduce AC losses in HTS coated conductors: a review", Francesco Grilli and Anna Kario, Supercond. Sci. Technol. 29 (2016) 083002 (15pp), which is hereby included by reference in entirety). Furthermore, twisting, and optionally transposing, may in embodiments be combined with staggering, such as spatially (and statistically) distributing joints.

[0103] The present invention may be particularly advantageous as it provides a method for forming a strand (or wire) and optionally a cable, made from superconducting coated conductors, and / or high temperature, and / or ceramic based, superconductors with narrow, or fine, twisted filaments.

[0104] In an embodiment, 'providing the plurality of filaments' comprises: i. Providing a substrate,

[0105] II. Coating said substrate with superconducting material, so as to provide the biaxially textured superconductor material on the substrate, ill. Segmenting, such as segmenting longitudinally, said substrate and the superconductor material so as to form the plurality of filaments.

[0106] By 'segmenting' may be understood 'dividing' or 'separating'.

[0107] By 'substrate' may be understood 'a substrate suitable for supporting a superconducting element' which in turn may be understood as a solid element upon which a superconducting material may be placed, such as deposited, so that the substrate and the superconducting element may together form a superconducting element. The substrate may comprise, such as consist of, one or more metallic elements (such as metals, semi-metals, semi-conductors, and / or metalloids) or alloys. The substrate may comprise, such as consist of, non-metals, such as one or more polymers. The substrate may comprise a substantially planar surface.

[0108] The substrate may be a substrate suitable as a substrate for coated conductors, such as 2ndgeneration HTS, such as REBCO.

[0109] The solid element may have any shape, where shape is understood as the geometrical form as seen in a cross-section in a plane being orthogonal to a length axis (such as corresponding to an axis parallel with a direction in which current is to be carried), such as an arbitrary shape, such as any one of a tape-shape, a rectangular shape (such as a quadratic shape), a triangular shape, an ellipsoidal shape (such as a circular shape).

[0110] According to an embodiment, the method includes forming a Rutherford cable from a plurality of filaments and / or from a plurality of strands. The filaments are each shaped so as to enable twist pitching, such as single element twisting, such pair twisting, such as a Litz wire configuration, such as a Roebel configuration (cf., the reference "Supercond. Sci. TechnoL 22 (2009) 034003" which is hereby incorporated by reference in entirety), such as a Conductor On Round Core (cf. the reference "Supercond. Sci. TechnoL 27 (2014) 125008" which is hereby incorporated by reference in entirety), or such as a geometry that enables transposition of the superconducting filaments. Said shaping may be given by a piecewise linear shape, such as a zig-zag shape.

[0111] In embodiments, the substrate is a 'tape', i.e., an element which has thickness (length along a first dimension) which is significantly smaller, such as 10, 100 or 1000 times smaller, than its width (length along a second dimension) and where the width is significantly smaller, such as 10, 100, or 1000 times smaller, than its length (length along a third dimension).

[0112] The solid element may comprise any material selected from the group comprising : a nickel based alloy, a copper based alloy, a chrome based alloy, iron, aluminum, silicon, titanium, tungsten (also known as wolfram (W)), silver, Hastelloy, Inconel® and stainless steel.

[0113] By 'Hastelloy' is understood an alloy wherein the predominant alloying ingredient is nickel and wherein other alloying ingredients are added, such as the alloy comprising varying percentages of one or more of, such as all of, the elements: molybdenum, chromium, cobalt, iron, copper, manganese, titanium, zirconium, aluminum, carbon, and tungsten. In a particular embodiment, Hastelloy is an alloy which comprises the elements Ni, Cr, Fe, Mo, Co, W, C. In a more particular embodiment, the alloy also comprises Ni, Cr, Fe, Mo, Co, W, C and one or more of the elements Mn, Si, Cu, Ti, Zr, Al and B. In a more particular embodiment, the alloy is understood to comprise approximately 47 wt percent Ni, 22 wt percent Cr, 18 wt percent Fe, 9 wt percent Mo, 1.5 wt percent Co, 0.6 wt percent W, 0.10 wt percent C, less than 1 wt percent Mn, less than 1 wt percent Si and less than 0.008 wt percent B. Hastelloy may be referred to as "superalloy" or a "high-performance alloy" within the art.

[0114] 'Stainless steel' is generally known in the art. In particular embodiments, there is provided stainless steel with nickel and / or chromium, such as to provide a stainless steel which is corrosion and / or oxidation resistant, mechanically stable and non-magnetic at the operation temperature of the superconducting layer.

[0115] 'Coating' is understood as is common in the art, such as a layer, such as a thin layer, of material being applied to a substate. Application of the coating may be carried out in several ways, such as a line-of-sight process, such as chemical vapor deposition, such as physical vapor deposition, such as pulsed laser deposition, such as metal organic vapor deposition, such as atomic layer deposition, such as ionized jet deposition, such as thermal evaporation, such as e-beam assisted deposition, such as anyone of die coating, bubble jet coating and ink jet coating. The coating may form, optionally with at least a part of the substrate, a coated conductor, such as a 2ndgeneration high temperature superconductor coated conductor. The coating of the superconductor material may be an epitaxial coating, such as for the purpose of providing the biaxial texturing.

[0116] The structure and / or texture of the superconducting material in the coating may be endowed to the superconducting layer via the substrate and / or via another layer in the coating, such as a buffer layer.

[0117] A 'buffer (layer)' is understood as is common in the art, and may for example be understood to optionally provide structure and / or texture to the superconducting layer and / or may for example be understood to provide an optionally inert chemical barrier.

[0118] According to an embodiment, there is presented a method wherein the method further comprises staggering the plurality of filaments prior to arranging the filaments in the strand, such as wherein staggering comprises longitudinally displacing one or more filaments with respect to one or more other filaments while maintaining a longitudinal overlap, such as wherein the filaments being longitudinally displaced with respect to each other originate from the same substrate, such as the same coated substrate, such as the same coated conductor tape.

[0119] By 'staggering' may be understood displacing the filaments longitudinally with respect to each other by differing amounts. An advantage may be that defects, which may have been provided during production of the coated conductor and / or the filaments at the same longitudinal position, are distributed longitudinally, which may in turn have the effect that defects are no longer placed at the same position, which may be beneficial for avoiding that the current carrying capacity is degraded due to current not being able to pass that longitudinal position with multiple defects.

[0120] According to an embodiment, there is presented a method, wherein providing the plurality of filaments (cf., e.g., step a of the method (such as the steps i-iii and / or the steps optionally including providing the substrate, coating said substrate and segmenting)) is carried out by sequentially:

[0121] Providing a substrate, such as wherein the substrate comprises metal, such as the substrate being a planar metal substrate, wherein the substrate has a first side and a second side, such as wherein the first side is opposite the second side, and wherein the substrate comprises a plurality of grooves in the first side of the substrate,

[0122] • Applying on the substrate a coating, wherein the coating is comprising a superconducting material, such as a said coating being a multi-layer structure comprising a superconducting material optionally comprising rare-earth barium copper oxide (also referred to as REBCO), such as said coating being a superconductor stack, such as said coating being a high-temperature superconductor stack, so that for each groove within the plurality of grooves, i. a first part of the coating on a first side of a feature of the groove, such as the groove, is separated, such as disconnected, such as physically disconnected, from

[0123] II. a second part of the coating on a second side of the feature of the groove, such as the groove, wherein the second side of the feature of the groove is opposite of the first side of the feature of the groove,

[0124] • Removing from the second side of the substrate, such as via electropolishing and / or etching, at least a part of the substrate, so as to remove at least a connection from the first part of the coating to the second part of the coating via the substrate, such as so as to provide the plurality of filaments, such as wherein portions of the substrate previously joining the filaments have been removed.

[0125] This embodiment is described in the patent application 'PLURALITY OF SUPERCONDUCTING FILAMENTS' with application number EP22177004.3 filed 02 June 2022 with the European Patent Office with Subra A / S as applicant, which application is hereby included by reference in entirety, and / or in the application 'PLURALITY OF SUPERCONDUCTING FILAMENTS' with application number PCT / EP2023 / 064749 filed 01 June 2023 with the European Patent Office as Receiving Office, which application is hereby included by reference in entirety.

[0126] This method relies, such a necessitates and / or relies in embodiments exclusively, on method steps, which are applicable for large scale manufacture and / or is realistically applicable for industrial scale manufacturing, i.e., methods according to embodiments of the invention may be realistically applicable for industrial scale manufacturing. For example, each of the steps of providing a substrate, such as a tape provided in a reel-to-reel setup, optionally applying grooves, such as applying grooves in a rolling process and / or in a lithographic process (such as via photolithography and subsequent etching), applying a coating, optionally providing a resist and removing, such as etching from a backside, is a step, which may realistically be applied on an industrial scale. It may be considered an insight of the present inventors, that a process for providing a plurality of superconducting filaments can be realized via, such as exclusively via, industrially applicable method steps.

[0127] It may furthermore be seen as an advantage, that methods according to embodiments of the invention are applicable, such as well-suited, for large-scale manufacturing, since they can be relatively simple and / or efficient. For example, long filaments, optionally in large numbers may be obtained in a relatively fast manner and / or a manner demanding relatively few resources, such as relatively little equipment, manpower, energy and / or materials. Thus, large scale manufacturing may be possible with embodiments of the invention, and furthermore, this may be possible while minimizing resources, such as the use of resources.

[0128] Embodiments of the invention may furthermore be seen as effective in terms of enabling providing substrates for superconducting structures facilitating relatively large critical currents and / or engineering currents, because it may be possible to obtain substrates with little or no damage zones (such as wherein a damage zone may be understood as a portion of superconducting material which is no longer functional, which in turn may reduce the critical current).

[0129] 'Grooves' are understood as is common in the art, such as an elongated depression, such as a depression with respect to adjoining portions of a substrate. A groove may serve to separate portions of a surface of a substrate into portions on either side of the groove so that deposition of material on top of the substrate, such as in a line-of-sight process, yields material portions, which are separated, such as disconnected, such as physically disconnected, by the groove. A possible advantage of such separation may be that a distance from the first side to the second (optionally planar) side of the substrate varies depending on position on the first side, which may in turn have the advantage that removal of material, e.g., in a spatially non-specific manner (e.g., where material is removed anywhere, such as removed in substantially equal amounts anywhere on an optionally planar surface), such as via etching or electropolishing, from the second side of the substrate may enable removing the full thickness of material from the first side to the second side of the substrate firstly at the positions of the grooves, i.e., portions with grooves can become disconnected from each other in a relatively simple and spatially non-specific removal step, e.g., via etching or electropolishing.

[0130] By a 'line-of-sight' process is understood any process which enables depositing material only on positions of a substrate which may be seen along a straight line from another position, such as a position above the substrate. 'Line-of-sight' process is thus construed broadly to comprise processes where the deposited material follows straight lines prior to deposition and processes for deposition which has a similar effect. In a particular embodiment, the line-of- sight process is any one of vapor deposition, chemical vapor deposition, physical vapor deposition, atomic layer deposition, thermal evaporation, e-beam assisted deposition, ionized jet deposition, die coating, bubble jet coating and ink-jet coating. In particular embodiments, 'line-of-sight' is understood to be a process wherein the deposited material has its origin from a source and travels in a direct line therefrom to the position where it is deposited. In other words, there can only be deposited material on positions from which there can be drawn a straight line to the source which does not traverse any obstacles. A possible advantage of using a line-of-sight process may be that it enables depositing material on both sides of each groove, while utilizing a feature of the groove to shadow a portion, such as a bottom part of the groove, so that not deposition takes place at said portion, thereby forming a disruptive strip in the deposited material. By 'disruptive strip' may be understood a line of lack of coating material, which separates coating material into elongated strips of coating material on both sides of the disruptive strip. A disruptive strip may be seen as a gap in an otherwise coherent coating material. If a coherent coating material, such as a coherent layer of coating material, is traversed by a disruptive strip, the continuity of the coherent coating material is thus disrupted into two separate (layers of) material, such as two portions of coating material.

[0131] The grooves may be parallel with each other, such as parallel with each other. By 'parallel' may be understood parallel within 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 degrees. It may be understood that the grooves may be piecewise parallel, such as the grooves themselves being non-rectilinear, such as curvilinear, such as piecewise linear, although immediately adjacent grooves may still be parallel.

[0132] By a 'superconductor stack' may be understood a layered construction, such as a multi-layer structure, optionally with distinct layers, comprising a buffer layer (e.g., 0.1-2 micrometer) and a superconducting layer (e.g., rare-earth-based barium copper oxide (REBCO) of thickness being, e.g., 1-10 micrometer). The superconductor stack may be a high- temperature superconductor stack.

[0133] By 'a first side of a feature of the groove' is understood an area on only one side of the feature of the groove.

[0134] By 'feature of the groove' is understood a portion of the groove or the groove in entirety. For example, the groove in entirety may serve to separate, such as disconnect, such as physically disconnect, portions of coating material applied in a line-of-sight process from directly above the groove (in which example there will be a portion on either side of the groove, wherein neither of these portions comprise material in the groove). In another example, an edge of the groove or a side of the groove may serve to separate, such as disconnect, such as physically disconnect, portions of coating material applied in a line-of- sight process from a position outside of a plane being orthogonal to a surface comprising the groove and parallel with the groove (in which example one portion of the coating may comprise material in the groove, such as in the bottom of the groove).

[0135] By 'separated' may be understood that elements being separated are spatially separated, such as the elements being separated by another material than the material of the elements, e.g., by having non-solid material between the elements. In embodiments, separated elements may be connected to each other via material identical to the material of the elements (e.g., portions of elements on tops of protrusions / hills on each side of a groove may be separated from each other but connected via material identical to the material of the elements extending via the groove from one protrusion / hill to the other protrusion / hill). In embodiments, separated elements may be disconnected, such as physically disconnected, from each other, due to absence of material identical to the material of the elements between the elements (e.g., elements on tops of protrusions / hills on each side of a groove may be separated from each other and physically disconnected due to no material identical to the material of the elements extending from one protrusion / hill to the other protrusion / hill).

[0136] By 'disconnected' may be understood physically and / or electrically disconnected, such as wherein disconnected elements are not electrically connected by an electrically conducting material and / or not physically connected by the material of the elements.

[0137] By 'removing from the second side of the substrate' is understood that material is removed from the surface of the second side of the substrate, such as from a backside of the substrate with respect to a frontside comprising grooves, such as sequentially removing, such as removing in each of a plurality of steps (which can follow-each other in a substantially continuous manner, such as by etching, or can be discretized, such as when moving material in a plurality if milling or grinding steps) the outermost material. It may furthermore be understood, that removing of material from the second side of the substrate comprises removing material from the second side of the substrate prior to removing material from a first side of the substrate and / or while there is still material on the first side of the substrate. When removing material from the second side of the substrate, a position of the surface of the second side of the substrate moves towards the first side of the substrate and / or the portions of coating.

[0138] By 'remove at least a connection from the first part of the coating to the second part of the coating via the substrate' may be understood that material of the substrate is removed so that there subsequently is no physical connection via the substrate from first part of the coating to the second part of the coating, such as the first part of the coating and the second part of the coating become detachable or detached from each other and / or whereby the first and second parts of the coating are no longer connected via the substrate, such as at least in a cross-sectional plane being orthogonal to a longitudinal direction of one or more or all filaments, such as for any part of the substrate, there is no path through the substrate from the first part of the coating to the second part of the coating.

[0139] In embodiments, 'remove at least a connection from the first part of the coating to the second part of the coating via the substrate' comprises splitting or breaking or severing or rupturing at least a connection from the first part of the coating to the second part of the coating via the substrate.

[0140] Removal of material may take place via, e.g., electropolishing and / or etching (such as electro-etching), and / or a grinding process, and / or a cutting process, and / or a laser process.

[0141] A step of 'removing from the second side of the substrate at least a part of the substrate' may be carried out via electropolishing and / or etching, such as electro-etching. A possible advantage may be that electropolishing and / or etching are well-established, applicable on an industrial scale and / or applicable for removing some material (such as the substrate) while being gentle on remaining materials (such as the coating, in particular if said remaining materials are covered with a protective covering).

[0142] By 'etching', 'electro-etching' or 'electropolishing' may be understood removal of (substrate) material by etching, electro-etching or electropolishing, such as with an etchant. The etchant may in particular embodiments be in any one of the following states of matter: plasma, liquid and gas. In a particular embodiment Reactive Ion Etching (RIE) is employed.

[0143] By ’a grinding process' is understood that a portion of the (substrate) material is removed by a grinding process or a polishing process, such as repeatedly scraping off minor portions of the (substrate) material to be removed. A 'polishing process' is understood to be similar to a 'grinding process' in the present context.

[0144] By a 'cutting process' is understood a process wherein material is displaced, such displaced rather than removed. This may be achieved using a relatively sharp tool.

[0145] A step of 'removing from the second side of the substrate at least a part of the substrate' may be carried out with a laser process, such as via laser marking and / or any one of laser engraving, laser etching, laser ablation and laser annealing. It may be an advantage, e.g., when using spatially specific or spatially well-defined or spatially well-definable methods (such as wherein material is removed or removable at spatially well-defined position, such as even on a planar surface, such as material at two positions with similar topography being removed at significantly different rates, such as wherein the rate of removal at one position being non-zero and the other being substantially zero), such as laser marking, that the grooves enable that a smaller distance from the first side to the second side (at positions corresponding to the bottom of the grooves) in turn enables that less substrate material must be removed (compared to a situation without grooves) to penetrate the substrate.

[0146] In an embodiment, the method further comprises adding a capping layer and / or a stabilizing material as a part of the coating and / or on top of the coating.

[0147] According to another aspect of the invention, there is presented use of the strand as provided according to the first aspect for conducting a current, such as conducting a current at superconducting conditions.

[0148] According to an embodiment, there is presented a method wherein the method comprises providing the substrate by:

[0149] • Providing a substrate without grooves in the first side of the substrate, and

[0150] • forming the plurality of grooves in the first side of the substrate.

[0151] The 'forming the plurality of grooves' can be carried out in several ways, such as by cutting or roll-cutting, which may be beneficial for industrial scape applicability.

[0152] According to an embodiment, there is presented a method wherein the method is further comprising :

[0153] • Twisting the plurality of filaments, or multiple pluralities of filaments, wherein each filament is twisted around its own axis and / or wherein a plurality of filaments are twisted around their common axis, such as wherein optionally twisted bundles of filaments are twisted around each other, thereby providing one or more superconducting structures each comprising a plurality of twisted filaments, such as wherein each filament has a helical shape with a centre axis within one or more other helical shaped filaments, and / or

[0154] • Transposition of the plurality of filaments, or multiple pluralities of filaments thereby providing one or more superconducting structures each comprising a plurality of transposed filaments.

[0155] By 'twisting' may be understood that one portion, such as an end, of the filament is rotated around a longitudinal axis with respect to another portion, such as the opposite end, such as wherein said rotation spans at least half a revolution or pi (radians) or 180 degrees, such as n times pi, where n is at least 1, such as at least 2 (corresponding to at least a full revolution or at least 360 degrees), such as at least 5, such as at least 10, such as at least 50, such as at least 100, such as at least 1000. Twisting may take place for each filament around its own axis and / or for a plurality (such as a bundle) of filaments, which are twisted together. An advantage of twisting may be that it enables reducing, minimizing or eliminating instability and coupling loss. Transposition of filaments may effectively decouple the filaments and this may be obtained by twisting of the filaments (cf., e.g., the article "How filaments can reduce AC losses in HTS coated conductors: a review", Francesco Grilli and Anna Kario, Supercond. Sci. TechnoL 29 (2016) 083002 (15pp), which is hereby included by reference in entirety, and where reference is in particular made to the end of section 2 on p. 3).

[0156] By 'transposition' may generally be understood the optionally periodic swapping of positions of the conductors of a transmission line, such as in order to reduce crosstalk and / or otherwise improve transmission, cf., e.g., the article "How filaments can reduce AC losses in HTS coated conductors: a review", Francesco Grilli and Anna Kario, Supercond. Sci. TechnoL 29 (2016) 083002 (15pp), which is hereby included by reference in entirety).

[0157] It may furthermore be advantageous to deposit an additional capping, such as metal, such as copper or silver, such as silver, before the individual filaments are twisted around their own axis (longitudinal, rolling axis). The capping can also be added after twisting, and / or, after transposing and / or twisting with other filaments. The extra capping provides additional mechanical and thermal stabilization. Metallization can be applied using electrodeposition, such as plating, or sputtering.

[0158] According to an embodiment, there is presented a method wherein the method is further comprising forming a coil by coiling up the strand, and optionally the cable. An advantage of providing a coil, is that such coil may be useful for numerous purposes, e.g., generating a magnetic field, such as is used in Nuclear Magnetic Resonance (NMR) scanners, Magnetic Resonance Imaging scanners, fusion reactor poloidal or toroidal field magnets, central column solenoid magnets, stellarator magnet coils, toroids, solenoids, accelerator magnets, or race track coil magnets.

[0159] According to an embodiment, there is presented a method wherein the superconducting strand comprises a reinforcing element, such as a reinforcing element comprising Hastelloy and / or carbon fibers, and wherein the reinforcing element is optionally embedded in a capping. A possible advantage may be increased strength of the resulting superconducting strand. The reinforcing element may be a fibrous material (optionally having a diameter of 50-500 micrometer, such as 100-300 micrometer, such as 150-250 micrometer, such as substantially 200 micrometer), such as a Hastelloy-fiber or a carbon-fiber wrapped or coiled around one or more filaments, and optionally embedded in a capping, optionally by being plated into the capping, such as a copper capping, such as produced by copper plating, such as soldering into the capping, such as cast into the capping.

[0160] According to an embodiment, there is presented a method, wherein providing a substrate comprises providing the substrate, such as a tape, in a reel-to-reel setup. A possible advantage may be that it facilitates efficient and / or large-scale processing.

[0161] According to an embodiment, there is presented a method, wherein applying on the substrate a coating comprises applying on the substrate, such as a tape, a coating in a reel-to-reel setup. A possible advantage may be that it facilitates efficient and / or large-scale processing.

[0162] According to an embodiment, there is presented a method, wherein removing from the second side of the substrate at least a part of the substrate comprises removing (such as removing via any one or more of electropolishing, etching, grinding and / or laser) from the second side of the substrate at least a part of the substrate, such as a tape, in a reel-to-reel setup. A possible advantage may be that it facilitates efficient and / or large-scale processing.

[0163] According to an embodiment, there is presented a method, wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre.

[0164] According to an embodiment, there is presented a method, said method comprising : a. subsequent to torsionally twisting each filament, arranging (2272) the filaments in the strand.

[0165] This may be advantageous for enabling and / or facilitating, increasing flexibility with regards to how filaments are arranged, such as with regards to how a first filament is arranged (e.g., in terms of angular and / or translational position) with respect to a second filament, wherein the first filament is the nearest neighbor of the second filament. This may in turn be beneficial for improving the electrical properties of the strand, such as the electrical properties of the (local) part of the strand, such as the part with the first and second filament. According to an embodiment, there is presented a method, wherein providing at least some matrix material takes place before arranging the filaments in the strand, and wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper.

[0166] According to an embodiment, there is presented a method, wherein each filament is wherein each filament is individually twisted.

[0167] This may be advantageous for enabling and / or facilitating, increasing flexibility with regards to how filaments are arranged, such as with regards to how a first filament is arranged (e.g., in terms of angular and / or translational position) with respect to a second filament, wherein the first filament is the nearest neighbor of the second filament. This may in turn be beneficial for improving the electrical properties of the strand, such as the electrical properties of the (local) part of the strand, such as the part with the first and second filament.

[0168] BRIEF DESCRIPTION OF DRAWNGS

[0169] The first, second, and third aspect according to the invention will now be described in more detail with regard to the accompanying figures. The figures show one way of implementing the present invention and is not to be construed as being limiting to other possible embodiments falling within the scope of the attached claim set.

[0170] In FIGs. 1-19 and the accompanying description below, the term strand' is referred to by the interchangeably word 'wire'.

[0171] FIG. 1 is a flowchart illustrating steps of a method according to an embodiment of the invention.

[0172] FIGs. 2-7 shows schematic illustrations depicting steps in a method according to an embodiment of the invention.

[0173] FIG. 8 shows a plurality of superconducting strands arranged as a cable.

[0174] FIG. 9 illustrates steps of a method of forming a plurality of filaments according to an embodiment. FIG. 10 shows a Hastelloy substrate with grooves formed in a 2LUPS process with a CC stack 1038.

[0175] FIG. 11 shows a zoom view of FIG. 10.

[0176] FIG. 12 shows a single filament 1242 etched out.

[0177] FIG. 13 shows I / V setup for characterizing superconducting performance of a filament.

[0178] FIG. 14 shows the I / V setup of FIG. 13 immersed in liquid nitrogen.

[0179] FIGs. 15-16 show Scanning Electron Microscope (SEM) images of 3D etched Hastelloy substrate.

[0180] FIG. 17 shows Scanning Electron Microscope image of Focused Ion Beam milled HTS stack deposited on a 3D etched Hastelloy substrate.

[0181] FIG. 18 shows a collage of two images of filaments.

[0182] FIG. 19 shows the result of twisting a plurality of filaments.

[0183] FIG. 20 shows a cross-sectional view of a strand in a plane being parallel with a longitudinal direction of the strand.

[0184] FIG. 21 shows a cross-sectional view of a strand in a plane being orthogonal to a longitudinal direction of the strand

[0185] FIG. 22 shows a flowchart illustrating steps of a method for manufacturing a strand according to the first aspect.

[0186] FIG. 23 shows a part of a filament, namely a part spanning one twist pitch (length).

[0187] FIG. 24 shows a view of three twisted filaments which have been coated jointly by Cu.

[0188] FIG. 25 shows a closeup view of the result of twisting, coating and arranging three filaments.

[0189] FIG. 26 shows a cross-sectional view of two Cu coated filaments joined in a strand in a plane being orthogonal to a longitudinal direction of the strand. FIG. 27 shows a cross-sectional view of three Cu coated filaments joined in a strand in a plane being orthogonal to a longitudinal direction of the strand.

[0190] DETAILED DISCLOSURE OF THE INVENTION

[0191] FIG. 1 is a flowchart illustrating steps of a method according to an embodiment of the invention, said method being a method 100 for forming a strand comprising a plurality of filaments, wherein each filament is superconducting, such as high-temperature superconducting (HTS), and furthermore forming a superconducting structure and providing a superconducting wire, said method sequentially comprising :

[0192] • Providing 102 a substrate being a planar metal substrate, wherein the substrate has a first side and a second side, such as wherein the first side is opposite the second side, wherein providing the substrate comprises: i. Providing the substrate without grooves in the first side of the substrate,

[0193] II. forming 104 a plurality of grooves in the first side of the substrate, and ill. forming 106 via etching and / or electropolishing, and optionally in a two- level undercut process (2LUPS), one or more undercuts at each groove (although it is noted that alternative embodiments are conceivable, such as embodiments being similar in all other regards to the present embodiment, but wherein undercuts are not present or formed),

[0194] • Applying 108 on the substrate a coating, such as an epitaxial coating, wherein the coating is comprising a high-temperature superconductor stack, so that for each groove within the plurality of grooves, i. a first part of the coating on a first side of a feature of the groove, such as the groove, is separated, such as disconnected, such as physically disconnected, from

[0195] II. a second part of the coating on a second side of the feature of the groove, such as the groove, wherein the second side of the feature of the groove is opposite of the first side of the feature of the groove,

[0196] • Applying 110 on some or all of the first part of the coating and on some or all of the second part of the coating, such as on the first part and / or the second part of the coating, a protective covering, such as a resist, wherein the protective covering partially or wholly fills vacant space in the grooves,

[0197] • Removing 112 from the second side of the substrate via electropolishing and / or etching at least a part of the substrate, so as to remove at least a connection from the first part of the coating to the second part of the coating via the substrate, such as to provide the plurality of filaments, such as wherein portions of the substrate previously joining the filaments have been removed,

[0198] • Stopping 114 the removing from the second side of the substrate at least a part of the substrate, while each part of the coating, such as the first part of the coating and the second part of the coating, is adjoining a remaining part of the substrate,

[0199] • Removing 116 the protective covering partially or wholly from some or all of the coating and remaining portions of the substrate, such as so as to remove at least a connection from the first part of the coating to the second part of the coating via the protective covering,

[0200] • Twisting 118 the plurality of filaments, or multiple pluralities of filaments, wherein each filament is twisted around its own axis and / or wherein a plurality of filaments are twisted around their common axis, such as wherein optionally twisted bundles of filaments are twisted around each other, thereby providing one or more superconducting structures each comprising a plurality of twisted filaments, such as wherein each filament has a helical shape with a center axis within one or more other helical shaped filaments,

[0201] • Forming 120 a superconducting wire by providing one or more superconducting structures with a core and a capping.

[0202] FIGs. 2-7 shows schematic illustrations depicting steps in a method according to an embodiment of the invention, said method being a method 100 for forming a plurality of filaments, wherein each filament is superconducting, such as high-temperature superconducting (HTS), and furthermore forming a superconducting structure and providing a superconducting wire.

[0203] FIG. 2 shows 102 a substrate 228 being a planar metal substrate without grooves in the first side, wherein the substrate has a first side 231 and a second side 232, such as wherein the first side is opposite the second side.

[0204] FIG. 3 shows the substrate 230 after forming 104 a plurality of grooves 234 in the first side of the substrate, and after forming 106 one or more undercuts 236 at each groove (as indicated by the dashed lines delimiting the shadowed, undercut portions of each groove).

[0205] FIG. 3 also illustrates dimensions of the grooves 234. FIG. 3 is indicated a distance 233a between a plane (as indicated with the upper horizontal dashed line) being parallel with an (upper (in the figure)) surface of the first side of the substrate, such as being tangential with the protrusions between the grooves 234, and a plane (as indicated with the lower horizontal dashed line) and a plane being tangential to the bottom of the plurality of grooves, i.e., a depth of the grooves as measured in a direction orthogonal to the plane of the first side of the substrate (i.e., measured in the vertical / up-down direction in the plane of the paper of the figure). Said distance 233a or depth is non-zero, such as at least 100 nm, such as at least 1 pm, such as at least 10 pm, such as at least 25 pm, such as at least 50 pm, such as at least 100 pm. Said distance 233a or depth may furthermore be at most 4 mm, such as at most 2 mm, such as at most 1 mm. Said distance 233a or depth may be within ]10 nm; 4 mm[, such as within ] 1 pm; 2 mm[, such as within ]10 pm; 1 mm[ (where the open brackets "]x,;y[ indicate that neither x nor y is included in the interval, yet all numbers therebetween are included). Furthermore is indicated a dimension or width 233b of the grooves, i.e., the distance from an edge (such as the beginning of an edge, such as the end of the planar portion of the substrate outside of the groove) of a protrusion on one side of groove to an edge of a protrusion on another side of a groove as measured in a direction parallel with the plane of the first side of the substrate and orthogonal to a longitudinal direction of the grooves (i.e., measured in the horizontal and left-right direction in the plane of the paper of the figure). The dimension or width 233b may be at least 1 micrometer, such as at least 2 micrometer, such as at least 5 micrometer, such as at least 10 micrometer, such as at least 30 micrometer, such as at least 100 micrometer, such as at least 200 pm. The dimension or width 233b may be at most 1 mm, such as at most 500 pm, such as at most 200 pm, such as at most 100 pm. The dimension or width 233b may be within 1 micrometer-1 mm, such as within 10 pm-500 pm. There is in Fig. 3 furthermore indicated a distance 233c between adjacent grooves which is measured in the same direction as the width 233b. The distance 233c may be at least 100 pm. The distance 233c may be at most 2 mm. The distance 233c may be within ]100 pm; 2 mm[, such as within ]200 pm; 1 mm[.

[0206] FIG. 4 shows the substrate 230 after applying 108 on the substrate a coating 238 comprising a high-temperature superconductor stack, so that for each groove within the plurality of grooves a first part of the coating on a first side of the groove is physically disconnected, from a second part of the coating on a second side of the groove, wherein the second side of the feature of the groove is opposite of the first side of the feature of the groove. Furthermore, portions of coating material can be seen in the grooves.

[0207] FIG. 5 shows the substrate 230 Applying 110 on some or all of the first part of the coating and on some or all of the second part of the coating, such as on the first part and / or the second part of the coating, a protective covering 240, being a resist, wherein the protective covering partially or wholly fills vacant space in the grooves. FIG. 6 shows the a plurality of filaments 242 after removing 112 from the second side of the substrate (where the substrate 230 is no longer present, and where dotted rectangle 244 indicates the position previously held by substrate 230) via electropolishing and / or etching at least a part of the substrate, so as to remove at least a connection from the first part of the coating to the second part of the coating via the substrate, such as so as to provide the plurality of filaments 242 wherein each filament is superconducting, such as wherein portions of the substrate previously joining the filaments have been removed, such as via the superconducting coating. FIG. 6 also shows the result of stopping 114 the removing from the second side of the substrate at least a part of the substrate, while each part of the coating, such as the first part of the coating and the second part of the coating, is adjoining a remaining part 246 of the substrate.

[0208] FIG. 7 shows the plurality of filaments 242 after removing 116 the protective covering 240 partially or wholly from some or all of the coating and remaining portions of the substrate, such as so as to remove at least a connection from the first part of the coating to the second part of the coating via the protective covering. FIG. 7 also indicates a width 248 and a thickness 250 of a filament. Length is a dimension orthogonal to the plane of the paper.

[0209] FIG. 8 shows a plurality of groups of filaments, such as strands, wherein each filament is twisted around its own axis and wherein a plurality of filaments in each group of filaments are twisted around their common axis thereby providing a plurality of superconducting structures 256 each comprising a plurality of twisted filaments wherein each filament has a helical shape and wherein these superconducting structures have been provided 120 in a superconducting wire 252 with a core 254 and a capping 258.

[0210] EXAMPLE A

[0211] According to an embodiment, there is presented a method of forming a plurality of filaments, wherein each filament is superconducting, said method comprising steps 1-9 as described in detail below (and schematically illustrated in FIG. 9):

[0212] A substrate which comprises a plurality of grooves is provided in steps 1-5, with forming the plurality of grooves in a first side (such as an over-side, a top side or a frontside) of the substrate in steps 2-5 (with the first side being opposite a second side, such as an underside, a bottom side or a backside):

[0213] Step 1 : Start with a substrate without grooves in the form of a polished 4 mm wide, 100 pm thick and 50 m long Hastelloy tape with surface roughness below 10 nm (where surface roughness is arithmetic surface roughness value over a 10x10 pm2atomic force microscopy scan). The surface quality is suitable for coated conductor (CC) chemical vapor deposition (CVD) / metal organic chemical vapor deposition (MOCVD), physical vapor deposition (PVD) or chemical deposition of buffer layers and superconducting layer. Polishing can be achieved by electrochemical polishing in a solution of phosphorous and sulfuric acid mixture following standard procedures from the literature, see, e.g., Wulff et al. 2015, Supercond. Sci. TechnoL 28 (2015) 072001, page 2, section 2.

[0214] Subfigure (a) of FIG. 9 shows a cross-sectional view of the tape in a plane being orthogonal to a longitudinal direction of the tape.

[0215] Step 2: Apply a masking material as described in Wulff et al. 2015, Supercond. Sci. TechnoL 28 (2015) 072001, page 2, section 2.

[0216] This could be a masking tape, such as a Kapton® film, a photoresist or similar. It is understood that ' Kapton® film' refers to the well-known product from DuPont™ which is a film of poly(4,4'-oxydiphenylene- pyromellitimide).

[0217] Subfigure (b) of FIG. 9 shows a cross-sectional view of the tape in a plane being orthogonal to a longitudinal direction of the tape with masking material.

[0218] Step 3: Remove part of the masking material using mechanical scribing, a wet / dry chemical lithography process, or by laser scribing. Here it is done using standard lithography steps to fully remove the masking material in areas where grooves are to be etched.

[0219] Subfigure (c) of FIG. 9 shows a cross-sectional view of the tape in a plane being orthogonal to a longitudinal direction of the tape with part of the masking material removed.

[0220] Step 4: Etch into the substrate using a mixture of phosphorous and sulfuric acid applying a current density between 0.01-1 A / cm2until grooves have been formed.

[0221] Subfigure (d) of FIG. 9 shows a cross-sectional view of the tape in a plane being orthogonal to a longitudinal direction of the tape with grooves formed by etching.

[0222] Step 5: Remove the masking material using an organic solvent (such as acetone) or a stripping agent such as sodium hydroxide. Applying on the substrate a coating, wherein the coating (coated conductor (CC) stack) is a high-temperature superconductor stack, so that for each groove within the plurality of grooves, a first part of the coating on a first side of the groove, is separated (such as separated, but still physically connected, e.g., as depicted in Fig. 9(e)), from a second part of the coating on a second side of the groove, wherein the second side of the feature of the groove is opposite of the first side of the feature of the groove, is carried out in step 6.

[0223] Step 6: Deposit a superconducting coated conductor (CC) stack on the material, cf., e.g., a method as described in Wulff et al 2015, Supercond. Sci. TechnoL 28 (2015) 072001, page 2, section 2, or Insinga et al 2018, IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 28, NO. 4, JUNE 2018, page 2, section 2.

[0224] Subfigure (e) of FIG. 9 shows a cross-sectional view of the tape in a plane being orthogonal to a longitudinal direction of the tape with the remaining parts of the masking material removed and a superconducting CC stack deposited on the tape.

[0225] Applying on some or all of the first part of the coating and on some or all of the second part of the coating a protective covering (protective material), which partially or wholly fills vacant space in the grooves is carried out in step 7.

[0226] Step 7: Apply a protective material, such as liquid photoresist and cover the top (and in this embodiment also covering the sides, such as to avoid etching of the sides of the substrate and / or the sides of the outer CC stacks) of the tape and CC stack so as to protect the superconducting stack. The grooves should also be fully or partly covered with protective material. The protective material can be applied in several ways, e.g., liquid photoresist applied with an inkjet (e.g., with an opposite side of the tape held firmly against a solid element to avoid photoresist on said opposite side), with a brush or with dip-coating (such as dip-coating with an opposite side of the tape temporarily covered, e.g., with Scotch tape®).

[0227] Subfigure (f) of FIG. 9 shows a cross-sectional view of the tape in a plane being orthogonal to a longitudinal direction of the tape with the protective material applied.

[0228] Removing from the second side (such as the backside or bottom side) of the substrate via etching, such as electrochemical etching, or via electropolishing, at least a part of the substrate, so as to remove at least a connection from the first part of the coating to the second part of the coating via the substrate, such as so as to provide the plurality of filaments, wherein portions of the substrate previously joining the filaments have been removed, is carried out in step 8. Step 8: Etch from the backside of the tape structure using mixture of phosphorous and sulfuric acid. Etching can be continued until these are only physically connected via the protective material.

[0229] Subfigure (g) of FIG. 9 shows a cross-sectional view of the resulting plurality of filaments, which are being connected by the protective covering in a plane being orthogonal to a longitudinal direction of the plurality of filaments (same view as in subfigure (g) of FIG. 9) after a portion of the substrate has been removed from the backside.

[0230] Removing the protective covering partially or wholly from some or all of the coating and remaining portions of the substrate, such as so as to remove at least a connection from the first part of the coating to the second part of the coating via the protective covering is carried out in step 9.

[0231] Step 9 : The protective material is removed either mechanically by peeling off the material, or dissolving in an organic solvent, such as ethanol or acetone, or a stripping solvent such as sodium hydroxide.

[0232] Subfigure (h) of FIG. 9 shows a cross-sectional view of the resulting plurality of filaments, which are no longer being connected by the protective covering in a plane being orthogonal to a longitudinal direction of the plurality of filaments, i.e., after the protective covering has been removed.

[0233] FIG. 10 shows a Hastelloy substrate 1030 with grooves formed in a 2LUPS process with a CC stack 1038 (without undercut). FIG. 10 could be seen as corresponding to the schematic illustrations in FIG. 4 and / or subfigure (e) of FIG.9.

[0234] By a two-level undercut-profile substrate (2LUPS) process may be understood providing undercuts in a process comprising a sandwich structure, wherein disruptive strips are formed in an outer layer, such as is described, e.g., in WO13174380A1, which is hereby incorporated in entirety, more particularly in FIGs. 3A-3H and accompanying description in WO13174380A1, which is hereby incorporated by reference. The 2LUPS process is alternatively or additionally described in the article "Multifilamentary coated conductors for ultra-high magnetic field applications", Anders Christian Wulff et aL, Supercond. Sci. TechnoL 34 (2021) 053003, which is hereby incorporated by reference in entirety, such as in particular in section 4.2.

[0235] FIG. 11 shows a zoom view of FIG. 10. FIG. 12 shows a single filament 1242 etched out, but with a remaining part 1246 of substrate, where a width (i.e., a size in a horizontal dimension left-right, i.e., in the plane of the paper, being ca. 500 pm, i.e., the image depicts a ca. 500 pm wide filament 1242 with CC stack). A thickness (dimension up-down in the plane of the paper) of the filament is ca. 80 pm. FIG. 12 could be seen as corresponding to the schematic illustrations in FIG. 7 and / or subfigure (h) of FIG.9.

[0236] FIG. 13 shows I / V setup for characterizing superconducting performance of a filament 1342 in liquid nitrogen, including current lead 1360 and voltage tap 1362. The dimensions can be retrieved from the ruler 1364 (with numbers being centimeters and the distance between adjacent smaller line markings being 1 mm). The washer 1366 is substantially circular, which indicates that the scale provided by the ruler applies both horizontally and vertically.

[0237] FIG. 14 shows the I / V setup of FIG. 13 immersed in liquid nitrogen. An electrical current ramping test with the filament immersed in liquid nitrogen while measuring the voltage drop between the contacts points showed no transition to normal conducting at more than 3 A at zero applied magnetic field and 77 K. With a width of estimated 500 pm and a total thickness of estimated 80 pm of the substrate and CC stack, an engineering current density of 9375 A / cm2at zero applied magnetic field and 77 K is estimated. A reference coated conductor sample had a recorded average Ic = 97 A at zero applied magnetic field at 77 K for a 4 mm tape width corresponding to an expected Ic for the 500 pm wide filament of more than 12 A. It is noted that an engineering current density could be improved with a factor of at least 3-5 with another choice of superconducting material. Furthermore, a (such as another) factor of at least 2 could be achieved by reducing a thickness of the substrate, such as by continuing for a longer time the etch removing the substrate from the backside (such as giving substrate being, e.g., less than half the thickness of the present substrate), such as a factor of approximately 20 by leaving only a small part of the substrate (about 4 pm in thickness), such as estimated with a situation where the substrate is etched away completely. Taking both the possible improvement in materials and reduced substrate thickness into account, an engineering current density of approximately 1,8 MA / cm2may be arrived at zero magnetic field and 77 K. It is also noted that additionally higher current densities at expected at decreased operating temperatures, such as 50 K, such as 30 K, such as 20 K or 4.2 K. In contrast, lower current densities are expected at increased applied magnetic fields.

[0238] FIG. 15 shows Scanning Electron Microscope (SEM) image (view: normal to tape flat surface) of 3D etched Hastelloy substrate. FIG. 15 could be seen as corresponding to the schematic illustration in FIG. 3 (except for the undercut) and / or subfigure (d) of FIG. 9 (except for the remaining masking material). FIG. 16 shows Scanning Electron Microscope image (view: angled) of 3D etched and Focused Ion Beam milled 3D etched Hastelloy substrate. The figure shows a protrusion (or elongated "hill") formed between two grooves (on the left and right side of the protrusion), where the protrusion has a width (left-right in the plane of the paper) of ca. 18 pm. FIG. 16 (except for the Focused Ion Beam milled cut-out) could be seen as corresponding to the schematic illustrations in FIG. 3 (except for the undercut) and / or subfigure (d) of FIG. 9 (except for the remaining masking material).

[0239] FIG. 17 shows Scanning Electron Microscope image of Focused Ion Beam milled 3D etched Hastelloy substrate with CC stack in the form of a substrate 1771 being Hastelloy C276, a 1- 2 pm thick buffer layer 1772 being Yttria-stabilized zirconia (YSZ) with 50 nm Cerium Oxide (as in Wulff et al. 2015, Supercond. Sci. TechnoL 28 (2015) 072001), a 1-2 pm thick layer 1773 of Yttrium barium copper oxide (YBCO) layer and a silver layer 1774 being 1-2 pm thick. All thicknesses refer to a dimension in the vertical / up-down direction in the figure, i.e., orthogonal to the plane of the respective layers. Width of the superconducting filament is ca. 25 pm. FIG. 17 could be seen as corresponding to the schematic illustrations in FIG. 4 (except for the undercut) and / or subfigure (e) of FIG. 9.

[0240] FIG. 18 shows a collage of two images of filaments (with the filaments in the image on the right side being held by a human hand), where a substrate has been etched from the backside so as to remove a connection between the filaments through the substrate in a plane orthogonal to a longitudinal direction of the substrates. A length of the filaments, such as the free portion of the filaments, spans several centimeters. The (full) width of the substrate is 4 mm (such as the full width shown in the up-down direction in the upper right corner of the left sub-figure).

[0241] FIG. 19 shows the result of twisting a plurality of filaments wherein the plurality of filaments is twisted around their common axis and wherein each filament is thereby also twisted around its own axis (by an angular amount corresponding to the twisting of the plurality of filaments) thereby providing a structure comprising a plurality of twisted filaments wherein each filament is twisted around its own axis and furthermore has a helical shape with a center axis within one or more other helical shaped filaments, and wherein a wire has been provided by providing a core. Kapton® tape is provided in each end, and a distance between the Kapton® tapes is 5 cm.

[0242] FIG. 20 shows a cross-sectional view of a strand 252, 2052 in a plane being parallel with a longitudinal direction of the strand, wherein the strand is a superconductor strand, comprising : a. A matrix 2060, b. A plurality of filaments 2056, wherein each filament is a superconductor filament, and wherein each filament is encircled by matrix material, wherein each of the filaments comprises a biaxially textured superconductor material, such as a coated conductor, and wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 50 mm. The matrix comprises copper. Each filament comprises rare-earth barium copper oxide (REBCO). A filament length 2004, such as a maximum dimension in a longitudinal direction of each filament, such as along the strand, is equal to or larger than 1 m. A strand length 2002, such as a maximum dimension in a longitudinal direction of the strand, such as along the strand, is equal to or larger than 10 m. Filaments within the strand are stagged and partially overlapping longitudinally with respect to each other, such as wherein the strand comprises filaments (such as the two middle filaments in the lower half of the depicted strand) both having parts at the same longitudinal position 2006 of the strand and at different positions 2008, 2010 of the strand (such as each filament extending beyond the overlapping position in each their direction).

[0243] FIG. 21 shows a cross-sectional view of a strand 252, 2052 in a plane being orthogonal to a longitudinal (x-)direction of the strand, wherein an aspect ratio of each filament 2056 in a cross-sectional plane orthogonal to a longitudinal axis of the filament is equal to or less than 100: 1. For each filament there exists a fictitious closed line (indicated with the dashed lines) in a cross-sectional plane orthogonal to a longitudinal axis of the strand, which line is entirely in matrix material and which line is encircling said filament, such as completely encircling, such as encircling around 360°, and wherein the other filaments within the plurality of filaments are outside of said closed line. In a cross-sectional plane orthogonal to a longitudinal axis of the strand, geometrical centres of the filaments are distributed in both dimensions, such as both in a y- and a z-direction. A density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 400 filaments pr. square centimetre.

[0244] FIG. 22 shows method 2200 for manufacturing a strand 252, 2052 according to the first aspect, said method comprising : a. Providing the plurality of filaments, comprising : i. Providing 2262 a substrate, optionally including one or more buffer layers,

[0245] II. Coating 2264 said substrate with superconducting material, so as to provide the biaxially textured superconductor material on the substrate, iii. Segmenting 2266, such as segmenting longitudinally, said substrate and the superconductor material so as to form the plurality of filaments, b. Torsionally twisting 2268 each filament, c. Providing 2270 at least some matrix material so as to encircle each filament with matrix material, wherein providing at least some matrix material optionally takes place before or after arranging the filaments in the strand, d. Optionally prior to or subsequent to torsionally twisting each filament, arranging 2272 the filaments in the strand, and e. Staggering 2274 the plurality of filaments prior to arranging the filaments in the strand.

[0246] FIG. 23 shows a part of a filament 2356, namely a part spanning one twist pitch (length) 2376.

[0247] Example B

[0248] Apply a metallic capping material, such as copper, onto superconducting filament with a length of e.g. 200 mm, or longer, such 500 mm, and a total thickness of e.g. 0.050 mm including metallic substrate (e.g. 0.045 mm thickness), buffer stack comprising e.g. a combination of MgO, CeO, GdZrzO? or YSZ, with e.g. a final layer of CeO, a superconducting REBCO layer (1-5 pm in thickness), protective Ag coating (1-2 pm in thickness). It is important that the REBCO layer is oxygenated prior to metal capping coating with for example copper to provide a superconducting structure. The copper capping can be applied by electroplating using a wet chemical bath with a standard solution consisting of copper sulfate, sulfuric acid and chloride. It does not allow for post-oxygenation of the superconducting layer.

[0249] Step 1 : Copper plating in cathodic ("-"-electrical termination on filament) setup. Solution example 24 g CuSCU, 6 g H2SO4, HCI 25 pL and 100 ml ion-free water. Operation temperature = 20-30 °C.

[0250] Step 2: Mount the superconducting filament with a length of 200 mm, or longer, such 500 mm, horizontally in a poly-propylene tank filled with the copper plating solution and place counter electrode (anode with "-(-"-electrical termination on anode material), such as electrolytic copper (ETP copper), phosphorous copper (DXP copper) or copper oxygen free (OF copper). Step 3: Apply a current density = 10-100 mA / cm2for 3-15 min to deposit several pm's of copper.

[0251] Step 4: Rinse the copper coated filament with water.

[0252] Step 5: Perform a torsional twist of the filament by, first, mechanically anchoring the filament to a rigid fixed body, such as a wall, then secondly, apply a twist to the filament by rotating the filament around its torsional axis. Continue the twisting until the desired twist pitch has been obtained, such a 10 mm.

[0253] Step 6: Assemble a number of twisted filaments, such as three pieces, by placing them in parallel next to each other, so as to make them substantially physically touch each other along the length of a single filament. Additional transposition and wrapping between adjacent filaments can be optionally applied.

[0254] Step 7 : Repeat 'Step 2 - 3' and continue the plating until the three filaments are completely connected into a solid matrix, such as for 15-30 min, to form a strand with three filaments joined in a solid metallic matrix.

[0255] Step 8: Optionally, more filaments can be joined into strands with a higher number of filaments, and multiple strands can be joined to form larger cable structures.

[0256] FIG. 24 shows a view of three individually twisted filaments arranged in a strand. Each filament was first torsionally twisted by applying a torque with a vector along the longitudinal direction. Subsequently each filament was electrochemically coated (electroplated) with Cu for a period of 15 minutes. The filaments were then bundled and further electrochemically Cu coated for 40 minutes, in order to substantially join these together.

[0257] FIG. 25 shows a closeup view of the result of twisting, coating, arranging and joining three filaments. It is observed that the individual filaments are joined by a common matrix of Cu.

[0258] FIG. 26 shows a cross-sectional view of two Cu coated filaments forming a strand in a plane being orthogonal to a longitudinal direction of the strand. The superconductor stacks and metallic substrates are observed within each filament, joined by a Cu matrix.

[0259] FIG. 27 shows a cross-sectional view of three Cu coated filaments forming a strand in a plane being orthogonal to a longitudinal direction of the strand. The superconductor stacks and metallic substrates are observed within each filament, joined by a Cu matrix. Although the present invention has been described in connection with the specified embodiments, it should not be construed as being in any way limited to the presented examples. The scope of the present invention is set out by the accompanying claim set. In the context of the claims, the terms "comprising" or "comprises" do not exclude other possible elements or steps. Also, the mentioning of references such as "a" or "an" etc. should not be construed as excluding a plurality. The use of reference signs in the claims with respect to elements indicated in the figures shall also not be construed as limiting the scope of the invention. Furthermore, individual features mentioned in different claims, may possibly be advantageously combined, and the mentioning of these features in different claims does not exclude that a combination of features is not possible and advantageous.

Claims

CLAIMS1. A strand (252, 2052), wherein the strand is a superconductor strand, comprising : a. A matrix (2060), b. A plurality of filaments (2056), such as at least 3 or at least 10 or at least 20 filaments, wherein each filament is a superconductor filament, and wherein each filament is encircled by matrix material, wherein each of the filaments comprises a biaxially textured superconductor material, such as a coated conductor, and wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 50 mm, such as less than 40 mm, such as less than 30 mm, such as less than 20 mm, such as less than 18 mm, such as less than 16 mm, such as less than 15 mm, such as less than 14 mm, such as less than 12, mm, such as less than 10 mm, such as less than 8 mm, such as less than 5 mm, such as less than 4 mm, such as less than 3 mm, such as less than 2 mm, such as less than 1 mm.

2. The strand (252, 2052) according to claim 1, wherein an aspect ratio of each filament (2056) in a cross-sectional plane orthogonal to a longitudinal axis of the filament is equal to or less than 100: 1, such as equal to or less than 75: 1, such as equal to or less than 50: 1, such as equal to or less than 25: 1, such as equal to or less than 20: 1, such as equal to or less than 10: 1, such as equal to or less than 5: 1, such as equal to or less than 2: 1.

3. The strand (252, 2052) according to any of the preceding claims, wherein for each filament there exists a fictitious closed line in a cross-sectional plane orthogonal to a longitudinal axis of the strand, which line is entirely in matrix material and which line is encircling said filament, such as completely encircling, such as encircling around 360°, and wherein the other filaments within the plurality of filaments are outside of said closed line.

4. The strand (252, 2052) according to any of the preceding claims, wherein in a cross- sectional plane orthogonal to a longitudinal axis of the strand, geometrical centres of the filaments are distributed in both dimensions, such as wherein a maximum distance between geometrical centres of filaments in any direction is at least 10 %, such as at least 25 %, such as at least 50 %, such as at least 75 %, such as at least 90 %, of a maximum distance between geometrical centres in the orthogonal direction.

5. The strand (252, 2052) according to any of the preceding claims, wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper.

6. The strand (252, 2052) according to any of the preceding claims, wherein each filament comprises superconducting material, which comprises, such as consists of, rare-earth barium copper oxide.

7. The strand (252, 2052) according to any of the preceding claims, wherein each filament has, such as in a cross-sectional plane orthogonal to a longitudinal direction of the filament, a largest dimension in a direction being orthogonal to a longitudinal direction of the filament, of less than 1 mm, such as less than 800 pm, such as less than 750 pm, such as less than 600 pm, such as less than 500 pm, such as less than 400 pm, such as less than 300 pm, such as less than 250 pm, such as less than 200 pm, such as less than 150 pm, such as less than 100 pm, such as less than 80 pm, such as less than 60 pm, such as less than 50 pm, such as less than 40 pm, such as less than 30 pm, such as less than 25 pm, such as less than 20 pm, such as less than 10 pm.

8. The strand (252, 2052) according to any of the preceding claims, wherein a length, such as a maximum dimension in a longitudinal direction of each filament, such as along the strand, is equal to or larger than 1 m, such as equal to or larger than 2 m, such as equal to or larger than 3 m, such as equal to or larger than 5 m, such as equal to or larger than 8, such as equal to or larger than 10 m, such as equal to or larger than 100 m, such as equal to or larger than 1 km, such as equal to or larger than 10 km, such as equal to or larger than 100 km, such as equal to or larger than 1000 km.

9. The strand (252, 2052) according to any of the preceding claims, wherein a length, such as a maximum dimension in a longitudinal direction of the strand, such as along the strand, is equal to or larger than 1 m, such as equal to or larger than 2 m, such as equal to or larger than 3 m, such as equal to or larger than 5 m, such as equal to or larger than 8, such as equal to or larger than 10 m, such as equal to or larger than 100 m, such as equal to or larger than 1 km, such as equal to or larger than 10 km, such as equal to or larger than 100 km, such as equal to or larger than 1000 km.

10. The strand (252, 2052) according to any of the preceding claims, wherein filaments within the strand are partially overlapping longitudinally with respect to each other, such as wherein the strand comprises filaments both having parts at the same longitudinal position of the strand and at different positions of the strand.

11. The strand (252, 2052) according to any of the preceding claims, wherein an engineering current density JE of the strand at a temperature of 77 Kelvin and at zero applied magnetic field is at least 1500 A / cm2, such as at least 2000 A / cm2, such as at least 3000 A / cm2, such as at least 5000 A / cm2, such as at least 10000 A / cm2, such as at least 20000 A / cm2, such as at least 40000 A / cm2, such as at least 70000 A / cm2and / or an engineering current density JE of the strand at a temperature of 20 Kelvin and in a magnetic field applied along any direction, perpendicular to the strand, is at least 7500 A / cm2, such as at least 10000 A / cm2, such as at least 15000 A / cm2, such as at least 25000 A / cm2, such as at least 50000 A / cm2, such as at least 100000 A / cm2, such as at least 200000 A / cm2, such as at least 350000 A / cm2.

12. The strand (252, 2052) according to any of the preceding claims, wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 400 filaments pr. square centimetre, such as at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre.

13. The strand (252, 2052) according to any of the preceding claims, wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 40 mm.

14. The strand (252, 2052) according to any of the preceding claims, wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 4 mm.

15. The strand (252, 2052) according to any of the preceding claims, wherein an aspect ratio of each filament (2056) in a cross-sectional plane orthogonal to a longitudinal axis of the filament is equal to or less than 10: 1, such as equal to or less than 5: 1, such as equal to or less than 2:1.

16. The strand (252, 2052) according to any of the preceding claims, wherein for each filament there exists a fictitious closed line in a cross-sectional plane orthogonal to a longitudinal axis of the strand, which line is entirely in matrix material and which line is encircling said filament, such as completely encircling, such as encircling around 360°, and wherein the other filaments within the plurality of filaments are outside of said closed line, and wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper.

17. The strand (252, 2052) according to any of the preceding claims, wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre.

18. The strand (252, 2052) according to any of the preceding claims, wherein for each filament there exists a fictitious closed line in a cross-sectional plane orthogonal to a longitudinal axis of the strand, which line is entirely in matrix material and which line is encircling said filament, such as completely encircling, such as encircling around 360°, and wherein the other filaments within the plurality of filaments are outside of said closed line, wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper, and wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 400 filaments pr. square centimetre, such as at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre.

19. The strand (252, 2052) according to any of the preceding claims, wherein in a cross-sectional plane orthogonal to a longitudinal axis of the strand, geometrical centres of the filaments are distributed in both dimensions, such as wherein a maximum distance between geometrical centres of filaments in any direction is at least 10 %, such as at least 25 %, such as at least 50 %, such as at least 75 %, such as at least 90 %, of a maximum distance between geometrical centres in the orthogonal direction, and wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper.

20. The strand (252, 2052) according to any of the preceding claims, wherein an engineering current density JE of the strand at a temperature of 77 Kelvin and at zero applied magnetic field is at least 40000 A / cm2, such as at least 70000 A / cm221. The strand (252, 2052) according to any of the preceding claims, wherein an engineering current density JE of the strand at a temperature of 20 Kelvin and in a magneticfield applied along any direction, perpendicular to the strand, is at least 7500 A / cm2, such as at least 10000 A / cm2, such as at least 15000 A / cm2, such as at least 25000 A / cm2, such as at least 50000 A / cm2, such as at least 100000 A / cm2, such as at least 200000 A / cm2, such as at least 350000 A / cm2.

22. The strand (252, 2052) according to any of the preceding claims, wherein each of the filaments is torsionally twisted with a torsional twist pitch being less than 40 mm, such as less than 30 mm, such as less than 20 mm, such as less than 18 mm, such as less than 16 mm, such as less than 15 mm, such as less than 14 mm, such as less than 12, mm, such as less than 10 mm, such as less than 8 mm, such as less than 5 mm, such as less than 4 mm, such as less than 3 mm, such as less than 2 mm, such as less than 1 mm, and wherein in a cross-sectional plane orthogonal to a longitudinal axis of the strand, geometrical centres of the filaments are distributed in both dimensions, such as wherein a maximum distance between geometrical centres of filaments in any direction is at least 10 %, such as at least 25 %, such as at least 50 %, such as at least 75 %, such as at least 90 %, of a maximum distance between geometrical centres in the orthogonal direction.

23. The strand (252, 2052) according to any of the preceding claims, wherein each of the superconductor filaments comprises, such as consists of, superconductor material and one or more adjacent buffer layers and / or a substrate.

24. The strand (252, 2052) according to any of the preceding claims, wherein each of the superconductor filaments comprises, such as consists of, superconductor material and a substrate.

25. The strand (252, 2052) according to any of the preceding claims, wherein the twist Tw for a given filament or a part of a filament may be given by:wherein t is the (local) torsion ts, and ds is a spatial segment along the length of the filament or part of the filament.

26. The strand (252, 2052) according to any of the preceding claims, wherein torsional twist pitch is the distance along the length of a twisted filament when the total angle of twistis 360°, such as the distance along a filament or a part of a filament for which a twist Tw, optionally wherein twist Tw is determined according to claim 25, is 1.

27. The strand (252, 2052) according to any of the preceding claims, wherein each filament is individually twisted.

28. The strand (252, 2052) according to any of the preceding claims, wherein the matrix material is comprising, such as consisting of, a metallic material.

29. The strand (252, 2052) according to any of the preceding claims, wherein for one or more cross-sectional planes orthogonal to a longitudinal axis of the strand, there exists one or more pairs of filaments within the strand, wherein a first filament within the pair is the nearest neighbor of a second filament within the pair, and wherein a minimum angle between a first line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a first filament within said pair, and a second line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a second filament within said pair, is at least 10°, such as at least 15°, such as at least 20°, such as at least 25°, such as at least 30°, such as at least 35°, such as at least 40°, such as at least 45°, such as at least 50°, such as at least 55°, such as at least 60°, such as at least 65°, such as at least 70°, such as at least 75°, such as at least 80°, such as at least 85°, such as 90°.

30. The strand (252, 2052) according to any of the preceding claims, wherein for one or more cross-sectional planes orthogonal to a longitudinal axis of the strand, there exists one or more pairs of filaments within the strand, wherein a first filament within the pair is the nearest neighbor of a second filament within the pair, and wherein a minimum angle between a first line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a first filament within said pair, and a second line within said cross-sectional plane defining an orientation of the biaxial ly textured superconductor material of a second filament within said pair, is at least 35°, such as at least 40°, such as at least 45°, such as at least 50°, such as at least 55°, such as at least 60°, such as at least 65°, such as at least 70°, such as at least 75°, such as at least 80°, such as at least 85°, such as 90°.

31. A cable comprising a plurality of strands according to any of the preceding claims, such as a. wherein each strand is individually torsionally twisted, b. wherein each strand is wrapped around an axis, such as an axis of the cable and / or an axis outside of the strand, and / or c. wherein the strands within the plurality of strands are transposed with respect to each other.

32. A method (2200) for manufacturing a strand (252, 2052) according to any of claims 1-30, said method comprising : a. Providing the plurality of filaments, b. Torsionally twisting (2268) each filament, c. Providing (2270) at least some matrix material so as to encircle each filament with matrix material, wherein providing at least some matrix material optionally takes place before or after arranging the filaments in the strand, and d. Optionally prior to or subsequent to torsionally twisting each filament, arranging (2272) the filaments in the strand.

33. A method according to claim 32, wherein the method further comprises staggering the plurality of filaments prior to arranging the filaments in the strand, such as wherein staggering comprises longitudinally displacing one or more filaments with respect to one or more other filaments while maintaining a longitudinal overlap, such as wherein the filaments being longitudinally displaced with respect to each other originate from the same substrate, such as the same coated substrate.

34. A method according to any of claims 32-33, wherein a density of filaments in the strand in a cross-sectional plane orthogonal to a longitudinal axis of the strand is at least 500 filaments pr. square centimetre, such as at least 750 filaments pr. square centimetre, such as at least 1000 filaments pr. square centimetre, such as at least 5000 filaments pr. square centimetre, such as at least 10000 filaments pr. square centimetre.

35. A method according to any of claims 32-34, said method comprising : a. subsequent to torsionally twisting each filament, arranging (2272) the filaments in the strand.

36. A method according to any of claims 32-35,wherein providing at least some matrix material takes place before arranging the filaments in the strand, and wherein the matrix comprises copper, such as a copper alloy, such as at least 50 % w / w copper, such as consists of copper.

37. A method according to any of claims 32-36, wherein each filament is individually twisted.

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