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Papers by Damian Hampshire

Research paper thumbnail of Computational Simulations Using Time-Dependent Ginzburg–Landau Theory for Nb–Ti-Like Microstructures

IEEE Transactions on Applied Superconductivity, 2022

Simulations based on time-dependent Ginzburg-Landau theory are employed to determine the critical... more Simulations based on time-dependent Ginzburg-Landau theory are employed to determine the critical current for a model system which represents a Nb-Ti-like pinning landscape at low drawing strain. The system consists of ellipsoids of normal metal, with dimensions 60ξ × 3ξ × 3ξ, randomly distributed throughout the superconducting bulk with their long axes parallel to the applied current and perpendicular to the field. These preciptates represent the α α α-Ti elongated precipitates which act as strong pinning centres in Nb-Ti alloys. We present the volume pinning force density as a function of field across the entire range of precipitate volume fractions and find that optimised material in our model system occurs at 32 vol.% ppt., whereas in real materials the optimum occurs at 25 vol.% ppt. The maximum pinning force density in our simulations is slightly higher (5.4 × 10 −3 JDBc2 vs. 17 GN•m −3 = 4.5 × 10 −3 JDBc2) and occurs at a lower reduced field (0.2Bc2 vs. 0.5Bc2) than in real materials. We conclude that the broad features of Nb-Ti-like systems are captured in our model, but that the details of the precipitate pinning mechanism are not yet included properly.

Research paper thumbnail of Critical Current Densities through Josephson Junctions in Low Magnetic Fields

IEEE Transactions on Applied Superconductivity, 2022

Understanding the properties of grain boundaries in polycrystalline superconductors is essential ... more Understanding the properties of grain boundaries in polycrystalline superconductors is essential for optimizing their critical current density. Here, we provide computational simulations of 2D Josephson junctions (JJs) in low magnetic fields using time-dependent Ginzburg-Landau theory, since they can be considered a proxy for a grain boundary between two grains. We present data for junctions with a wide range of superconducting electrodes of different Ginzburg-Landau parameter (κ) values and geometries, as well as normal barriers with different strengths of pair-breaking-characterized by the thickness of the junction and the junction condensation parameter (αn). We describe our results using analytic solutions, and hence provide a detailed description of Josephson junctions in low fields up to that required for a single fluxon to penetrate the junction.

Research paper thumbnail of Supporting data for: Superconducting and mechanical properties of low-temperature solders for joints

All large superconducting applications require electrical connections between superconductors or ... more All large superconducting applications require electrical connections between superconductors or between superconductors and other metallic parts of the systems. Such connections are essential components for these applications and are usually made by melting the solder (or soft soldering). In general, the melting point, electrical resistivity, mechanical and wetting properties and toxicity are all important criteria when choosing the best solder for a specific application. If the solder itself is superconducting under the operating conditions of the application then there is also the possibility of extremely low resistance joints. In this work we report on the superconducting properties of six low melting point solders: Bi49Pb18In21Sn12 (Cerrolow 136), Pb20Sn34Bi46, Pb20Sn60Bi20, In52Sn48, Pb38Sn62 and Pb57Bi36Sb7 and the mechanical properties of three of the six solders (Pb38Sn62, Cerrolow 136 and Pb20Sn34Bi46). We have found that all the solders except Pb38Sn62 and In52Sn48 have r...

Research paper thumbnail of Weakly-Emergent Strain-Dependent Properties of High Field Superconductors

Scientific Reports, 2019

All superconductors in high field magnets operating above 12 T are brittle and subjected to large... more All superconductors in high field magnets operating above 12 T are brittle and subjected to large strains because of the differential thermal contraction between component parts on cool-down and the large Lorentz forces produced in operation. The continuous scientific requirement for higher magnetic fields in superconducting energy-efficient magnets means we must understand and control the high sensitivity of critical current density Jc to strain ε. Here we present very detailed Jc(B, θ, T, ε) measurements on a high temperature superconductor (HTS), a (Rare−Earth)Ba2Cu3O7−δ (REBCO) coated conductor, and a low temperature superconductor (LTS), a Nb3Sn wire, that include the very widely observed inverted parabolic strain dependence for Jc(ε). The canonical explanation for the parabolic strain dependence of Jc in LTS wires attributes it to an angular average of an underlying intrinsic parabolic single crystal response. It assigns optimal superconducting critical parameters to the unstr...

Research paper thumbnail of Chevrel phases

Handbook of Superconducting Materials

Page 1. Chevrel phases 4/ Dl.¿ Chevrel phases Damián P Hampshire Dl.5.1 Introduction Chevrel phas... more Page 1. Chevrel phases 4/ Dl.¿ Chevrel phases Damián P Hampshire Dl.5.1 Introduction Chevrel phase superconductors are a class of materials that have generated enormous interest in the superconductivity community. There ...

Research paper thumbnail of Relationship between then-value and critical current in Nb3Sn superconducting wires exhibiting intrinsic and extrinsic behaviour

Superconductor Science and Technology, 2005

The relationship between the n-value and critical current (I C) is investigated for six different... more The relationship between the n-value and critical current (I C) is investigated for six different ITER-candidate Nb 3 Sn wires characterized as a function of magnetic field (B 28 T), temperature (4.2 K T 12 K) and intrinsic axial strain (−1% ε I +0.4%). For the five wires exhibiting intrinsic behaviour, n(I C) can be parameterized by a modified power law of the form n = 1 + r I s C , where s is a constant with a value of 0.41 ± 0.03. The parameter r decreases as the magnitude of the intrinsic strain increases and is a relatively weak function of temperature. For one of the wires, the n-value saturates at high critical currents (low magnetic fields), characteristic of extrinsic filament nonuniformities.

Research paper thumbnail of Properties of helical springs used to measure the axial strain dependence of the critical current density in superconducting wires

Superconductor Science and Technology, 2005

The use of helical (Walters) springs is an effective technique for measuring the critical current... more The use of helical (Walters) springs is an effective technique for measuring the critical current density (J C) of superconducting wires in high fields as a function of both compressive and tensile axial strains. We report J C versus strain measurements for Nb 3 Sn wires on a number of helical springs of different materials and geometries, together with results from finite element analysis (FEA) of these systems. The critical current density, n-value and effective upper critical field data are universal functions of intrinsic strain (to within ±5%) for measurements on four different spring materials. The strains on the wire due to the differential thermal contraction of the spring are equivalent to the applied mechanical strains and hence only produce a change in the parameter ε M (the applied strain at the peak in J C). Variable-strain J C data for springs having turns with rectangular and tee-shaped cross-sections (and hence different transverse strain gradients across the wire) show good agreement when the strain-gauge calibration data are corrected to give the strain at the midpoint of the wire. The correction factors can be obtained from FEA or analytical calculations. Experimental and FEA results show that the applied strain varies periodically along the wire with an amplitude that depends on the spring material and geometry. We suggest that Ti-6Al-4V springs with an integer number of turns and optimized tee-shaped cross-sections enable highly accurate measurements of the intrinsic properties of superconducting wires.

Research paper thumbnail of Scaling law for the strain dependence of the critical current in an advanced ITER Nb3Sn strand

Superconductor Science and Technology, 2007

... superconducting wires David MJ Taylor and Damian P Hampshire Superconductivity Group, Physics... more ... superconducting wires David MJ Taylor and Damian P Hampshire Superconductivity Group, Physics Department, Durham University, Durham DH1 3LE, UK and Grenoble High Magnetic Field Laboratory, BP 166, 38042 Grenoble Cedex 9, France ...

Research paper thumbnail of Critical current density of superconductors as a function of strain in high magnetic fields

Cryogenics, 1998

A probe has been designed and built to measure the critical current density (J C) of short superc... more A probe has been designed and built to measure the critical current density (J C) of short superconducting wires and tapes as a function of strain (⑀) in small bore high field magnets. The probe can measure currents of up to 100 Amps and strains of ± 1.0% on both low and high temperature superconductors. Measurements can be made in our 40 mm bore 17 T high magnetic field system in pumped cryogens. Strain is measured using commercial strain gauges pasted directly onto the samples. A Agsheathed Bi 2 Sr 2 Ca 2 Cu 3 O X tape has been measured at 4.2 K in magnetic fields up to 12 T. J C is hysteretic in high magnetic fields and is weakly dependent on magnetic field and tensile strain up to ෂ 0.29%. Beyond ෂ 0.29% strain, the filaments break and J C drops precipitously. Results are also presented for the effect of tensile and compressive strain for a 0.37 mm diameter Nb 3 Sn wire at 4.2 K and 2.9 K from 10 T up to 14 T. The data confirm that a simple scaling law that includes the upper critical field (B C2 (T,⑀)) and the reduced field (B/B C2 (T,⑀)) alone cannot accurately describe the field, temperature and strain dependence of J C .

Research paper thumbnail of Weak emergence in the angular dependence of the critical current density of the high temperature superconductor coated conductor REBCO

Superconductor Science and Technology

Research paper thumbnail of Critical current density of coated conductors determined from rescaled magnetic moment at temperatures close to 77 K

Physica C: Superconductivity and its Applications

The possibility of rescaling (or calibrating) of the magnetization results to predict the transpo... more The possibility of rescaling (or calibrating) of the magnetization results to predict the transport critical current density (J c) of commercial coated conductors (REBCO tapes) is discussed from both the experimental and theoretical point of view. For this purpose the critical current density in tapes from three different producers was investigated by means of transport and magnetization measurements, in perpendicular magnetic fields of 0.25 T-2 T at temperatures 65 K-77 K. Two kinds of samples were tested in the magnetization measurementssquare samples 2 × 2 mm 2 cut from the central parts of the tapes and elongated rectangular samples of the full tape width (4 mm nominally) and 8 mm length. The transport measurements were performed on full-width samples in a subcooled liquid nitrogen bath. The presented results show that it is possible to empirically rescale the measured magnetization data on the basis of a single transport measurement, achieving the overall accuracy of the transport J c prediction between 4% and 10% for different tested tapes. Simple theoretical justification and analysis of the empirical scaling is presented, based on the critical state model with the power law currentvoltage relation considered to account for different level of electric field in the transport and magnetization measurements.

Research paper thumbnail of The Biaxial Strain Dependence of <formula> <tex>$J_C$</tex> </formula> of a (RE)BCO Coated Conductor at 77 K in Low Fields

IEEE Transactions on Applied Superconductivity

Recently, we designed and commissioned a 'crossboard' sample holder which can apply biaxial strai... more Recently, we designed and commissioned a 'crossboard' sample holder which can apply biaxial strains in the plane of a (RE)BCO coated conductor. It allows us to measure the critical current density for arbitrary combinations of x-and y-strain. Understanding the in-field, in-plane, biaxial strain dependence of a tape's (, ,) is crucial for applications such as CORC® or Roebel cables, as the cables are subjected to multiaxial strains during manufacturing and operation. Here we present experimental data for (, ,) on a SuperPower SCS4050 APC tape in magnetic fields up to 0.7 T, at 77 K. We also outline a theoretical model for the biaxial strain dependence of and use it to parameterise our data and show that the fraction of A-domains and B-domains are roughly equal (= 0.49 ± 0.03) and that the strain sensitivity of the critical temperature is 1.8 ± 0.1 K%-1 and-1.3 ± 0.1 K%-1 along their a-and b-axes respectively, for all the domains in this (RE)BCO tape. For the first time, we show both parabolic and linear strain dependencies of in a single tape by changing the angle between the applied strain direction and the twin boundaries in the (RE)BCO layer.  Index Terms-Critical current, strain measurement, 2G HTS conductors, cuprates.

Research paper thumbnail of 3D Properties in (RE)BCO Tapes Measured in Fields up to 35 T

IEEE Transactions on Applied Superconductivity

The full-text may be used and/or reproduced, and given to third parties in any format or medium, ... more The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.

Research paper thumbnail of Modelling the Critical Current of Polycrystalline Su-perconducting Films in High Magnetic Fields

IEEE Transactions on Applied Superconductivity

We have performed simulations using time-dependent Ginzburg-Landau theory on a 2D polycrystalline... more We have performed simulations using time-dependent Ginzburg-Landau theory on a 2D polycrystalline system where grain boundaries are modelled as narrow regions with a locally reduced critical temperature (Tc). For the small system sizes investigated, we find that the critical current density (Jc) is not sensitive to changes in grain size until the grain size is sufficiently small that it limits the average superparticle density in the system through the proximity effect. Furthermore, once Tc in the boundary regions is sufficiently low relative to the surrounding superconductor that grain boundary regions act as preferred channels for flux flow, further reductions in the boundary Tc only weakly reduce Jc across the superconductor.

Research paper thumbnail of Could high H98-factor commercial tokamak power plants use Nb-Ti toroidal field coils?

IEEE Transactions on Applied Superconductivity

Elizabeth (2019) 'Could high H98-factor commercial tokamak power plants use Nb-Ti toroidal eld co... more Elizabeth (2019) 'Could high H98-factor commercial tokamak power plants use Nb-Ti toroidal eld coils?', IEEE transactions on applied superconductivity., 29 (5). p. 4200405.

Research paper thumbnail of A derivation of Maxwell's equations using the Heaviside notation

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Maxwell's four differential equations describing electromagnetism are among the most famous e... more Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E -fields and B -fields and that Faraday's Law can be deriv...

Research paper thumbnail of A new apparatus for measuring the critical currents of hard type-II superconductive wires and tapes in high fields as a function of temperature throughout their superconducting phase

Journal of Physics E: Scientific Instruments

Describes an update of a earlier apparatus which measures the critical current of superconducting... more Describes an update of a earlier apparatus which measures the critical current of superconducting wires and tapes as a function of magnetic field and temperature. The critical element is a compact probe of 25 mm diameter which can be inserted into the bore of one of the several high-field magnets. The design and critical features of the probe which incorporates

Research paper thumbnail of A detailed investigation of the E-J characteristic and the role of defect motion within the flux-line lattice for high-current-density, high-field superconducting compounds with particular reference to data on NbSN throughout its entire field-temperature phase space

Journal of Physics C: Solid State Physics

A detailed investigation of the E-J characteristic and the role of defect motion within the flux-... more A detailed investigation of the E-J characteristic and the role of defect motion within the flux-line lattice for highcurrent-density , high-field superconducting compounds with particular reference to data on Nb,Sn throughout its entire field-temperature phase space

Research paper thumbnail of Critical currents and the critical state in superconductors with magnetic ions

Physica C: Superconductivity

The critical state model is used to derive equations that relate the additional magnetic moment (... more The critical state model is used to derive equations that relate the additional magnetic moment (AM) produced by the flux pinning to the critical current density (J,) measured in transport measurements. The equations derived for conventional superconductors can be used for superconductors that contain magnetic ions, if AM is replaced by A M/(1 + ,$(H)) where x'(H) is the differential susceptibility. In the critical state, the field gradient has contributions from both the macroscopic supercurrents and the Amperian currents from the magnetic ions. Magnetic measurements are sensitive to both contributions. Transport measurements only characterise the macroscopic supercurrents. For superconductors which contain rare-earth elements, the J, values calculated using hysteretic magnetisation measurements without including the term x'(H), can be in error by factors of-7. 0 1997 Elsevier Science B.V.

Research paper thumbnail of Design, fabrication and performance of a 1.29 T Bi-2223 magnet

Superconductor Science and Technology

The design and fabrication procedure of a laboratory-scale Bi-2223 tape superconducting magnet wi... more The design and fabrication procedure of a laboratory-scale Bi-2223 tape superconducting magnet with a bore of 40 mm and a maximum field of 1.29 T at 4.2 K is presented. The magnet comprises six resin impregnated double-wound pancakes of bore diameter 40 mm fabricated via the react-and-wind route. Critical current density (J c) measurements have been made as a function of magnetic field, angle and strain at 4.2 K and 77 K on short samples. In zero field, the critical current density for the superconducting cross-sectional area of the tape was 8.3 × 10 4 A cm −2 (4.2 K) and 1.18 × 10 4 A cm −2 (77 K). The electric field-current density characteristics of all the components of the coils when individually energized or with the whole magnet energized have been measured. Comparison between short sample measurements and performance of the magnet show that minimal additional damage occurred beyond the ∼20% that was produced by the bending strain during the wind-and-react fabrication procedure and the ∼10% variation of the long length J c of the tape. Sufficient detail is provided for the non-specialist to assess both the use of potential brittle superconducting tapes for magnet technology and to construct a laboratory-scale magnet.

Research paper thumbnail of Computational Simulations Using Time-Dependent Ginzburg–Landau Theory for Nb–Ti-Like Microstructures

IEEE Transactions on Applied Superconductivity, 2022

Simulations based on time-dependent Ginzburg-Landau theory are employed to determine the critical... more Simulations based on time-dependent Ginzburg-Landau theory are employed to determine the critical current for a model system which represents a Nb-Ti-like pinning landscape at low drawing strain. The system consists of ellipsoids of normal metal, with dimensions 60ξ × 3ξ × 3ξ, randomly distributed throughout the superconducting bulk with their long axes parallel to the applied current and perpendicular to the field. These preciptates represent the α α α-Ti elongated precipitates which act as strong pinning centres in Nb-Ti alloys. We present the volume pinning force density as a function of field across the entire range of precipitate volume fractions and find that optimised material in our model system occurs at 32 vol.% ppt., whereas in real materials the optimum occurs at 25 vol.% ppt. The maximum pinning force density in our simulations is slightly higher (5.4 × 10 −3 JDBc2 vs. 17 GN•m −3 = 4.5 × 10 −3 JDBc2) and occurs at a lower reduced field (0.2Bc2 vs. 0.5Bc2) than in real materials. We conclude that the broad features of Nb-Ti-like systems are captured in our model, but that the details of the precipitate pinning mechanism are not yet included properly.

Research paper thumbnail of Critical Current Densities through Josephson Junctions in Low Magnetic Fields

IEEE Transactions on Applied Superconductivity, 2022

Understanding the properties of grain boundaries in polycrystalline superconductors is essential ... more Understanding the properties of grain boundaries in polycrystalline superconductors is essential for optimizing their critical current density. Here, we provide computational simulations of 2D Josephson junctions (JJs) in low magnetic fields using time-dependent Ginzburg-Landau theory, since they can be considered a proxy for a grain boundary between two grains. We present data for junctions with a wide range of superconducting electrodes of different Ginzburg-Landau parameter (κ) values and geometries, as well as normal barriers with different strengths of pair-breaking-characterized by the thickness of the junction and the junction condensation parameter (αn). We describe our results using analytic solutions, and hence provide a detailed description of Josephson junctions in low fields up to that required for a single fluxon to penetrate the junction.

Research paper thumbnail of Supporting data for: Superconducting and mechanical properties of low-temperature solders for joints

All large superconducting applications require electrical connections between superconductors or ... more All large superconducting applications require electrical connections between superconductors or between superconductors and other metallic parts of the systems. Such connections are essential components for these applications and are usually made by melting the solder (or soft soldering). In general, the melting point, electrical resistivity, mechanical and wetting properties and toxicity are all important criteria when choosing the best solder for a specific application. If the solder itself is superconducting under the operating conditions of the application then there is also the possibility of extremely low resistance joints. In this work we report on the superconducting properties of six low melting point solders: Bi49Pb18In21Sn12 (Cerrolow 136), Pb20Sn34Bi46, Pb20Sn60Bi20, In52Sn48, Pb38Sn62 and Pb57Bi36Sb7 and the mechanical properties of three of the six solders (Pb38Sn62, Cerrolow 136 and Pb20Sn34Bi46). We have found that all the solders except Pb38Sn62 and In52Sn48 have r...

Research paper thumbnail of Weakly-Emergent Strain-Dependent Properties of High Field Superconductors

Scientific Reports, 2019

All superconductors in high field magnets operating above 12 T are brittle and subjected to large... more All superconductors in high field magnets operating above 12 T are brittle and subjected to large strains because of the differential thermal contraction between component parts on cool-down and the large Lorentz forces produced in operation. The continuous scientific requirement for higher magnetic fields in superconducting energy-efficient magnets means we must understand and control the high sensitivity of critical current density Jc to strain ε. Here we present very detailed Jc(B, θ, T, ε) measurements on a high temperature superconductor (HTS), a (Rare−Earth)Ba2Cu3O7−δ (REBCO) coated conductor, and a low temperature superconductor (LTS), a Nb3Sn wire, that include the very widely observed inverted parabolic strain dependence for Jc(ε). The canonical explanation for the parabolic strain dependence of Jc in LTS wires attributes it to an angular average of an underlying intrinsic parabolic single crystal response. It assigns optimal superconducting critical parameters to the unstr...

Research paper thumbnail of Chevrel phases

Handbook of Superconducting Materials

Page 1. Chevrel phases 4/ Dl.¿ Chevrel phases Damián P Hampshire Dl.5.1 Introduction Chevrel phas... more Page 1. Chevrel phases 4/ Dl.¿ Chevrel phases Damián P Hampshire Dl.5.1 Introduction Chevrel phase superconductors are a class of materials that have generated enormous interest in the superconductivity community. There ...

Research paper thumbnail of Relationship between then-value and critical current in Nb3Sn superconducting wires exhibiting intrinsic and extrinsic behaviour

Superconductor Science and Technology, 2005

The relationship between the n-value and critical current (I C) is investigated for six different... more The relationship between the n-value and critical current (I C) is investigated for six different ITER-candidate Nb 3 Sn wires characterized as a function of magnetic field (B 28 T), temperature (4.2 K T 12 K) and intrinsic axial strain (−1% ε I +0.4%). For the five wires exhibiting intrinsic behaviour, n(I C) can be parameterized by a modified power law of the form n = 1 + r I s C , where s is a constant with a value of 0.41 ± 0.03. The parameter r decreases as the magnitude of the intrinsic strain increases and is a relatively weak function of temperature. For one of the wires, the n-value saturates at high critical currents (low magnetic fields), characteristic of extrinsic filament nonuniformities.

Research paper thumbnail of Properties of helical springs used to measure the axial strain dependence of the critical current density in superconducting wires

Superconductor Science and Technology, 2005

The use of helical (Walters) springs is an effective technique for measuring the critical current... more The use of helical (Walters) springs is an effective technique for measuring the critical current density (J C) of superconducting wires in high fields as a function of both compressive and tensile axial strains. We report J C versus strain measurements for Nb 3 Sn wires on a number of helical springs of different materials and geometries, together with results from finite element analysis (FEA) of these systems. The critical current density, n-value and effective upper critical field data are universal functions of intrinsic strain (to within ±5%) for measurements on four different spring materials. The strains on the wire due to the differential thermal contraction of the spring are equivalent to the applied mechanical strains and hence only produce a change in the parameter ε M (the applied strain at the peak in J C). Variable-strain J C data for springs having turns with rectangular and tee-shaped cross-sections (and hence different transverse strain gradients across the wire) show good agreement when the strain-gauge calibration data are corrected to give the strain at the midpoint of the wire. The correction factors can be obtained from FEA or analytical calculations. Experimental and FEA results show that the applied strain varies periodically along the wire with an amplitude that depends on the spring material and geometry. We suggest that Ti-6Al-4V springs with an integer number of turns and optimized tee-shaped cross-sections enable highly accurate measurements of the intrinsic properties of superconducting wires.

Research paper thumbnail of Scaling law for the strain dependence of the critical current in an advanced ITER Nb3Sn strand

Superconductor Science and Technology, 2007

... superconducting wires David MJ Taylor and Damian P Hampshire Superconductivity Group, Physics... more ... superconducting wires David MJ Taylor and Damian P Hampshire Superconductivity Group, Physics Department, Durham University, Durham DH1 3LE, UK and Grenoble High Magnetic Field Laboratory, BP 166, 38042 Grenoble Cedex 9, France ...

Research paper thumbnail of Critical current density of superconductors as a function of strain in high magnetic fields

Cryogenics, 1998

A probe has been designed and built to measure the critical current density (J C) of short superc... more A probe has been designed and built to measure the critical current density (J C) of short superconducting wires and tapes as a function of strain (⑀) in small bore high field magnets. The probe can measure currents of up to 100 Amps and strains of ± 1.0% on both low and high temperature superconductors. Measurements can be made in our 40 mm bore 17 T high magnetic field system in pumped cryogens. Strain is measured using commercial strain gauges pasted directly onto the samples. A Agsheathed Bi 2 Sr 2 Ca 2 Cu 3 O X tape has been measured at 4.2 K in magnetic fields up to 12 T. J C is hysteretic in high magnetic fields and is weakly dependent on magnetic field and tensile strain up to ෂ 0.29%. Beyond ෂ 0.29% strain, the filaments break and J C drops precipitously. Results are also presented for the effect of tensile and compressive strain for a 0.37 mm diameter Nb 3 Sn wire at 4.2 K and 2.9 K from 10 T up to 14 T. The data confirm that a simple scaling law that includes the upper critical field (B C2 (T,⑀)) and the reduced field (B/B C2 (T,⑀)) alone cannot accurately describe the field, temperature and strain dependence of J C .

Research paper thumbnail of Weak emergence in the angular dependence of the critical current density of the high temperature superconductor coated conductor REBCO

Superconductor Science and Technology

Research paper thumbnail of Critical current density of coated conductors determined from rescaled magnetic moment at temperatures close to 77 K

Physica C: Superconductivity and its Applications

The possibility of rescaling (or calibrating) of the magnetization results to predict the transpo... more The possibility of rescaling (or calibrating) of the magnetization results to predict the transport critical current density (J c) of commercial coated conductors (REBCO tapes) is discussed from both the experimental and theoretical point of view. For this purpose the critical current density in tapes from three different producers was investigated by means of transport and magnetization measurements, in perpendicular magnetic fields of 0.25 T-2 T at temperatures 65 K-77 K. Two kinds of samples were tested in the magnetization measurementssquare samples 2 × 2 mm 2 cut from the central parts of the tapes and elongated rectangular samples of the full tape width (4 mm nominally) and 8 mm length. The transport measurements were performed on full-width samples in a subcooled liquid nitrogen bath. The presented results show that it is possible to empirically rescale the measured magnetization data on the basis of a single transport measurement, achieving the overall accuracy of the transport J c prediction between 4% and 10% for different tested tapes. Simple theoretical justification and analysis of the empirical scaling is presented, based on the critical state model with the power law currentvoltage relation considered to account for different level of electric field in the transport and magnetization measurements.

Research paper thumbnail of The Biaxial Strain Dependence of <formula> <tex>$J_C$</tex> </formula> of a (RE)BCO Coated Conductor at 77 K in Low Fields

IEEE Transactions on Applied Superconductivity

Recently, we designed and commissioned a 'crossboard' sample holder which can apply biaxial strai... more Recently, we designed and commissioned a 'crossboard' sample holder which can apply biaxial strains in the plane of a (RE)BCO coated conductor. It allows us to measure the critical current density for arbitrary combinations of x-and y-strain. Understanding the in-field, in-plane, biaxial strain dependence of a tape's (, ,) is crucial for applications such as CORC® or Roebel cables, as the cables are subjected to multiaxial strains during manufacturing and operation. Here we present experimental data for (, ,) on a SuperPower SCS4050 APC tape in magnetic fields up to 0.7 T, at 77 K. We also outline a theoretical model for the biaxial strain dependence of and use it to parameterise our data and show that the fraction of A-domains and B-domains are roughly equal (= 0.49 ± 0.03) and that the strain sensitivity of the critical temperature is 1.8 ± 0.1 K%-1 and-1.3 ± 0.1 K%-1 along their a-and b-axes respectively, for all the domains in this (RE)BCO tape. For the first time, we show both parabolic and linear strain dependencies of in a single tape by changing the angle between the applied strain direction and the twin boundaries in the (RE)BCO layer.  Index Terms-Critical current, strain measurement, 2G HTS conductors, cuprates.

Research paper thumbnail of 3D Properties in (RE)BCO Tapes Measured in Fields up to 35 T

IEEE Transactions on Applied Superconductivity

The full-text may be used and/or reproduced, and given to third parties in any format or medium, ... more The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.

Research paper thumbnail of Modelling the Critical Current of Polycrystalline Su-perconducting Films in High Magnetic Fields

IEEE Transactions on Applied Superconductivity

We have performed simulations using time-dependent Ginzburg-Landau theory on a 2D polycrystalline... more We have performed simulations using time-dependent Ginzburg-Landau theory on a 2D polycrystalline system where grain boundaries are modelled as narrow regions with a locally reduced critical temperature (Tc). For the small system sizes investigated, we find that the critical current density (Jc) is not sensitive to changes in grain size until the grain size is sufficiently small that it limits the average superparticle density in the system through the proximity effect. Furthermore, once Tc in the boundary regions is sufficiently low relative to the surrounding superconductor that grain boundary regions act as preferred channels for flux flow, further reductions in the boundary Tc only weakly reduce Jc across the superconductor.

Research paper thumbnail of Could high H98-factor commercial tokamak power plants use Nb-Ti toroidal field coils?

IEEE Transactions on Applied Superconductivity

Elizabeth (2019) 'Could high H98-factor commercial tokamak power plants use Nb-Ti toroidal eld co... more Elizabeth (2019) 'Could high H98-factor commercial tokamak power plants use Nb-Ti toroidal eld coils?', IEEE transactions on applied superconductivity., 29 (5). p. 4200405.

Research paper thumbnail of A derivation of Maxwell's equations using the Heaviside notation

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Maxwell's four differential equations describing electromagnetism are among the most famous e... more Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E -fields and B -fields and that Faraday's Law can be deriv...

Research paper thumbnail of A new apparatus for measuring the critical currents of hard type-II superconductive wires and tapes in high fields as a function of temperature throughout their superconducting phase

Journal of Physics E: Scientific Instruments

Describes an update of a earlier apparatus which measures the critical current of superconducting... more Describes an update of a earlier apparatus which measures the critical current of superconducting wires and tapes as a function of magnetic field and temperature. The critical element is a compact probe of 25 mm diameter which can be inserted into the bore of one of the several high-field magnets. The design and critical features of the probe which incorporates

Research paper thumbnail of A detailed investigation of the E-J characteristic and the role of defect motion within the flux-line lattice for high-current-density, high-field superconducting compounds with particular reference to data on NbSN throughout its entire field-temperature phase space

Journal of Physics C: Solid State Physics

A detailed investigation of the E-J characteristic and the role of defect motion within the flux-... more A detailed investigation of the E-J characteristic and the role of defect motion within the flux-line lattice for highcurrent-density , high-field superconducting compounds with particular reference to data on Nb,Sn throughout its entire field-temperature phase space

Research paper thumbnail of Critical currents and the critical state in superconductors with magnetic ions

Physica C: Superconductivity

The critical state model is used to derive equations that relate the additional magnetic moment (... more The critical state model is used to derive equations that relate the additional magnetic moment (AM) produced by the flux pinning to the critical current density (J,) measured in transport measurements. The equations derived for conventional superconductors can be used for superconductors that contain magnetic ions, if AM is replaced by A M/(1 + ,$(H)) where x'(H) is the differential susceptibility. In the critical state, the field gradient has contributions from both the macroscopic supercurrents and the Amperian currents from the magnetic ions. Magnetic measurements are sensitive to both contributions. Transport measurements only characterise the macroscopic supercurrents. For superconductors which contain rare-earth elements, the J, values calculated using hysteretic magnetisation measurements without including the term x'(H), can be in error by factors of-7. 0 1997 Elsevier Science B.V.

Research paper thumbnail of Design, fabrication and performance of a 1.29 T Bi-2223 magnet

Superconductor Science and Technology

The design and fabrication procedure of a laboratory-scale Bi-2223 tape superconducting magnet wi... more The design and fabrication procedure of a laboratory-scale Bi-2223 tape superconducting magnet with a bore of 40 mm and a maximum field of 1.29 T at 4.2 K is presented. The magnet comprises six resin impregnated double-wound pancakes of bore diameter 40 mm fabricated via the react-and-wind route. Critical current density (J c) measurements have been made as a function of magnetic field, angle and strain at 4.2 K and 77 K on short samples. In zero field, the critical current density for the superconducting cross-sectional area of the tape was 8.3 × 10 4 A cm −2 (4.2 K) and 1.18 × 10 4 A cm −2 (77 K). The electric field-current density characteristics of all the components of the coils when individually energized or with the whole magnet energized have been measured. Comparison between short sample measurements and performance of the magnet show that minimal additional damage occurred beyond the ∼20% that was produced by the bending strain during the wind-and-react fabrication procedure and the ∼10% variation of the long length J c of the tape. Sufficient detail is provided for the non-specialist to assess both the use of potential brittle superconducting tapes for magnet technology and to construct a laboratory-scale magnet.