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Papers by Damian Hampshire

Research paper thumbnail of Resistivity Measurements of the Strain, Temperature and Angular Dependence of the Upper Critical Field of REBCO Tapes up to 8 T

IEEE Transactions on Applied Superconductivity, Aug 1, 2023

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 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 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

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

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

IEEE Transactions on Applied Superconductivity

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

IEEE Transactions on Applied Superconductivity

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

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

Physica C: Superconductivity

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

Superconductor Science and Technology

Research paper thumbnail of Flux flow in high-temperature type II superconductors governed by the activation of Frank-Read sources and the resultant motion of core dislocations

Journal of Physics C: Solid State Physics

The functional form of the volume pinning force Fp for high-temperature type II superconductors i... more The functional form of the volume pinning force Fp for high-temperature type II superconductors is derived as the degree of distortion in the flux-line lattice changes. A single mechanism operates in both NbTi and Nb3Sn, namely the activation of Frank-Read sources where Fp=(1/100)( mu 0H2c2/DK2)b(1-b/0.95) for 0.3&lt;or=b&lt;or=0.9 and Fp=(1/21)( mu 0H2c2/DK2)b12/(1-b)2 for 0.1&lt;or=b&lt;or=0.9 respectively. Above the critical state, flux flow

Research paper thumbnail of How resistive must grain boundaries in polycrystalline superconductors be, to limit J c?

Superconductor Science and Technology

Although we can use misorientation angle to distinguish the grain boundaries that can carry high ... more Although we can use misorientation angle to distinguish the grain boundaries that can carry high critical current density J c () in high temperature superconductors (HTS) from those that cannot, there is no established normal state property equivalent. In this paper, we explore the superconducting and normal state properties of the grains and grain boundaries of polycrystalline YBa 2 Cu 3 O 7−x (YBCO) using complementary magnetisation and transport measurements, and calculate how resistive grain boundaries must be to limit J c in polycrystalline superconductors. The average resistivity of the grain boundaries, , GB r in our micro-and nanocrystalline YBCO are 0.12 Ωm and 8.2 Ωm, values which are much higher than that of the grains G r () and leads to huge GB G r r values of 2×10 3 and 1.6×10 5 respectively. We find that the grain boundaries in our polycrystalline YBCO are sufficiently resistive that we can expect the transport J c to be several tens of orders of magnitude below the potential current density of the grains in our YBCO samples, as is found experimentally. Calculations presented show that increasing J c values by ∼2 orders of magnitude in high fields is still possible in all state-of-the-art technological high-field superconductors. We conclude: grain boundary engineering is unlikely to improve J c sufficiently in randomly aligned polycrystalline YBCO, to make it technologically useful for high-field applications; in low temperature superconducting intermetallics, such as Nb 3 Sn, large increases in J c may be achieved by completely removing the grain boundaries from these materials and, as is the case for thin films of Nb, Ba(FeCo) 2 As 2 and HTS materials, by incorporating additional artificial pinning.

Research paper thumbnail of Superconducting Properties of Titanium Alloys (Ti-64 and Ti-6242) for Critical Current Barrels

IEEE Transactions on Applied Superconductivity, 2016

Research paper thumbnail of Design and Evaluation of Joint Resistance in SSC Rutherford type cable splices for Torus magnet for the Jefferson Lab 12 GeV Upgrade

IEEE Transactions on Applied Superconductivity, 2016

Research paper thumbnail of Oxygen stoichiometry and the electronic structure of high-temperature superconductors

AIP Conference Proceedings, 1988

The oxygen content determines the transport properties of Ba2YCu3O7+x and EuBa2Cu3O7+x, and in pa... more The oxygen content determines the transport properties of Ba2YCu3O7+x and EuBa2Cu3O7+x, and in particular their superconducting behavior at high temperatures. We studied the changes in the Ba2YCu3O7+x electronic structure which are caused by modifications in the amount of oxygen. The modifications were achieved either by thermal annealing or by exposure to ``white'' synchrotron radiation which causes oxygen desorption, with similar results. We found that the decrease in oxygen content affects the lineshape of the upper valence band features and the relative intensity of the Cu satellite features. The lineshape changes simplify the identification of oxygen-related features in the upper valence band region. The exposure to ``white'' synchrotron radiation of Ba2EuCu3O7+x did not produce similarly large spectral changes.

Research paper thumbnail of Resistivity Measurements of the Strain, Temperature and Angular Dependence of the Upper Critical Field of REBCO Tapes up to 8 T

IEEE Transactions on Applied Superconductivity, Aug 1, 2023

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 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 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

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

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

IEEE Transactions on Applied Superconductivity

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

IEEE Transactions on Applied Superconductivity

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

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

Physica C: Superconductivity

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

Superconductor Science and Technology

Research paper thumbnail of Flux flow in high-temperature type II superconductors governed by the activation of Frank-Read sources and the resultant motion of core dislocations

Journal of Physics C: Solid State Physics

The functional form of the volume pinning force Fp for high-temperature type II superconductors i... more The functional form of the volume pinning force Fp for high-temperature type II superconductors is derived as the degree of distortion in the flux-line lattice changes. A single mechanism operates in both NbTi and Nb3Sn, namely the activation of Frank-Read sources where Fp=(1/100)( mu 0H2c2/DK2)b(1-b/0.95) for 0.3&lt;or=b&lt;or=0.9 and Fp=(1/21)( mu 0H2c2/DK2)b12/(1-b)2 for 0.1&lt;or=b&lt;or=0.9 respectively. Above the critical state, flux flow

Research paper thumbnail of How resistive must grain boundaries in polycrystalline superconductors be, to limit J c?

Superconductor Science and Technology

Although we can use misorientation angle to distinguish the grain boundaries that can carry high ... more Although we can use misorientation angle to distinguish the grain boundaries that can carry high critical current density J c () in high temperature superconductors (HTS) from those that cannot, there is no established normal state property equivalent. In this paper, we explore the superconducting and normal state properties of the grains and grain boundaries of polycrystalline YBa 2 Cu 3 O 7−x (YBCO) using complementary magnetisation and transport measurements, and calculate how resistive grain boundaries must be to limit J c in polycrystalline superconductors. The average resistivity of the grain boundaries, , GB r in our micro-and nanocrystalline YBCO are 0.12 Ωm and 8.2 Ωm, values which are much higher than that of the grains G r () and leads to huge GB G r r values of 2×10 3 and 1.6×10 5 respectively. We find that the grain boundaries in our polycrystalline YBCO are sufficiently resistive that we can expect the transport J c to be several tens of orders of magnitude below the potential current density of the grains in our YBCO samples, as is found experimentally. Calculations presented show that increasing J c values by ∼2 orders of magnitude in high fields is still possible in all state-of-the-art technological high-field superconductors. We conclude: grain boundary engineering is unlikely to improve J c sufficiently in randomly aligned polycrystalline YBCO, to make it technologically useful for high-field applications; in low temperature superconducting intermetallics, such as Nb 3 Sn, large increases in J c may be achieved by completely removing the grain boundaries from these materials and, as is the case for thin films of Nb, Ba(FeCo) 2 As 2 and HTS materials, by incorporating additional artificial pinning.

Research paper thumbnail of Superconducting Properties of Titanium Alloys (Ti-64 and Ti-6242) for Critical Current Barrels

IEEE Transactions on Applied Superconductivity, 2016

Research paper thumbnail of Design and Evaluation of Joint Resistance in SSC Rutherford type cable splices for Torus magnet for the Jefferson Lab 12 GeV Upgrade

IEEE Transactions on Applied Superconductivity, 2016

Research paper thumbnail of Oxygen stoichiometry and the electronic structure of high-temperature superconductors

AIP Conference Proceedings, 1988

The oxygen content determines the transport properties of Ba2YCu3O7+x and EuBa2Cu3O7+x, and in pa... more The oxygen content determines the transport properties of Ba2YCu3O7+x and EuBa2Cu3O7+x, and in particular their superconducting behavior at high temperatures. We studied the changes in the Ba2YCu3O7+x electronic structure which are caused by modifications in the amount of oxygen. The modifications were achieved either by thermal annealing or by exposure to ``white'' synchrotron radiation which causes oxygen desorption, with similar results. We found that the decrease in oxygen content affects the lineshape of the upper valence band features and the relative intensity of the Cu satellite features. The lineshape changes simplify the identification of oxygen-related features in the upper valence band region. The exposure to ``white'' synchrotron radiation of Ba2EuCu3O7+x did not produce similarly large spectral changes.