CHAPTER 10: CRITICAL-CURRENT DATA ANALYSIS

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FIG. 10.1: Methods for determining the critical current from a set of V–I curves obtained at different magnetic fields: (a) electric-field criterion, (b) resistivity criterion, and (c) offset criterion

FIG. 10.2: Illustration of the critical current of a superconductor as a function of magnetic field that results from using different criteria

FIG. 10.3: Illustration of V-I curves affected by current-transfer voltage at low current levels

FIG. 10.4: Log–log plot of electric-field vs. current (E-I) for a short Nb<span id="subscript">3</span>Sn sample

FIG. 10.5: Critical-current density as a function of magnetic field for a number of high-current-density superconductors at liquid-helium temperature

FIG. 10.6: Critical-current density as a function of magnetic field for high-Tc superconductors at liquid-nitrogen temperature

FIG. 10.7: Representation of a vortex lattice in a Type II superconductor

FIG. 10.8: Critical Lorentz-force density FL of several high-field superconductors fitted by using the general pinning-force parameters

FIG. 10.9: Example showing a three-parameter fit of the general pinning-force function

FIG. 10.10: Deviation of the high-field flux-pinning curve from the Kramer-model expression in a high-quality (high-n) Nb

FIG. 10.11: Kramer plot of a low-<em>n</em> Nb<span id="subscript">3</span>Sn sample with hydrogen additions, showing a depressed value of the effective depinning field Bc2 due to material inhomogeneities

FIG. 10.12: The first measurement of the transport critical current as a function of magnetic field in granular YBCO, demonstrating extreme weak-link behavior

FIG. 10.13: Transport critical-current density vs. applied field, showing that the Josephson weak-link theory fits the data well without adjustable parameters

FIG. 10.14: Critical-current density versus magnetic field at 77 K of an early YBCO bulk sample, a high-quality Bi-2223 tape, and a YBCO coated conductor

FIG. 10.15: Upper critical field vs. temperature for several low-Tc superconductors

FIG. 10.16: Irreversibility field vs. temperature for several high-Tc superconductor films and round-wire data for high-pressure sintered polycrystalline MgB2

FIG. 10.17: Temperature dependence of the critical-current density of a Nb-Ti/Cu multifilamentary wire at different magnetic fields

FIG. 10.18: Temperature dependence of the critical current of Nb3Sn multifilamentary wire at different magnetic fields

FIG. 10.19: Temperature dependence of the critical current of V3Ga at different magnetic fields

FIG. 10.20: Temperature dependence of the critical current of several high-Tc superconducting thin films at zero magnetic field

FIG. 10.21: Temperature dependence of the critical current of a YBCO coated conductor at different magnetic fields

FIG. 10.22: Temperature dependence of the critical current of a Bi-2212 multifilamentary tape at different magnetic fields

FIG. 10.23: Temperature dependence of the critical current of a Bi-2223 multifilamentary tape at different magnetic fields

FIG. 10.24: Illustration of bending strain and pretensioning axial stress incurred during magnet winding

FIG. 10.25: Representation of a current-carrying loop showing the current density J, the magnetic field B, and the hoop stress sigmahoop generated by the Lorentz force FL

FIG. 10.26: Critical current Ic of a Nb3Sn conductor as a function of axial strain for different magnetic fields

FIG. 10.27: Effect of strain on the critical current of a Bi-2223 superconductor, illustrating the field-independent irreversible strain limit epsilonirr for permanent damage

FIG. 10.28: Illustration of strain distribution introduced into a conductor from bending

FIG. 10.29: Dependence of critical current on bending strain for Nb<span id="subscript">3</span>Sn superconductors measured at 8 T

FIG. 10.30: Correlation of data for binary multifilamentary Nb3Sn wires showing the nearly universal effect of axial strain on (a) the effective upper critical field Bc2*(ε0) at 4.2 K and (b) the strain-scaling prefactor g(ε0)

FIG. 10.31: Data correlations showing the nearly universal effect of axial strain on the effective upper critical field Bc2*(ε0) of different types of bronze-process A-15 multifilamentary superconductors at 4.2 K

FIG. 10.32: Fundamental basis of the power law at moderate intrinsic strains (–0.5 % < ε0 < ε0irr): Strain dependence of the critical temperature of binary Nb3Sn calculated by introducing phonon anharmonicity into the McMillan/Kresin equation

FIG. 10.33: Critical temperature of binary Nb3Sn calculated over an extended strain range from a three-dimensional deviatoric strain model by Markiewicz

FIG. 10.34: Power-law fits to the effective upper critical field scaling law prefactor for binary Nb3Sn

FIG. 10.35: Illustration of transformation method for scaling Jc(B) curves to different strains

FIG. 10.36: Data correlation showing the scaling parameter w has the constant value 3 for many different types of Nb3Sn conductors

FIG. 10.37: Data correlation showing the temperature scaling parameter v has the constant value 1.5 indepent of compositional phase and measurement method

FIG. 10.38: Data correlation showing the temperature scaling parameter v has the constant value 1.5 indepent of strain

References: Listing of all References for Chapter 10 Figures