This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical...

Flux vortices and transport currents in type II superconductors

For all hard high‐field superconductors examined to date, there is a maximum in the pinning force density Fp as a function of the reduced magnetic field h. Fietz and Webb first demonstrated in dilute Nb alloys that the peak in Fp scales as [Hc2(T)]2.5 if the temperature is changed; the maximum value of Fp occurred at the same value of reduced field regardless of temperature. Recent data on the temperature dependence of pinning in Nb3Sn, Nb–25% Zr and a Nb–Ti alloy, which exhibits the ``peak effect'', are analyzed to show that similar scaling laws are obeyed by these materials. All presently available evidence indicates however that the reduced field hp at which the maximum Fp occurs, as well as the height and shape of this maximum, can be altered by metallurgical treatment. Apparently weak pinning defects, or widely spaced ones, produce a small peak in Fp(h) at high h whereas strong closely spaced pins produce a large peak in Fp(h) at low h without producing much change in Fp(h) at high h. A model which p...

Scaling laws for flux pinning in hard superconductors

Expressions for flux-pinning in type II superconductors are derived from considerations of the nature of the interaction between individual flux-lines and pinning-centres, and of the geometry of th...

Flux pinning mechanisms in type II superconductors

We report a new process which promises high critical current density in oxide superconductors. The process consists of three stages. Firstly a YBa2Cu3Ox sample is rapidly heated and quenched from the Y2O3 plus liquid region. Subsequently the quenched sample is reheated to the Y2BaCuO5 plus liquid region, and then slowly cooled with a temperature gradient in flowing oxygen. The process enables us to grow a superconducting phase unidirectionally and to suppress the second phase intrusion, leading to the production of well textured YBa2Cu3Ox which yields a high Jc value in the presence of magnetic fields. It is also found that Bean's critical state is realized in such high Jc samples.

https://iopscience.iop.org/article/10.1143/JJAP.28.1189/pdf

A new process with the promise of high Jc in oxide superconductors

Quasiclassic Usadel equations for two-band superconductors in the dirty limit are derived with the account of both intraband and interband scattering by nonmagnetic impurities. From these equations, the Ginzburg-Landau equations, and the equations for the critical temperature ${T}_{c}$ and the upper critical field ${H}_{c2}$ are obtained. The equation for ${H}_{c2}$ determines both the temperature dependence of ${H}_{c2}(T)$ and the orientational dependence of ${H}_{c2}(\ensuremath{\theta})$ as a function of the angle $\ensuremath{\theta}$ between $\mathbf{H}$ and the c axis. It is shown that the shape of the ${H}_{c2}(T)$ curve essentially depends on the ratio of the intraband electron diffusivities ${D}_{1}$ and ${D}_{2},$ and can be very different from the one-gap dirty-limit theory. In particular, value ${H}_{c2}(0)$ can considerably exceed ${0.7T}_{c}{\mathrm{dH}}_{c2}{/dT}_{c},$ which can have important consequences for applications of ${\mathrm{MgB}}_{2}.$ Based on a general equation for ${H}_{c2}(T,\ensuremath{\theta}),$ a scaling relation, which enables one to get the angular dependence of ${H}_{c2}(\ensuremath{\theta})$ from the equation for ${H}_{c2}$ at $\mathbf{H}\ensuremath{\Vert}c,$ is proposed. The behavior of ${H}_{c2}(\ensuremath{\theta})$ and ${H}_{c1}(\ensuremath{\theta})$ can deviate markedly from the results of the anisotropic Ginzburg-Landau theory, and the ratio of the upper critical field ${H}_{c2}^{\ensuremath{\Vert}}{/H}_{c2}^{\ensuremath{\perp}}$ for $\mathbf{H}\ensuremath{\Vert}\mathrm{ab}$ and $\mathbf{H}\ensuremath{\perp}\mathrm{ab}$ can both increase and decrease with temperature, depending on the relation between ${D}_{1}$ and ${D}_{2}.$ Implications of the obtained results for ${\mathrm{MgB}}_{2}$ are discussed.

https://arxiv.org/pdf/cond-mat/0212129.pdf

Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors

Critical current and pinning-force densities in a series of niobium alloys subjected to severe plastic deformation have been determined from measurements of complete hysteretic magnetization curves on alloys with Ginzburg-Landau parameter $\ensuremath{\kappa}$ between 1.3 and 13 at temperatures from the critical temperature ${T}_{c}$ down to $0.14{T}_{c}$. Systematic scaling rules were found that accurately describe all of the results over the entire range of fields and temperatures. The pinning-force density scales with magnetic induction as a single function of $\frac{B}{{H}_{c2}}$; it scales with temperature as the $\frac{5}{2}$ power of the upper critical field ${H}_{c2}(T)$, is roughly proportional to ${\ensuremath{\kappa}}^{\ensuremath{-}\ensuremath{\gamma}}$, where $1l\ensuremath{\gamma}l3$, and is otherwise independent of $T$. A model for the pinning process that takes into account deformation of the fluxoid lattice by the pinning forces is proposed to account for the observed scaling rules. The results are consistent with a pinning interaction based on a second-order elastic interaction between dislocations and the fluxoid lattice, but other mechanisms are not excluded. Cooperative effects seem to be an essential feature of the pinning process, leading to a dependence of the pinning-force density on the square of the pinning-point strength, and on the arrangement of pinning points.

Hysteresis in Superconducting Alloys-Temperature and Field Dependence of Dislocation Pinning in Niobium Alloys

The magnetization and critical transport-current densities of samples of superconducting niobium-25% zirconium cold-worked wire have been measured quantitatively up to 40 kOe applied field. All of the magnetization characteristics, as measured by several techniques, and the critical transport currents conform to critical-state concepts provided that the equilibrium magnetization is included in the analysis. The equilibrium magnetization curves could be deduced from the hysteretic measured magnetization data, and the results agree with the theory of Abrikosov for type-II superconductors. The irreversible magnetization-current densities ${J}_{c}(B)$, where B is the local magnetic induction, just equal the critical transport-current densities ${J}_{t}(H)$ in the range 4 to 40 kOe applied field. They are accurately fitted by an empirical critical-state expression of the form ${J}_{c}(B)={a}_{0}\mathrm{exp}(\ensuremath{-}\frac{B}{{b}_{o}})+{c}_{o}$ where ${a}_{o}$, ${b}_{o}$, and ${c}_{o}$ are measured constants of the material. The methods used appear to be generally applicable to the study of hysteretic superconducting wire.

W. A. Fietz

Papers

Hysteresis in Superconducting Alloys-Temperature and Field Dependence of Dislocation Pinning in Niobium Alloys

Magnetization of Superconducting Nb-25%Zr Wire

Magnetic Properties of Some Type-II Alloy Superconductors near the Upper Critical Field

Annihilation Instability in Hard Superconductors