Flux Line Spacing Research Articles

The process of magnetic flux penetration into superconductors

Abstract In the present paper the magnetic flux penetration dynamics of type-II superconductors in the flux creep regime is studied by analytically solving the nonlinear diffusion equation for the magnetic flux induction, assuming that an applied field parallel to the surface of the sample and using a power-law dependence of the differential resistivity on the magnetic field induction. An exact solution of nonlinear diffusion equation for the magnetic induction B(r, t) is obtained by using a well-known self-similar technique. We study the problem in the framework of a macroscopic approach, in which all length scales are larger than the flux-line spacing; thus, the superconductor is considered as a uniform medium.

Anharmonicity of flux lattices and thermal fluctuations in layered superconductors

We study elasticity of a perpendicular flux lattice in a layered superconductor with Josephson coupling between layers. We find that for flux displacements \ensuremath{\rho} the energy contains ${\ensuremath{\rho}}^{2}\mathrm{ln}\ensuremath{\rho}$ terms, so that elastic constants cannot be strictly defined. Instead we define effective elastic constants by a thermal average. The tilt moduli have terms $\ensuremath{\sim}\mathrm{ln}T$ which for ${\ensuremath{\lambda}}_{J}\ensuremath{\ll}a,$ where ${\ensuremath{\lambda}}_{J}$ is the Josephson length and $a$ is the flux-line spacing, lead to $〈{\ensuremath{\rho}}^{2}〉\ensuremath{\sim}T/|\mathrm{ln}T|.$ The expansion parameter indicates that the dominant low-temperature phase transition is either layer decoupling at high fields $({\ensuremath{\lambda}}_{J}\ensuremath{\gg}a)$ or melting at low fields $({\ensuremath{\lambda}}_{J}\ensuremath{\ll}a).$

Longitudinal elastic correlation length of flux lines along the c-axis in superconducting Bi-2212 single crystal

The longitudinal elastic correlation length, l 44, of flux lines along the c-axis is measured using the Campbell method with the magnetic field parallel to the c-axis for a superconducting Bi-2212 single crystal. It is found that l 44 is of the order of 10μm and four orders of magnitude longer than the distance between the CuO 2 planes. In addition, l 44 increases with increasing magnetic field and/or temperature. These results agree well with the theoretical estimate of the pinning correlation length using the observed critical current density. The apparent pinning potential associated with the magnetic relaxation rate is calculated using these results and compared with the experimental result. Agreement is satisfactory. It is also found that the transverse flux-bundle size is as short as the flux-line spacing. It is concluded from these results that the flux lines are rather one-dimensional and strongly coupled along the c-axis.

Scaling of the flux pinning force in epitaxial Bi2Sr2Ca2Cu3Ox thin films.

Magnetic-field and temperature dependence of the critical current density ${\mathit{J}}_{\mathit{c}}$ is investigated in epitaxial ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{x}}$ thin films. For the magnetic field H applied parallel to the c axis, the flux pinning force density ${\mathit{E}}_{\mathit{p}}$ (=${\mathit{J}}_{\mathit{c}}$B) exhibits clear scaling behavior when H is normalized by the irreversibility field ${\mathit{H}}^{\mathrm{*}}$. The maximum pinning force density scales linearly with ${\mathit{H}}^{\mathrm{*}}$. This is the first observed scaling of ${\mathit{E}}_{\mathit{p}}$ in high-quality thin films of Bi oxides, which we can reasonably explain with flux-creep theory by assuming that the activation energy is proportional to the flux line spacing.

The effect of strong flux line correlations on the irreversibility line of high temperature superconductors

A phenomenological model is proposed to account for a recently observed crossover in the temperature dependence of the irreversibility line of high temperature superconductors from a (1 - T/ T c) 3 2 to a (1 - T/ T c) 3 dependence. The model, which distinguishes between weak correlations and strong correlations in the flux line lattice, indicates that the crossover should occur at magnetic fields corresponding to a flux line spacing of about λ/4, λ being the penetration depth transverse to the field.

Flux pinning mechanism in unorientated grains of YBa 2Cu 3O 7−δ

Magnetization measurements of the intragranular pinning force in polycrystalline YBa 2Cu 3O 7−δ and YBa 2(Cu 1− x M x) 3O 7−δ, where M = Fe, Ni, address two major questions of flux pinning: 1, what are the dominant pinning sites; and 2, what is the relevant pinning mechanism in these materials. It is demonstrated that the microstructure, i.e. the twin spacing, is unaltered by Ni, but drastically decreased by addition of Fe. Thus these systems provide an ideal tool with which to examine the role of twin boundaries in flux pinning. The volume pinning force is interpreted in terms of flux line shear, i.e. F P is related to the onset of dissipative flux flow within weakly pinning channels in the (inhomogeneous) superconductor. The theoretically expected field and temperature scaling agrees with the experimental data. A quantitative analysis of the data yields a channel width comparable to the flux line spacing, a o. This indicates that single rows of flux lines move once the Lorentz force exceeds the flow stress of the flux line lattice. The applicability of this pinning mechanism to YBa 2Cu 3O 7−α more homogeneous than the metallurgically prepared powder used here is discussed.

Pinning force of twin planes or grain boundaries in high Tc superconductors

The elementary interaction of a grain boundary or twin plane is computed using Thuneberg's formulation in the Ginzburg-Landau regime and simply extending this to low temperatures. The computation is carried out both for isolated flux lines and close to B c2 for strongly overlapping vortices. The volume pinning force is subsequently derived for three relevant situations: isolated vortices with flux line spacing either much smaller or larger than the twin plane spacing, and for overlapping flux lines. The resulting F p( B) curve has a dome-shaped character. The reduced field at which it attains its maximum value is a function of temperature. At 70 K it lies at B/ B c2 ≈ 0.5. The low field and low temperature prediction is in good agreement with the experimental data. Predictions for the potential values of F p and J c at 77 K are given. These are much larger than the experimental results. We believe this discrepancy is caused by thermally assisted flux motion.

Local pinning-force distribution in NbN films

The authors performed measurements of the flux-flow resistivity on a thin film of NbN. By fitting the resistivity, measured as a function of the current, to a theoretical expression, they were able to obtain the distribution function of local depinning forces in the film. It appears that the distribution is very broad and that only a minor fraction of flux lines is flowing at what is usually defined as J/sub c/. These observations are in agreement with the results of the pinning-force measurements. The measurements reveal that at high fields pinning is limited by flux-line shear and that the effective channel width for shear is equal to the flux-line spacing. They suggest that variations of the local depinning force on various length scales always allow the flow of single rows of flux lines. >

Calculation of AC losses in ultra fine filamentary NbTi wires

The advent of Low loss Filamentary NbTi wires with very Fine Filaments, First developed hy Alsthom and the Laboratoires de Marcoussis, has led to the possibility of using superconductors in many AC 50/60 Hz applications. A computer program, based on the Bean Model, for any spacetime variation of the magnetic induction predicts losses successfully for filaments of diameter greater than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim 1 \mu</tex> m. However, for filaments of diameter less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim 1 \mu</tex> m the theoretical calculation underestimates the losses dramatically. This is because the filament dimensions become comparable to ξ, the coherence length, λ the magnetic penetration depth, a <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> the flux line spacing and λ, the pinning penetration depth leading to electromagnetic coupling effects between filaments. In this paper these effects on loss calculations are investigated with a view to obtaining an improved prediction of the loss behaviour in these materials. The results are consistent with a model of flux penetration, whereby, due to proximity effects, the matrix is essentially behaving as a type II superconductor. The main effect of this is to strongly couple flux lines in the first compaction bundles so that hysteretic losses in A.C. fields are greater than those predicted by the Bean Model.

Grain Boundary Pinning in Polycrystalline NbN Films

An approximate closed form expression for the elementary pinning force of a grain boundary is used to evaluate the bulk pinning force, in the isolated vortex regime, of a type-II superconductor with grain sizes smaller than the flux line spacing. A comparison is made with experimental results on NbN films.

The elementary interaction force between a dislocation loop and the flux line lattice of a type II superconductor

Abstract The elementary interaction force f between prismatic dislocation loop and the flux line lattice due to both first- and second-order strain field interactions is computed. A new Fourier transform method for defects radially symmetric about the flux line direction is developed and used to compute the second-order interaction as well as to check the results of the first-order interaction calculated previously by the Peach-Koehler formula. Small interstitial loops are attracted to flux line cores by the first-order interaction and repelled by the second-order interaction whereas small vacancy loops are repelled by both interactions. For both interactions, the maximum interaction force f p of a loop much smaller than the flux line spacing a 0 increases with loop diameter D approximately as D 2. For larger loops f p increases less rapidly with D, goes through a maximum at D≈a 0/2 and rapidly decreases to zero at D≈a 0. For still larger D the sign of the interaction force is reversed (repulsive pins become attractive). A pattern of maxima and sharp minima in f p is observed as D is increased further. The minima are pinning interferences, caused by neighbouring flux lines exerting equal and opposite forces on opposite sides of the loop.