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It is well known that the point charge, line charge and homogeneously charged plane of infinite extent are sources of electrostatic fields with straight flux lines. It is proved in this note that provided these flux lines occupy all of three-dimensional space, then these charge configurations and appropriate variants of them are the only sources of straight-line electrostatic fields in R 3.

Flux-density profiles of cylindrical type-ii superconductors The magnetization process of type-II superconductors leads to shear stresses in the flux-line lattice. These shear stresses give rise to plastical deformations of the flux-line lattice. As a consequence, in the relationship between flux-density gradient and pinning force the flow stress of the flux line lattice has to be taken into account. The average pinning force of crystal edge dislocations oriented parallel to the flux lines is calculated and the flux-density profiles and the ascending branch of the magnetization curve are determined for long cylindrical samples. Bei der Magnetisiemng von Supraleitern zweiter Art treten Schubspannungen im Flusliniengitter auf. Diese fuhren zu plastischen Deformationen des Flusliniengitters und erfordern eine Berucksichtigung der Fliesspannung des Flusliniengitters in der Beziehung zwischen dem Flusdichtegradienten und der auf Fluslinien ausgeubten Haftkraft. Es werden die gemittelte Haftkraft fur K...

It is shown from the Ginzburg—Landau theory that some pinning forces in type II superconductors may be expressed as potential gradients, but that others may not. A potential does not exist if a pinning centre acts on one flux line only; in this case the strain of the flux-line lattice depends on the shear modulus and is therefore large. In the more common case where a pinning centre acts on two or more flux lines simultaneously, it behaves as a potential well or hill. The strain in the flux-line lattice is then independent of the shear modulus and is much smaller than previously expected. This reduction is partly compensated by the correct non-local treatment of the elastic response. It is further shown that the total force exerted on the flux-line lattice by a sufficiently weak pinning centre vanishes if the forces derive from a potential and if the imperfection is embedded in a homogeneous matrix. As a consequence, elementary pinning forces can be exerted only either by imperfections with prono...

Flux Pinning In Superconductors With Diferent Defect Distributions Critical currents in transverse magnetic fields have been measured in type-II superconducting PbNa single crystals with rod-shaped Pb3Na precipitates. Depending on the field direction the precipitates interact with the flux lines in a statistical or regular manner (‘matching’). In the statistical case the volume pinning force is given by a quadratic summation of the elementary pinning forces considering the arrangement of the precipitates. The interaction mechanism is identified as the core interaction. In the matching case the volume pinning force is given by linear summation. The elementary pinning forces are compared for both cases.

When the surface barrier is removed from reversible PbTl specimens, it is found that they do not obey the Bean model in a.c. conditions. The response is nearly linear with large penetrations of the a.c. signal. However, a model which takes into account the reversible oscillations of flux lines can explain the results. Critical current densities obtained from this model agree with those measured by other methods. Critical current densities as low as 4 A/sq cm were found and the factors affecting reversibility are discussed.

The Influence of Plastic Deformation on the Bulk and Surface Pinning of Flux Lines in Type-II-Superconductors The field and temperature dependence of the pinning forces of flux lines in a Pb-5 at.%-In single crystal was determined by differential magnetization measurement of small hysteresis loops. The increase of the bulk pinning force by plastic tension can be explained qualitatively by the arrangement of dislocations in deformed f.c.c. single crystals. The existing statistical theories which are strictly valid only for equipartition of isotropic pinning centres do not hold for a quantitative explanation of our results. The influence of deformation on the surface pinning force can be understood by the arrangement of slip lines.

The distortion of flux lines in the vicinity of a dislocation in a flux line lattice is examined. With this knowledge the interaction of a dislocation with other flux line lattice defects such as interstitial flux lines, edge dislocations and screw dislocations is studied to determine how flux can flow through its own lattice. It is concluded that Frank-Read sources can only occur infrequently, but dislocation line expansion can occur extensively for certain interactions of a moving dislocation with a stationary screw dislocation. One of the products of this expansion is a dislocation dipole which is more mobile than a single dislocation but does not produce as much translation of the lattice. The significance of dislocations in a flux line lattice is discussed.

By treating the flux lines in a type II superconductor as a compressible fluid Friedel et al. (1963) have shown that, for a non-uniform distribution of lines, the force per unit length acting on one line is (φ04π). dH(B)/dx. Here B is the induction at x and H(B) the external field which would be in equilibrium with B if the material were reversible. The flux lines in an irreversible type II superconductor in the critical state of Kim et al. (1963) are in virtual equilibrium under the forces due to the flux concentration gradient and a pinning force F. F arises from the interaction between the flux lines and structural defects in the material. It follows that F = (φ0/4π)(dH/dB) a(dB/dx) s, where (dH/dB) a is the gradient of the reversible B/H curve and (dB/dx) s the field gradient in the specimen.

Direct observation of the flux distribution on the end faces of inhomogeneous Pb-2 at. % In discs at 4·2°k, in a transverse field cycled from 0 to 550 oe to 165 oe, showed intermediate state structures in regions of low indium concentration, and a triangular flux lattice in regions of high indium concentration. The normal regions of the intermediate state, however, consisted of flux lines arranged either as laminae or as bundles. In spite of the compositional inhomogeneities it was estimated that the indium concentration in every region of the specimens was in excess of that required for type II superconductivity. It is proposed that at 550 oe a flux lattice exists in every region of the specimen and that as the field is reduced the flux lattice breaks down into intermediate state structures first in regions of low indium content and last in regions of high nidium content.