Abstract
We have calculated the Gibbs free-energy barrier against irreversible magnetic flux entry into a superconductor for a long cylinder with elliptical cross section which approximates a long, flat strip. Our model is simplified to the two-dimensional case by assuming magnetic flux to enter in the form of a long, narrow, normal domain parallel to the axis of the cylinder. The following four contributions to the Gibbs free energy have been taken into account: (1) loss of condensation energy and gain of magnetic field energy inside the superconductor, (2) magnetic field energy outside the superconductor, (3) energy of interaction of the domain with an applied magnetic field, and (4) energy of interaction with an applied electrical transport current. Because of the Gibbs free-energy barrier, the critical magnetic field for entry of magnetic flux can be enhanced considerably above that calculated using Silsbee's rule. This enhancement is found to be proportional to the square root of the width of the superconducting cylinder. Important consequences of this are the enhancement of the critical current in a superconducting strip in zero magnetic field at which electrical resistance starts to appear and a corresponding modification of Silsbee's rule. We have demonstrated these effects experimentally through measurements of the onset of the current-induced resistive state in a series of superconducting indium strips of different widths and thicknesses. The experimental results confirm the theoretical predictions. The Gibbs free-energy-barrier effect described here can be interpreted as a novel flux-pinning mechanism, which might be called edge pinning.
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Work performed in part in the Ames Laboratory and in part in the Argonne National Laboratory of the U.S. Atomic Energy Commission.
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Clem, J.R., Huebener, R.P. & Gallus, D.E. Gibbs free-energy barrier against irreversible magnetic flux entry into a superconductor. J Low Temp Phys 12, 449–477 (1973). https://doi.org/10.1007/BF00654950
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DOI: https://doi.org/10.1007/BF00654950