Thin superconductors in a perpendicular magnetic ac field: General formulation and strip geometry

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Abstract
The sheet current, electric field, and penetrating magnetic field in response to an applied perpendicular ac magnetic field are calculated for a thin type-II superconducting strip characterized completely by its sheet resistivity, which may be either nonlinear and frequency independent or linear, complex, and frequency dependent. The general formulation is given for the linear or nonlinear response of a strip and a circular disk in perpendicular time-varying magnetic field. An elegant and rapid numerical method is presented which solves this, in general, nonlinear one-dimensional integrodifferential equation with high precision on a personal computer and which accounts for the facts that the integral kernel has a logarithmic singularity and the sheet current for nearly ideal shielding (occurring at short times or high frequencies or for strong pinning of flux lines) has a one-over-square-root singularity near the specimen edges. As examples the linear Ohmic response of the strip to a sudden change of the applied field and to an ac field are given; Ohmic response is realized during flux flow or thermally activated flux flow. The complex magnetic susceptibility and the ac losses of the Ohmic strip are computed and approximated by simple expressions. This work completes the calculation of dissipation peaks in vibrating superconductors caused by various diffusion modes of the flux lines.