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Nonlinear nonlocal diffusion of magnetic flux in thin type-II superconductors and Josephson junction arrays: Exact solutions

S. N. Dorogovtsev
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Abstract

An exact solution of the nonlinear nonlocal diffusion problem is obtained that describes the evolution of the magnetic flux injected into a soft or hard type-II superconductor film or a two-dimensional Josephson junction array. (The magnetic field in vortices is assumed to be perpendicular to the film; the electric field induced by the vortex motion is proportional to the local magnetic induction; flux creep in the hard superconductors under consideration is described by the logarithmic U(j) dependence.) Self-similar flux distributions with sharp square-root fronts are found. The fronts are shown to expand with power law time-dependence. A sharp peak in the middle of the distribution appears in the hard superconductor case.

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S. N. Dorogovtsev. 1998-07-10. Nonlinear nonlocal diffusion of magnetic flux in thin type-II superconductors and Josephson junction arrays: Exact solutions. https://arxiv.org/abs/cond-mat/9807165

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