Nonlinear Current Flow around Defects in Superconductors

Abstract

We consider nonlinear two-dimensional transport current flow J(r) in superconductors with the power-law voltage-current characteristics E∝Jn and n≫1. We propose a general method based on a hodograph transformation which reduces this nonlinear problem to the solution of a linear London equation with the inverse screening length β=(n−1)/2n for a plate with cuts. We obtained analytical solutions for nonlinear current flow around a planar defect which causes anisotropic long-range disturbances of J(r) on the scale L∼an much larger than the defect width 2a and large stagnation regions of magnetic flux near the defect. A nonanalytic crossover in J(r) was traced from the small but finite resistivity for large n to the true critical state with n→∞.

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