Nonlinear Current Flow around Defects in Superconductors

Abstract

We consider nonlinear two-dimensional transport current flow Jsrd 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 b ­ sn 2 1dy2 p n for a plate with cuts. We obtained analytical solutions for nonlinear current flow around a planar defect which causes anisotropic longrange disturbances of Jsrd on the scale L , a p n much larger than the defect width 2a and large stagnation regions of magnetic flux near the defect. A nonanalytic crossover in Jsrd was traced from the small but finite resistivity for large n to the true critical state with n ! `. [S0031-9007(98)07136-1]