No abstract

The behavior of superconducting weak links in an ac magnetic field is considered. Both small and long uniform junctions are analyzed. Analytical results are presented for various limiting cases. The general case is solved numerically for different parameter choices and the results are presented. Both similarities and significant differences are found between the small junction and the long uniform junction. ͓S0163-1829͑97͒02845-2͔

We consider nonlinear two-dimensional transport current flow J͑r͒ in superconductors with the power-law voltage-current characteristics E~J n 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 ͑n 2 1͒͞2 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 J͑r͒ on the scale L ϳ a p n much larger than the defect width 2a and large stagnation regions of magnetic flux near the defect. A nonanalytic crossover in J͑r͒ was traced from the small but finite resistivity for large n to the true critical state with n !`. [S0031-9007(98)07136-1] PACS numbers: 74.60.GeThe calculation of two-dimensional (2D), nonlinear flow has been an important problem in aero and hydrodynamics [1], crystal growth [2], plasma physics [3], and many areas of condensed matter physics. Unlike linear 2D current flow, which can be treated by the powerful theory of analytic functions [1], the nonlinearity of the electric field-current density ͑E-J͒ characteristics considerably complicates both analytical and numerical calculations of J͑r͒. This problem is particularly important for the electrodynamics of high-temperature superconductors (HTS), where the strong thermally activated flux creep results in a highly nonlinear E͑J͒ below the critical current density J , J c defined at a crossover electric field E c between flux flow and flux creep regimes. For J , J c , E-J curves are often approximated by the power-law dependence E E c ͑J͞J c ͒ n with n ¿ 1 for magnetic field H below the irreversibility field [4,5].The limit n !`corresponds to the critical state model [6] which approximates E͑J͒ by the stepwise function J J c E͞E for E . 0 and E 0 for J , J c . Although very efficient for obtaining 1D and simple 2D current distributions [6,7], this model neglects the finite resistivity at J , J c , and thus allows many metastable current configurations J͑r͒ which satisfy divJ 0. This makes it very difficult to use this model to calculate transport current distribution in inhomogeneous HTS, which often exhibit percolative current flow [8,9]. A more general approach is to solve Maxwell's equations for J͑r͒ in nonlinear conductors connected to a dc power supply,Equations (1) enable a universal description of macroscopic electrodynamics of HTS [5,10] and describe a steady-state transport current flow set in after relaxation of transient regimes of local or nonlocal magnetic flux diffusion investigated in detail numerically by Brandt [5]. In this Letter we propose an analytical approach based on the hodograph transformation [1], which reduces Eqs. (1) to a single linear equation. This enabled us to obtain exact solutions of Eqs. (1), which exhibit novel features of the 2D nonlinear current flow around planar defects. In order to solve Eqs.(1), we introduce the scalar potential w, resistivity r͑J͒ E͑J͒͞J, and complex ...