Current Injection and Collection in a Rectangular Superconductor

I A general two-dimensional analytical solution is presented for the / problem of transport current injection from a normal conductor into a I 1 superconductor and collection back into a normal conductor. The current distribution is solved for the general case which takes in the full range from essentially point source to full-width injection and collection. The current distribution also represents that in a split ring superconductor joined by a link of variable width. A comparison is made with current injection into and collection from a normal conductor. Computer calculations are included showing a virtual anomaly which is reconciled. Speculation is made regarding the formation of transport current vortices in an initially simplyconnected superconductor. (Submitted for publication) *Work supported by the U. S. Atomic Energy Commission. ** Fellow of Centro de Investigacicn y de Estudios Avanzados de1 IPN and Consejo National de Ciencia y Tecnologia (Mexico). I. Analysis of Injection and Collection in a Superconductor With the increasing use of superconductors in electromagnets, in power transmission, and in electrical machinery, the normal to superconducting interface becomes a more scientifically and technologically important boundary to understand. It is of interest to consider the, general case of current injection from a normal conductor into a superconductor and collection back into a normal conductor, The results are also valid for the current distribution in a superconducting split ring joined by a link of variable width. For generality, let the injection and collection regions be of arbitrary width 2d in a rectangular superconductor of width 2a and length 2b, as shown in Fig. 1. So that the problem may be treated two-dimensionally, the superconductor may be either a thin film or infinitely thick. The current, I, is homogeneous within the injection region of current density, J = 1/2d, per unit length. By taking the curl of the London equation v x vx-j+=L -1 PA2 s , I and combining it with Maxwell’s equation pp vxg (no displacement current) and the continuity condition v . F= 0 for steady state, we have as the differential equation to solve to obtain the distribution of supercurrent density Fin the superconductor. For convenience, we have defined p as the inverse of the penetration depth A. Due to the symmetry provided by our choice of coordinates, jy and jz, the (1)