Critical Current Distribution in Composite Superconductors

It has long been known that for the description of the E(I)-characteristics of composite superconductors a distribution function can be used instead of a power law relation. With this approach, the conductor is represented by a serial connection of short subsections where the electrical resistance of each subsection is given by a parallel connection of the flux flow resistance of the superconductor and the resistance of the normal conducting matrix. Furthermore the local critical currents are assumed to be normally distributed around a mean value mu with a standard deviation sigma. If the local critical current in a subsection is exceeded a voltage is generated. The current distribution function is then given by the second derivative of the E (I)-characteristics divided by R/L with R being the overall resistance and L the measuring length. In general only the lower part of the distribution function is apparent. By soldering the conductor in a copper bar the whole distribution can be made visible. In this paper we will give examples of the suitability of the description with Gaussian distribution functions for the low temperature superconductors NbTi and Nb₃Sn as well as for a Bi2223 tape. A comparison will be made between measurements with and without additional copper.