Dependence of the shape of the resistive transition on composite inhomogeneity in multifilamentary wires

The shape of the resistive critical current transition is an important factor in the specification of a multifilamentary superconducting composite. We have made a detailed analysis of the relation of the shape of the resistive transition to the scale and distribution of inhomogeneity within a composite. In particular we are able to show that the ´n-value´ of a transition often has a simple inverse power law relation to the standard deviation of the spatial critical current distribution. The expression for the voltage at a particular current level depends on both the geometry of the composite and the detailed form of the critical current distribution. Two limits are discernable; the ´single filament´ limit, applicable when a given filament conserves its transport current and the ´coupled filament´ limit, applicable when current transfer between filaments dominates. The problem of deconvolution of an experimental transition to give the critical current distribution is discussed with specific reference to Nb3Sn multifilaments. A method of analysis is outlined which combines data from both the resistive transition in a multifilament, and the resistive transition in single filaments extracted from the multifilament.