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

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Abstract
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.