Analysis of Transverse Resistance Measurements in ${\rm Nb}_{3}{\rm Sn}$ Superconducting Wires

The superconducting wires are generally made of several hundreds or thousands of fine superconducting filaments embedded in a metallic matrix. Several relevant properties of the superconducting wires depend on the transverse resistances between filament bundles. In
${\rm Nb}_{3}{\rm Sn}$
wires realized with Bronze Route or Internal Tin technology, the presence of the bronze matrix can determine a significant increase of the transverse interfilament resistance with respect to wires with copper matrix. This increased resistivity in turn plays a role in determining the ac losses, thermal stability, and sensitivity to mechanical bending of the wire. The direct measurements of the transverse electrical resistances give useful information both for stability computations and to analyze the mechanical performance of the wire. The complexity of these measurements is however remarkable, due to the current distribution phenomena that occur among superconducting filaments during these tests. This paper presents the application of a 2D FEM model of the wire cross section and of a 3D electrical circuit model of the wire sample to derive qualitative and quantitative information about the transverse electrical resistance matrix. The paper shows that a detailed qualitative and quantitative description of the measurement results can only be obtained by means of a 3D model, that allows computing the current distribution along and across the sample length during the measurements.