Quantitative Analysis and Optimization of Nb$_3$Sn Wire Designs Toward Future Circular Collider Performance Targets

In the context of the Future Circular Collider (FCC) study, industrial and academic partners are developing novel N$_3$Sn superconducting wires with a wide variety of layouts, production methods, and compositions, with the aim of achieving challenging performance targets including a non-copper critical current density of 1500 A mm–2 at 16 T and 4.2 K. There is a clear need for a systematic and quantitative approach to analyze these conductors, identifying correlations between performance, microstructure, and wire design, in order to optimize designs and heat treatments, and to identify the most promising directions for future trials. Image analysis methods have been developed to provide a quantitative description of key geometrical characteristics of a wire with an impact on N$_3$Sn phase formation and superconducting performance. In this paper, these methods are introduced, examples are presented of their application to prototype conductors produced for the FCC study, and opportunities for improving the performance of these prototype conductors are identified. Finally, initial steps toward models of diffusion and phase transformations are reported, and the potential for establishing a quantitative, analytical approach to wire design is evaluated, identifying topics requiring further research.