Study on Internal Strain Distribution of the High-Field Nb₃Sn Superconducting Accelerator Magnets With Homogenization Theory

To fabricate 10–16 Tesla high-field accelerator magnets, the high-Jc Nb
₃
Sn superconductor is one of the most practical choices. However, it is a brittle material and is strain-sensitive. To reduce the potential Jc degradation of the conductor, it is crucial to accurately evaluate the stress of the coils owing to the large Lorentz force during magnet excitation. In the traditional stress analysis of magnets, the coils are usually regarded as homogenized structures using isotropic material coefficients; however, most superconducting (SC) coils have hierarchical and complicated structures. To obtain a more accurate estimation, it is necessary to consider the detailed internal structure of the coils during stress analysis. In this study, the homogenization method was applied to multi-scale stress analysis of a high-field accelerator SC magnet. The effective material coefficients of Nb
₃
Sn coils were calculated using this method. Stress analysis of the magnet was performed using the effective material coefficients and isotropic material coefficients for comparison. Compared with the result obtained using isotropic material coefficients, the Von-Mises stress of the coil using effective material coefficients is larger at different load steps. The stress level of most Nb
₃
Sn filaments in the strand was higher than that of the coil. The maximum stress of the Nb
₃
Sn filaments appeared in the strand contact regions. In addition, there was a significant difference in the average stress of all materials in the strand. These findings will help develop more accurate analysis and simulation models for high-field SC magnets.