Comparison of Multi-Scale Nonlinear and Conventional Linear Methods for Stress Analysis of Nb3Sn Superconducting Magnets

This is an extension of the work on a multi-scale nonlinear procedure that demonstrated how to conduct nonlinear stress analysis of Nb
₃
Sn superconducting accelerator magnets. The nonlinear procedure uses measured stress-strain curves of annealed copper, Nb
₃
Sn strands and coil samples as inputs, which reduces the number of assumptions made for material properties—key uncertainties of any engineering analysis. The results from nonlinear analysis, semi-nonlinear analysis, and linear analysis of the same QFFB2 Nb
₃
Sn quadrupole magnet under the same temperature and loads, were compared and discussed. The comparison illustrates that nonlinear stress analysis is significantly more accurate than other methods. As the superconducting coil block is a complex, composite material, it would be inadequate to assume the whole coil block to be linear, either isotropic or orthotropic. It is imperative to conduct nonlinear analysis by simulating the superconducting coil to the level of detail of the individual cables and individual strands. The nonlinear stress analysis procedure can be used to simulate not only Nb
₃
Sn magnets, but also NbTi and HTS magnets.