UC Berkeley

The large range of length scales present within accelerator magnets suggests the incorporation of a hierarchical structure into computational models. Evaluation of the strain state present within the superconducting filaments is necessary in order to determine the critical current of Nb3Sn based magnets. As part of an ongoing investigation at LBNL, a three-dimensional nonlinear multiscale model is developed to investigate the behavior of Nb3Sn filaments due to macroscopic loading. The major building blocks within a superconducting magnet are used to represent each length scale within the multiscale model: Coil, Rutherford cable, strand, filament, Nb3Sn crystal lattice. Using the developed model, loads at the coil level due to precompression, thermal contraction, and Lorenz forces are translated into lattice strain within the Nb3Sn phase of the composite. Jc can then be calculated through use of measurements performed on bulk samples of Nb3Sn. In addition, the physical effects on each scale due to loading is examined. Each level of the hierarchical model is solved using Finite Element Methods, taking into account effects due to thermal contraction and plasticity. A conjugate gradient algorithm is coupled with a Netwon's method with line search in order to solve resulting systems of equations.