The shielding-current-induced field is a serious concern for the applications of coated conductors to magnets. The striation of the coated conductor is one of the countermeasures, but it is effective only after the decay of the coupling current, which is characterised with the coupling time constant. In a non-twisted striated coated conductor, the coupling time constant is determined primarily by its length and the transverse resistance between superconductor filaments, because the coupling current could flow along its entire length. We measured and numerically calculated the frequency dependences of magnetisation losses in striated and copper-plated coated conductors with various lengths and their stacks at 77 K and determined their coupling time constants. Stacked conductors simulate the turns of a conductor wound into a pancake coil. Coupling time constants are proportional to the square of the conductor length. Stacking striated coated conductors increases the coupling time constants because the coupling currents in stacked conductors are coupled to one another magnetically to increase the mutual inductances for the coupling current paths. We carried out the numerical electromagnetic field analysis of conductors wound into pancake coils and determined their coupling time constants. They can be explained by the length dependence and mutual coupling effect observed in stacked straight conductors. Even in pancake coils with practical numbers of turns, i.e. conductor lengths, the striation is effective to reduce the shielding-current-induced fields for some dc applications.

We developed a novel software for large-scale electromagnetic field analyses of coils wound with coated conductors based on current-vector-potential formulation with thin-strip approximation. Although this formulation was effective for obtaining the precise solutions of the electromagnetic field, the strong nonlinear property of superconducting materials frequently led to highly ill-conditioned linear systems of equations, which were difficult to solve efficiently. Moreover, the memory consumption and computation time required for the analyses rapidly increased with the size of the analysis due to dense matrix operations. In our software, the first difficulty was addressed by a novel preconditioning technique based on the algebraic multigrid method. Algebraic multigrid preconditioning enabled us to efficiently and stably solve the ill-conditioned linear systems of equations encountered in our analyses. It also improved the robustness of the analyses containing multifilament-coated conductors. As regards the second difficulty, the hierarchical matrices representation drastically reduced the memory consumption related to the dense matrices, as well as computation time. Meanwhile, our implementation of the hierarchical matrices representation was quite compatible with parallel computations on distributed memory computers. Finally, we presented some practical examples of large-scale analyses, which became possible by using the new software. For instance, the analysis of a cosine-theta dipole magnet whose number of degrees of freedom was more than 1.5 million was successfully completed in 78 h by 56 parallel processes and with a total memory consumption of 177 GB.

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