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Superconductors in practical use can be subjected to spatially non-uniform and time-varying external field as well as carrying a transport current, for example, in an electrical machine. This paper verifies that the integral method can be used in situations in which the external field is spatially non- uniform, by providing both theoretical reasoning and simulation results. Variations in the integral method are reviewed, such as how to impose transport current. Further, the integral method is applied to calculate ac loss in superconducting tapes in an air-cored electrical machine in a two-stage process: the external field is calculated in a COMSOL model without superconducting tapes, and exported into the integral method model that consists of the tapes only. The time taken by the integral method is a small fraction of the time taken by the full machine model in COMSOL, which uses the T-A formulation. There are good agreements between the full COMSOL model and two-stage method incorporating the integral method.

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