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We intend to develop and obtain a compact, high-efficiency and high-performance cyclotron using the high-temperature superconducting (HTS) magnet technology. In cyclotron applications, a high-accuracy magnetic field distribution with an isochronous field and an azimuthally varying field is spatially and temporally required for an HTS coil. In coils wound with HTS tapes, large shielding currents are induced in the HTS tape by the radial component of the magnetic field. The magnetic field generated by the shielding current affects the magnetic field distribution in the cyclotron application in the following issues: (1) field reduction by the shielding current, (2) accuracy of the field distribution, (3) temporal stability of the time-dependent shielding currents, and (4) field repeatability after charge and discharge repetitions. These effects are very critical in cyclotron applications. We developed a novel numerical simulation based on the finite element method, boundary integral equation, and fast multipole method. We investigated the spatial and temporal behavior of the magnetic field attributed to the shielding current in the HTS coil for the HTS cyclotron application.