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In this paper, we simulate the effects of eddy currents induced by switched gradient coils in the cylindrical cryostat structures of a high-temperature superconducting (HTS) magnetic resonance imaging magnet. A novel network method was used with spectral decomposition of the current density in the φ- and z-directions to simulate the effects of X-gradient coils. Two types of active magnetic shielding were simulated, and it was found that one type is able to reduce the power of the eddy currents in the cryostat to a greater extent than the other. These results will inform the design of gradient coils that protect the HTS magnet from eddy-current-induced heating and vibrations.