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Boron Neutron Capture Therapy (BNCT) is a cell-level precision targeted treatment modality. This paper designs a scanning magnet system for an 18 MeV/1 mA proton cyclotron-based BNCT facility. By continuously scanning in both horizontal and vertical directions using two scanning magnets, the system delivers a flat-topped square beam density distribution of 100 mm × 100 mm with uniformity exceeding 90% on the target, thereby preventing thermal overload on the target. Additionally, the scanning magnets operate at a maximum frequency of 200 Hz, inducing significant eddy current effects. The paper first introduces the layout of the scanning magnet system. Subsequently, the study compares the electromagnetic characteristics and eddy current effects of silicon steel and ferrite yokes, analyzing the temperature rise in the magnetic yokes caused by eddy current losses. Particle tracking was employed to validate the effective deflection of the beam, while the designed scanning waveforms verified the uniformity of the beam density distribution.