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Alpha particle accelerators hold significant potential for applications in the production of medical radioisotopes, particularly demonstrating unique advantages in obtaining At-211 medical radioisotope, which is difficult to produce via traditional neutron reactions, such as reactor neutron irradiation. In this paper, a high-frequency resonant cavity operating at 36.8 MHz was designed for a 30 MeV alpha particle cyclotron and multi-physics simulations were employed to analyze the electromagnetic characteristics, thermal distribution, mechanical deformation and frequency deviation of the cavity. Through the implementation of a deep-valley and stepped-impedance coaxial cavity, 36.8 MHz frequency resonance was achieved within a relatively compact volume while maintaining high Q-factor and low power consumption at 90 kV accelerating voltage. Furthermore, an inductive power coupler was placed near the short-circuit wall that was avoided in the constrained engineering environment. The reflection coefficient of RF coupler can be adjusted to below -35dB by rotating power coupler, which indicates excellent matching. The maximum electric field strength and thermal stress of water-cooled RF window during high-power operation have been analyzed. The engineering design will be informed by the physical analysis of RF cavity,which will be finished before 2026.