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The bell-shaped single-cell cavities used in the SPring-8 storage ring are devised to suppress the coupled-bunch instabilities arising from the coupling impedances associated with higher-order mode resonances. The inner structures of the cavities are designed to have low longitudinal or transverse shunt impedances of the higher-order modes. The cavities are provided with a systematic modification of inner structures of the cavities and with multiple movable plungers to shift the resonant frequencies of higher-order modes thereby preventing higher-order mode resonances from being excited.