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A newly designed RF accelerating cavity resonating 508.58 MHz is proposed for reinforcement of beam current in the SPring-8 storage ring. Since an increase in beam current induces coupled-bunch instabilities arising from coupling impedances of higher-order modes in RF cavities, the new RF cavity is provided with three ways for damping the higher-order modes: a re-entrant quasi-half-cell structure, ports skewing the field distributions of the higher-order modes and a grooved beam pipe terminated by materials absorbing RF power. The RF properties of the higher-order modes in the RF cavity were examined by the MAFIA frequency-domain simulation. The measured RF properties of the higher-order modes in an aluminum model cavity were consistent with the simulations and verified the performance of damping the higher-order modes in the RF cavity. [Copyright &y& Elsevier]