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A compact HOM-damping beam-accelerating rf cavity was developed to mitigate coupled-bunch instabilities in electron storage rings. This cavity operates in the TM020 mode, characterized by a high Q -value and a high shunt impedance. The new HOM-damping mechanism leverages the unique field distributions of the TM020 mode, allowing direct embedding of rf absorbing materials into the cavity body. This novel structure underwent validation through rf simulations and measurements using a model cavity resonating at 508.58 MHz in the TM020 mode with a shunt impedance of 6.8 MΩ and designed to have HOM impedances of less than 0.1 MΩ longitudinally and 0.5 MΩ/m transversely. We also fabricated and tested a prototype cavity, showcasing its HOM-damping efficacy and high-power functionality at 120 kW, generating an accelerating voltage of 900 kV. This prototype operated successfully at full power, confirming the viability of both the damping structure and its high-power application. [ABSTRACT FROM AUTHOR]