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In this paper, we propose to combine two promising research topics in accelerator physics, i.e., optical stochastic cooling (OSC) and steady-state microbunching (SSMB). The motivation is to provide a powerful radiation source which could benefit fundamental science research and industry applications. Our study shows that such a compact OSC-SSMB storage ring using present technology can deliver EUV light with an average power of kilowatt, and spectral flux phs/s/0.1%b.w., which is four orders of magnitude higher than existing synchrotron sources. It is expected that the presented work is of value for the development of both OSC and SSMB.

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