  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
$>10^{20}$ 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.
