Resonant conditions for a storage ring short wavelength FEL with power exceeding Renieri limit

In this paper we discuss the possibility of operating a storage ring FEL with resonant conditions providing for preservation of electron beam structure on an optical wave scale. We suggest tuning the storage ring betatron and synchrotron tunes on one of the high (Nth) order resonances to compensate dynamic diffusion of optical phase. This mode of operation does not require isochronicity of the ring lattice. In these conditions optical phase will be restored after N turns around the ring and stochastic conditions used in the derivation of Renieri limit are no longer applicable. We discuss the influence of high order terms in electron motion, RF frequency stability, and synchrotron radiation effects on preservation of optical phase.