Fundamental restriction to the isochronus ring FEL

It is proved that the longitudinal radiation excitation is a fundamental restriction to the isochronus ring FEL. The micro-bunch structure produced by the laser potential cannot exist stationary in the isochronus or quasi-isochronus storage ring. Especially, in a compact storage ring, isochronus ring FEL of shorter wave length than 10−1 mm is fundamentally forbidden.