Longitudinal radiation excitation in an electron storage ring

In an electron storage ring, even if electrons lose the same amount of energy by photoemissions in one turn, their path lengths vary according to where the photoemissions take place. Usually this fluctuation of the path length hides behind the well-known radiation excitation of energy spread. In a quasi-isochronous ring, however, the fluctuation of path length dominates over the bunch stretch owing to the radiation excitation of energy spread. We give an analytical expression for the equilibrium state within linear optics including the fluctuation of the path length. This formula gives an intrinsic lower limit of the equilibrium bunch length in a quasi-isochronous storage ring.