Nonlinear optimization for longitudinal beam injection in diffraction-limited synchrotron light sources

Storage rings of the next generation synchrotron light sources have quite small dynamic apertures with which transverse beam injection can hardly be efficient. The longitudinal beam injection may be a solution to this problem. To apply a longer kicker pulse, it is necessary to increase time offset of the injected beam to the stored one by reducing RF frequency. The beam with a longer time offset will have a higher momentum deviation due to synchrotron motion, thus full injection of this method requires the storage ring to provide large enough energy acceptance and off-momentum dynamic aperture. A candidate lattice of the upgraded Shanghai Synchrotron Radiation Facility (SSRF-U) was used to nonlinearly optimize the longitudinal beam injection. With the optimal results of a series of RF frequencies, it is found that there is a critical RF frequency below which lowering frequency could not help to lengthen the kicker pulse in a given lattice. The beam injection into the SSRF-U storage ring was simulated and reached high efficiency with its critical RF frequency and optimal sextupole gradients.