Tracking simulations for the HLS-Ⅱ with a passive harmonic cavity in the symmetricand asymmetric fill patterns

A simulation code that executes the tracking of longitudinal oscillations of the bunches for the double rf system of the Hefei Light Source Ⅱ Project (HLS-Ⅱ) is presented to estimate the mean beam lifetime and the Robinson instabilities. The tracking results show that the mean beam lifetime is in agreement with the analytical results and the system is stable when we tune the harmonic cavity in the optimum lengthening conditions. Moreover, the simulated results of the asymmetric fill pattern show that some bunches are compressed only with a 7% gap (3 gaps), which will lead to the reduction in the mean bunch lengthening and potential beam lifetime. It is demonstrated that HLS-Ⅱ with a passive higher harmonic cavity is not suitable for operating in an asymmetric fill pattern.