Tracking code simulation for passive harmonic cavity in the SSRF storage ring

Background A passive third harmonic cavity is planned to install in the Shanghai Synchrotron Radiation Facility (SSRF) storage ring to increase the beam lifetime. Transient beam loading effect generated by the gap between the bunch trains can suppress the bunch lengthening effect of the third harmonic cavity. Besides, the field excited in the passive operation of the harmonic cavity depends on the bunch distribution. Purpose To estimate the effect of transient beam loading, the tracking codes have been developed. Methods The tracking simulation has been performed for three uniform filling cases and a nonuniform filling case. The lengthened bunch distribution has also been included into tracking code simulation. The effect of the lengthened bunch has also been investigated. Results The uniform filling pattern with shorter bunch trains shows lower transient beam loading effect and can give much higher bunch lengthening factors compared to those of non-uniform filling case. The effect caused by the reduction of the harmonic voltage generated by lengthened bunch distribution causes a great reduction on bunch lengthening effect in uniform filling case, while the lengthening factor of non-uniform filling case does not affect much in this issue. Conclusion The tracking codes have been developed to estimate the effect of transient beam loading for three uniform filling cases and a non-uniform filling case. The larger gap in the filling pattern can cause the higher transient beam loading effect and lower bunch lengthening effect. The lengthened bunch distribution has also been included into tracking code simulation. The effect of the lengthened bunch has also been investigated. The more the bunch is lengthened, the greater reduction on bunch lengthening effect.