Periodic transient beam loading effect with passive harmonic cavities in electron storage rings

In our previous study of bunch lengthening for the planned Hefei Advanced Light Facility (HALF) storage ring, a periodic transient beam loading effect was found in the presence of passive harmonic cavities for some cases, which can dramatically affect the bunch lengthening as well as the beam stability [T. L. He et al., Bunch lengthening of the HALF storage ring in the presence of passive harmonic cavities, in Proceedings of the IPAC2021, Campinas, SP (JACoW, Campinas, SP, Brazil, 2021), pp. 2082-2085, TUPAB265]. In this paper, we continue to use HALF as an example, via both tracking simulation and semianalytical calculation, to comprehensively study the characteristics of this periodic transient effect, analyze its dependence on some relevant factors and investigate the impact of fill pattern on its periodicity. It is found that there exits a threshold current for this periodic transient effect, which can be increased by the reduction of R/Q of harmonic cavity (HC) and the increase of main cavity (MC) voltage, HC detuning, momentum compaction, and energy spread, as well as the inclusion of short-range wake. In addition, the periodicity of bunch centroid oscillation can be affected by the damping time and MC beam loading, and completely interrupted due to the nonuniform fill pattern, but this is not helpful for improvement of bunch lengthening.