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Computed transient beam loading effects with harmonic RF systems

Harmonic cavities have been used in storage rings to lengthen bunches and increase beam lifetimes dominated by Touschek scattering. Transient beam loading in the harmonic cavities generated by asymmetries in the fill pattern can cause significant variation of the beam phase and bunch length along the bunch train when the longitudinal restoring force has been reduced, resulting in a significant reduction in the mean bunch lengthening and potential lifetime increase. We describe how beam current modulations give rise to transient effects much larger than expected from the linear model of the beam-cavity interaction. We also develop a tracking simulation to predict results and apply this simulation to an analysis of the beam loading transients for the case of a passive and active normal and superconducting third harmonic RF systems using ALS parameters.