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Modeling and Simulation of Longitudinal Dynamics for LER-HER PEP II Rings

A time domain modeling and simulation tool for beam-cavity interactions in LER and HER rings at PEP II are presented. The motivation for this tool is to explore the stability margins and performance limits of PEP II RF systems at higher currents and upgraded RF configurations. It also serves as test bed for new control algorithms and can define the ultimate limits of the architecture. The time domain program captures the dynamical behavior of the beam-cavity interaction based on a reduced model. The ring current is represented by macro-bunches. Multiple RF station in the ring are represented via one or two macro-cavities. Each macro-cavity captures the overall behavior of all the 2 or 4 cavity RF station. Station models include nonlinear elements in the klystron and signal processing. This allows modeling the principal longitudinal impedance control loops interacting with the longitudinal beam model. Validation of simulation tool is in progress by comparing the measured growth rates for both LER and HER rings with simulation results. The simulated behavior of both machines at high currents are presented comparing different control strategies and the effect of non-linear klystrons in the growth rates.