Modeling and simulation of longitudinal dynamics for Low Energy Ring –High Energy Ring at the Positron-Electron Project

A time domain dynamic modeling and simulation tool for beam-cavity interactions in the Low Energy Ring (LER) and High Energy Ring (HER) at the Positron-Electron Project (PEP-II) is presented. Dynamic simulation results for PEP-II are compared to measurements of the actual machine. The motivation for this tool is to explore the stability margins and performance limits of PEP-II radio-frequency (RF) systems at future higher currents and upgraded RF configurations. It also serves as a test bed for new control algorithms and can define the ultimate limits of the low-level RF (LLRF) architecture. The time domain program captures the dynamic behavior of the beam-cavity-LLRF interaction based on a reduced model. The ring current is represented by macrobunches. Multiple RF stations in the ring are represented via one or two macrocavities. Each macrocavity captures the overall behavior of all the 2 or 4 cavity RF stations. Station models include nonlinear elements in the klystron and signal processing. This enables modeling the principal longitudinal impedance control loops interacting via the longitudinal beam model. The dynamics of the simulation model are validated by comparing the measured growth rates for the LER with simulation results. The simulated behavior of the LER at increased operation currents is presented via low-mode instability growth rates. Different control strategies are compared and the effects of both the imperfections in the LLRF signal processing and the nonlinear drivers and klystrons are explored.