Speaker
Description
Summary
This paper presents the dynamic model and simulation of the beam-cavity interactions
in both Low Energy Ring (LER) and High Energy Ring (HER) at PEP II. The motivation
for development of this toll is to explore the stability margins and performance
limits of PEP II LLRF systems at higher currents and possible upgraded RF
configurations. In addition, it will serve as test bed for new control algorithms
and
strategies. The goal is to develop a simulation tool that allows understanding the
impact of new LLRF processing functions in each RF station such as complex comb
loops, klystron linearizers including limitations, etc. as well as better define the
ultimate limits of the architecture and implementation.
The program, based on the singular perturbation concept, captures the dynamical
behavior of the system based on a reduced model valid at a time-scale where the
beam-cavity interaction occurs, and considers in that time frame, the slow dynamics
as a constant in the model formulation. The simulation is a time-domain model, so
that nonlinear elements in the klystron and processing can be included. The ring
current is represented by macro-bunches, with time structure consistent with the
time
resolutionof the simulation and necessary modal frequency resolution to explore
coupled-bunch modes within the RF system bandwidth. The effect of multiple RF
stations in the ring is represented via one or two single macro-cavities. Each
macro-cavity capture the overall behavior of all the RF stations composed by two or
four cavities, respectively. This allows modeling of the principal longitudinal
impedance control loops. The macro-cavities interact with a longitudinal beam model
to study the effects of bunch interactions.
This work is in progress and the program has been validated with data collected from
PEP II and SPEAR. Measured transfer functions of the cavity and control system are
compared with the simulation results to show the agreement between both results.
Measured grow rates for the beam in different conditions at PEP II and SPEAR rings
are compared with the preliminary grow rate predictions using the simulation.
