Modeling nonlinear behavior in the Fermilab Main Ring

Recent simulations of the Fermilab Main Ring indicate that the systematic nonlinearities of decapole order and higher lead to chaotic behavior and slow or sudden amplitude growth after many thousands of turns. This behavior is seen in the model at emittances very near the measured acceptance of the Main Ring. The simulation and results are discussed. The methods discussed have two objectives. First, the goal is to determine the dynamic aperature of a given accelerator model. Tracking provides an answer, although many thousands of turns are needed and many initial conditions must be explored. The concept of smear can be used to converge on the dynamic aperture more quickly. Second, tools are applied to the model in order to gain insight into the features of the model that lead to emittance growth. In particular, the eigenvalue technique can provide an early indicator showing that the orbit is visiting regions in phase space that are unstable on a single- or few-turn basis.<>