The Poincaré map, lie generator, nonlinear invariant, parameter dependance, and dynamic aperture for rings

In earlier work related to the NSLS-II project we have outlined a control theory approach for the dynamic aperture problem. In particular, an algorithm for the joint optimization of the Lie generator and the working point for the Poincare map. This time we report on how the Lie generator provides guidelines on acceptable magnitudes for e.g. the intrinsic nonlinear effects from insertion devices, and the nonlinear pseudo-invariant from the map normal form can be used to optimize the dynamic aperture. We also show how a polymorphic beam line class can be used to study the parameter dependence and rank conditions for control of optics and dynamic aperture.