THSCI1
MSU, East Lansing, Michigan, USA
A common task in the design and analysis of an accelerator is the study of the transfer map of the system. Of particular interest is the estimation of the region of stability of a given system. Typically, this is done using symplectic particle tracking and visual analysis of the resulting Poincare maps for signatures of chaoticity and island structures near high-period fixed points. We describe a method to compute rigorous enclosures of all periodic points of a given order in a given map based on Taylor Model methods. We then apply this algorithm to a real world transfer map of the Tevatron accelerator to rigorously identify islands and resonances in its transfer map. This mathematically rigorous method to locate resonances in the transfer map automatically yields all regions where resonances up to a certain order appear. The island structure exhibited by the map in those regions is then studied further by computing the invariant manifolds associated with the hyperbolic periodic points of the map. This manifold structure can provide further insight into the dynamics of the map, including the emergence of chaotic motion at the appearance of crossings of the manifolds.
