Online regularization of Poincaré map of storage rings with Shannon entropy

Abstract

Shannon Entropy is adopted to quantify the chaos of measured Poincar\'e maps in the National Synchrotron Light Source-II (NSLS-II) storage ring. The recurrent Poincar\'e maps, constructed from beam position monitor's turn-by-turn readings, are commonly used to observe the nonlinearity in ring-based accelerators. However, these observations typically only provide a qualitative observation. With some canonical transformations on Poincar\'e maps, not only can the commonly used nonlinear characterizations be extracted, but more importantly, the chaos can be quantitatively measured with entropy. Entropy, therefore as a chaos indicator, is used for online Poincar\'e map regularization and dynamic aperture optimization in the NSLS-II ring.