Online regularization of Poincaré map of storage rings with Shannon entropy

Abstract

Shannon entropy, as a chaos indicator, is used for online Poincaré map regularization and dynamic aperture optimization in the National Synchrotron Light Source-II (NSLS-II) ring. Although various chaos indicators are widely used in studying nonlinear dynamical systems, including modern particle accelerators, it is the first time to use a measurable one in a real-world machine for online nonlinear optimization. Poincaré maps, constructed with the turn-by-turn beam trajectory readings from beam position monitors, are commonly used to observe the nonlinearity in ring-based accelerators. However, such observations typically only provide a qualitative interpretation. We analyze their entropy to quantify the chaos in measured Poincaré maps. After some canonical transformations on the Poincaré maps, not only can the commonly used nonlinear characterizations be extracted, but more importantly, the chaos can be quantitatively calibrated with Shannon entropy, and then used as the online optimization objectives.

6 pages, 6 figures

References in corpus (4)

• Detecting chaos in particle accelerators through the frequency map analysis method
• The Reversibility Error Method (REM): a new, dynamical fast indicator for planetary dynamics
• Performance analysis of indicators of chaos for nonlinear dynamical systems
• Dedicated beam position monitor pair for model-independent lattice characterization at NSLS-II

Cited by in corpus (2)

• Construction of approximate invariants for non-integrable Hamiltonian systems
• Sextupole reduction via chaos suppression at the National Synchrotron Light Source II