Chaos indicators for nonlinear dynamics in circular particle accelerators

The understanding of nonlinear effects in circular storage rings and colliders based on superconducting magnets is a key issue for the luminosity and the beam lifetime optimisation. A detailed analysis of the multidimensional phase space requires a large computing effort when many variants of the magnetic lattice, representing the realisation of magnetic errors or configurations for performance optimisation, have to be considered. Dynamic indicators for chaos detection have proven to be very effective in finding and distinguishing the weakly chaotic regions of phase space where diffusion takes place and regions that remain stable over time scales in the order of multiple hours of continuous operation. This paper explores the use of advanced chaos indicators, including the fast Lyapunov indicator with Birkhoff weights and the reverse error method, in realistic lattice models for the CERN Large Hadron Collider. Their convergence, predictive power, and potential to define a magnetic lattice quality factor linked to long-term dynamic aperture are assessed. The results demonstrate the efficiency of these indicators in identifying chaotic dynamics, offering valuable insights of these chaos indicators for optimising accelerator lattices with reduced computational cost compared to the classical approach based on CPU-demanding long-term tracking campaigns.