Hamiltonian estimation of island width threshold for stochasticity onset on edge pedestal top in the presence of a resonant magnetic perturbation

This study applies the Hamiltonian method to analyze the nonlinear magnetic topology induced by Resonant Magnetic Perturbations (RMPs) in tokamaks. We investigate the system's chaotic behavior by comparing three methods: the renormalization method, Lyapunov exponents, and weighted Birkhoff average. A strong consistency is found among these methods in predicting the large-scale stochasticity threshold. The magnetic island width threshold provides a quantitative criterion for optimizing RMP-based edge-localized modes control, bridging a critical gap in plasma control strategies.