Speaker
Description
We present an analytic phase-space and spectral framework for single-particle dynamics near the third-integer resonance in circular accelerators, emphasizing amplitude-dependent nonlinear effects. Starting from a resonant Hamiltonian in action–angle variables, we derive closed-form relations among island action, separatrix geometry, and the amplitude-dependent tune for both the primary orbit and the resonance islands. Mapping this parameterization into the frequency domain yields analytic predictions for the main spectral line and higher-order sidebands, enabling a quantitative interpretation of fine spectral structures, including tune plateaus (step-like tune locking). Multi-turn tracking with ELEGANT shows good agreement in both phase space and spectra, establishing a rigorous and interpretable basis for analyzing nonlinear resonance effects in Transverse Resonance Island Buckets (TRIBs), RF knock-out, and other resonance-island-based beam operations.
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