Work

Analytic Phase-Space and Spectral Modeling of Amplitude-Dependent Resonance Island Dynamics near the Third-Integer Resonance

Year: 2026

Type: article

Abstract: 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 obtain elliptic-function solutions that give closed-form relations between island action, separatrix geometry, and 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, providing a quantitative interpretation of structures such as the devil’s staircase. Multiturn tracking with ELEGANT shows good agreement in both phase space and spectra, establishing a rigorous, interpretable basis for analyzing nonlinear resonance effects in transverse resonance-island buckets, RF knock-out, and other resonance-island-based beam operations.

Source: Progress of Theoretical and Experimental Physics

DOI: 10.1093/ptep/ptag071

Authors: Ki Moon Nam, Moses Chung, Seunghwan Shin, Hyunchang Jin, Yong Woon Parc

Institutions: Korea Basic Science Institute, Pohang University of Science and Technology, Pohang Accelerator Laboratory

Language: English

Topic: Particle accelerators and beam dynamics

Subfield: Aerospace Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $979

Funders: Korea Basic Science Institute, National Research Foundation of Korea, Ministry of Science and ICT, South Korea