Determination of the linear coupling resonance strength using two-dimensional invariant tori

Abstract

Experimentally obtained Poincar\'e maps in the resonant rotating frame for particle motion with linear coupling revealed invariant tori of the two-dimensional Hamiltonian. Using these tori, we obtained the linear coupling strength, the tune shift with betatron amplitude coefficients, and the proximity parameter to the resonance. The coupling strength obtained with this method agreed well with that obtained from measuring the betatron tune separation of the normal modes.