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Synchrotron motion with rf phase modulation was studied experimentally. Poincarb maps in the resonant precessing frame were obtained from the experimental data and compared with the tori of the resonant Hamiltonian. Our experimental data revealed island structure in longitudinal phase space. Experimental results for synchrotron motion excited by phase modulation at the third harmonic of the synchrotron frequency are also reported. '

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The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the Indiana University Cyclotron Facility Cooler Ring. Particles were kicked onto resonance islands and the properties of these islands were studied. The island tune was determined with high precision by Fourier analyzing the spectrum containing the island oscillations. The island width was estimated based on a single-resonance model. The Hamiltonian of particle motion near a resonance condition was thus deduced.

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