Experimental determination of the Hamiltonian for synchrotron motion with rf phase modulation

Synchrotron motion with rf phase modulation was studied experimentally. Poincar\'e 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.