EFFECTS OF RF VOLTAGE MODULATION ON PARTICLE MOTION

The effects of rf voltage modulation on synchrotron motion were studie d experimentally. The experimental data revealed the resonance islands generated by the rf voltage modulation, With electron cooling, beam p articles were observed to damp to the basins of these resonance island s or attractors, which were observed to rotate about the origin of the phase space at a half of the modulation frequency. The measured ampli tude of the attractors as a function of the modulation frequency agree d very well with the theoretical prediction. The Poincare maps in the resonance rotating frame were obtained from the experimental data and compared with tori of the Hamiltonian flow. Based on our theoretical f ormulation, slow beam extraction using rf voltage modulation and a ben t crystal are also studied.