Abstract
The quasi-isochronous (QI) dynamical system, in the presence of synchrotron radiation damping and rf phase modulation, exhibits a sequence of period-2 bifurcations en route towards global chaos (instability) in a region of modulation tune. The critical modulation amplitude for the onset of the global chaos shows a cusp as a function of the modulation tune. This cusp is shown to arise from the transition from the 2:1 to the 1:1 parametric resonances. We have also studied the effect of the rf voltage modulation on the QI dynamical system and found that the tolerance of the rf voltage modulation is much larger than that of the rf phase modulation. \textcopyright{} 1996 The American Physical Society.
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