ROLE OF PARAMETRIC RESONANCES IN GLOBAL CHAOS

The quasi-isochronous (QI) dynamical system, in the presence of synchr otron radiation damping and rf phase modulation, exhibits a sequence o f period-2 bifurcations en route towards global chaos (instability) in a region of modulation tune. The critical modulation amplitude for th e onset of the global chaos shows a cusp as a function of the modulati on 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 t he rf voltage modulation on the QI dynamical system and found that the tolerance of the rf voltage modulation is much larger than that of th e rf phase modulation.