Relaxation oscillations of the synchrotron motion caused by narrow-band impedances

Although the linearized theory of small amplitude synchrotron oscillations and the instability thresholds derived from it have long been understood, t here is no satisfactory description of the large amplitude highly nonlinear synchrotron motion of a bunched beam. With an appropriate tuning of the RF cavity impedance, large amplitude, low frequency, self-sustained relaxatio n oscillations of this synchrotron motion are generated. This paper present s detailed experimental data on such behavior, tracking code results that r eproduce the important characteristics, and a simple analytical model that explains the key features of the relaxation oscillation: growth of the inst ability, saturation of the oscillation, breakup of the bunch, and subsequen t damping of the system back to the beginning of the next cycle of the rela xation oscillation. [S1063-651X(99)10110-7].