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Measurements and simulations of longitudinal relaxation oscillations induced by HOMs

Although the linear theory of stable and unstable synchrotron oscillations has long been understood, there is no such satisfactory description of the large amplitude highly non-linear synchrotron motion. With an appropriate tuning of RF cavity impedance, large amplitude, low frequency, self-sustained relaxation oscillations of this synchrotron motion can be observed. This paper presents experimental data and computer simulations that give insights into the details of the mechanism involved.