Observation of Non-linear Effects in the Synchrotron Tune at LEP

For the purpose of energy calibration of LEP 2, the synchrotron tune was measured as a function of total accelerating voltage. Since the synchrotron tune also depends on energy loss, this method can be used to extract the beam energy with a very good precision. In the last year of LEP running, the synchrotron oscillations were excited with RF phase noise during the measurements, and a frequency shift was observed. The generic description of the oscillation does not account for large amplitudes. A higher-order approximation reveals a frequency correction to be added to the model if the oscillation enters the nonlinear regime. This paper presents the observations and compares the measurements with the extended model.