Evaluation of non-linear phase space distortions via frequency analysis

Several methods have been developed recently to measure the frequencies of a time series to much higher precision than ordinary FFT. The decomposition of tracking or experimental data into a Fourier transform can therefore also be done with largely enhanced precision. On the one hand this allows to free these data from complicated phase space distortions. On the other hand, these high precision spectrum lines can be interpreted as being the result of the excitation of certain resonances. In this report we study how this information can be used to tackle resonances. It has to be stresses that this techniques requires no knowledge concerning the simulation model or the accelerator being studied. the only input needed is a series of tracking data or, in the case of the experiment, a set of turn-by-turn data after kicking the beam.