Longitudinal peak detected Schottky spectrum

The "peak detected Schottky" spectrum is a diagnostic used since the late seventies for beam observation in the SPS and now already applied to the LHC. This tool was always believed, however without proof, to give a good picture of the particle distribution in synchrotron frequencies similar to the longitudinal Schottky spectrum of unbunched beam for revolution frequencies.In this paper an analysis of this measurement technique is presented both in a general form and for the particular realisation in the SPS. In addition the limitations of the present experimental set-up are discussed together with possible improvements. The analysis shows that for an optimised experimental set-up the spectrum of the peak detected signal is very close to the synchrotron frequency distribution inside the bunch - much closer than that given by the traditional longitudinal bunched-beam Schottky spectrum.