Analysis of coupled bunch instability spectra

Beam spectra observed during the development of a coupled bunch instability contains information about the coupled bunch mode n, which describes the phase shift between adjacent bunch oscillations. This number indicates the possible frequency of the guilty impedance with accuracy up to an integer multiple of the bunch spacing frequency. When there are many possible candidates with imprecisely known frequencies this can be insufficient. In this paper we discuss what additional information about the frequency of the source of instability can be obtained from the analysis of the unstable beam spectra envelope. This is applied to the measurements in the CERN SPS.