Estimation of Longitudinal Profiles of Ion Bunches in the LHC Using Schottky-Based Diagnostics

The Large Hadron Collider (LHC) Schottky monitors have been designed to measure various parameters of relevance to beam quality, namely tune, momentum spread and chromaticity. We present another application of this instrument - the evaluation of longitudinal bunch profiles. The relation between the distribution of synchrotron amplitudes within the bunch population and the longitudinal bunch profile is derived from probabilistic principles. Our approach, limited to bunched beams with no intra-bunch coherent motion, initially fits the cumulative power spectral density of acquired Schottky spectra with the underlying distribution of synchrotron amplitudes. The result of this fit is then used to reconstruct the bunch profile using the derived model. The results obtained are verified by a comparison with measurements from the LHC Wall Current Monitors.