Reconstruction of Transverse Phase Space From Transverse Feedback Data for Real Time Extraction of Vital LHC Machine Parameters

The LHC transverse feedback system (ADT) provides bunch by bunch, turn by turn, normalized and digitized beam position signals from four pick-ups per plane and for each beam. Together with already existing powerful computer-based observation systems, this data can be used to reconstruct in real-time the transverse phase space coordinates of the centre-of-charges, for each individual bunch. Such information is extremely valuable for machine operation, or transverse instability diagnostics. This paper aims on discussing and evaluating methods of combining four position signals for such analysis in the presence of noise and with active transverse feedback. Comparisons are made based on the extraction of vital parameters like the fractional tune or transverse activity. Analytical and numerical results are further benchmarked against real beam data.