Bunch-by-bunch detection of coherent transverse modes from digitized single-bpm signals in the Tevatron

A system was developed for bunch-by-bunch detection of transverse proton and antiproton coherent oscillations based on the signal from a single beam-position monitor (BPM) located in a region of the ring with large amplitude functions. The signal is digitized over a large number of turns and Fourier-analyzed offline with a dedicated algorithm. To enhance the signal, the beam is excited with band-limited noise for about one second, and this was shown not to significantly affect the circulating beams even at high luminosity. The system is used to measure betatron tunes of individual bunches and to study beam-beam effects. In particular, it is one of the main diagnostic tools in an ongoing study of nonlinear beam-beam compensation studies with Gaussian electron lenses. We present the design and operation of this tool, together with results obtained with proton and antiproton bunches