Bunch-by-bunch measurement of transverse coherent beam-beam modes in the Fermilab Tevatron collider

A system for bunch-by-bunch detection of transverse proton and antiproton coherent oscillations in the Tevatron is described. It is based on the signal from a single beam-position monitor 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, band-limited noise is applied to the beam for about 1 s. This excitation does not adversely affect the circulating beams even at high luminosities. The device has a response time of a few seconds, a frequency resolution of 1.6e-5 in fractional tune, and it is sensitive to oscillation amplitudes of 60 nm. It complements Schottky detectors as a diagnostic tool for tunes, tune spreads, and beam-beam effects. Measurements of coherent mode spectra are presented to show the effects of betatron tunes, beam-beam parameter, and collision pattern, and to provide an experimental basis for beam-beam numerical codes. Comparisons with a simplified model of beam-beam oscillations are also described.