Coupled bunch dipole mode measurements of accelerating beam in the Fermilab Booster

The dipole oscillation of a coupled bunch mode was measured using a fast single shot digitizing oscilloscope. The phase centroid of the bunches was determined from the digitized waveform. The phase error of the bunches as a function of bunch number was then Fourier analyzed, which provides the coupled bunch mode spectrum. The resulting spectrum was used to determine the evolution of coupled bunch mode instabilities in the Fermilab Booster. This method can determine the coupled bunch mode spectrum in a single turn in contrast to frequency domain methods which take at least a full synchronous period to complete the measurement.<
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