The synchroton motion of a beam was tracked for the first time by digitizing the phase of the beam signal from a high bandwidth wall gap monitor relative to the rf phase and the momentum deviation with a transverse beam position measurement in a high dispersion region. The measured synchrotron tune as a function of the synchrotron amplitude agrees well with theory. When the rf stable phase angle was modulated harmonically, the response of the synchrotron motion showed characteristics of chaos and bifurcations of a parametric resonant system. Manipulating the rf system to create islands in the synchrotron phase space may offer applications in future hadron colliders.

• Received 2 November 1992

DOI:https://doi.org/10.1103/PhysRevLett.70.591