Experimental observations of nonlinear coupling of longitudinal modes in unbunched beams

In an unbunched beam in a synchrotron, under conditions where the beam distribution is marginally stable, coherent fluctuations can cause a nonlinear coupling of longitudinal modes. Experimental observations of this parametric resonance have been reported previously. Frequency domain measurements in the Fermilab Main Ring show pathological beam distributions associated with regions of marginal stability in longitudinal phase space; these are believed to be a requirement for the manifestation of the observed coupling. We have extended this investigation to the case of the beam response to an impulse excitation. The temporal development of the response indicates the formation of soliton-like structures within the beam distribution whose characteristics depend on beam conditions and the machine impedance.