The synchro-betatron coupling induced by modulating a transverse dipole field at a frequency close to the synchrotron frequency was studied experimentally. The combination of the electron cooling and transverse-field modulation on the synchrotron oscillation is equivalent to a dissipative parametric resonant system. Six-dimensional Poincar\'e maps were measured at ten-turn intervals. The proton bunch was observed to split longitudinally into two pieces, or beamlets, converging toward attractors of the dissipative system within a rf bucket. Based on our experimental results, the effects of ground vibration on the superconducting supercollider beam and the effects of power-supply ripple on the relativistic heavy-ion collider beam are examined.
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Wang et al. (1994) studied this question.
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