Synchro-betatron coupling in a proton storage ring with electron cooli
ng was studied experimentally by modulating a transverse dipole field
close to the synchrotron frequency. The combination of the electron co
oling and transverse field modulation on the synchrotron oscillation i
s equivalent to a dissipative parametric resonant system. The proton b
unch was observed to split longitudinally into two pieces, or beamlets
, converging toward attractors of the dissipative system. These phenom
ena might be important in understanding the effect of ground vibration
on the Superconducting Super Collider beam, and the effect of power s
upply ripple on the Relativistic Heavy-Ion Collider beam.