NEGATIVE-RESISTANCE INSTABILITY DUE TO NONLINEAR DAMPING

The longitudinal dynamics of a stored proton beam bunch, acted upon by a nonlinear damping force, was studied experimentally at the Indiana University Cyclotron Facility Cooler Ring. The effect of the nonlinear damping force on synchrotron motion was explored by varying the relat ive velocity between the cooling electron and the stored proton beams. Maintained longitudinal oscillations were observed, whose amplitude g rew rapidly once a critical threshold in the relative velocity between the proton and electron beams was exceeded. We attribute this phenome non to a negative resistance instability occurring after a Hopf bifurc ation.