Abstract
In order to understand the beam behavior under rf phase modulation, which has been used to improve the beam lifetime, we studied the response of induced bunch oscillations. By applying a phase modulation at frequencies around two-times the synchrotron frequency, both the quadrupole-mode and the dipole-mode longitudinal oscillations were excited. We found that the bunch oscillated resonantly at two separate frequencies, which could be assigned to the coherent quadrupole-mode frequency and twice the coherent dipole-mode frequency, respectively.
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