Nonlinear Longitudinal Beam Response Measurements at the ALS

We report on longitudinal beam-transfer function BTF measurements at the Advanced Light Source ALS for large phase-modulation amplitudes. As the amplitude of the swept-frequency excitation is increased, the dipole beam response around the synchrotron frequency develops a notch in the amplitude response with a corresponding sharp jump in the phase response. These observations are explained by a splitting of the beam into two beamlets created by the nonlinearity of the forced synchrotron oscillations. This is demonstrated with measurements of the longitudinal bunch proole using a streak camera. We also present measurements of the diiusion rate from one stable island to the other for a xed modulation frequency and compare the measured rates with those expected from Touschek scattering. Finally, w e comment on BTF measurements for sub-and superharmonic resonances. ABSTRACT We report on longitudinal beam-transfer function BTF measurements at the Advanced Light Source ALS for large phase-modulation amplitudes 1; 2. As the amplitude of the swept-frequency excitation is increased, the dipole beam response around the synchrotron frequency develops a notch in the amplitude response with a corresponding sharp jump in the phase response. These observations are explained by a splitting of the beam into two beamlets created by the nonlinearity of the forced synchrotron oscillations. This is demonstrated with measurements of the longitudinal bunch proole using a streak camera. We also present measurements of the diiusion rate from one stable island to the other for a xed modulation frequency and compare the measured rates with those expected from Touschek scattering. Finally , w e comment on BTF measurements for sub-and superharmonic resonances.