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Effect of RF phase modulation on the longitudinal beam dynamics

When the frequency of the RF noise is close to the synchrotron frequency, it will cause longitudinal beam instability. In order to study the effect of the instability, a sinusoidal phase modulation was applied to the RF system. The beam instability was observed with a streak camera. The oscillation amplitude and frequency of the beam versus the frequency of applied phase modulation was measured. The beam splitting into two beamlets in the same RF bucket was also observed when the frequency of phase modulation was close to the synchrotron frequency.