Analysis of the TLS longitudinal feedback system

Effectiveness of the TLS longitudinal feedback system to damp bunch phase oscillations has been studied under various operation conditions. The maximum kick voltage that is available for bunch phase correction is limited by power amplifier saturation. Operation of the feedback system in the linear and nonlinear regions of the power amplifier have been simulated. In the case of power amplifier saturation, the damping time is proportional to the initial oscillation amplitude. The oscillation amplitude decrease linearly before the power amplifier reaches its linear regime. The effects of a hold buffer in the DAC/MUX unit and time delay of the feedback loop will also be discussed.