An Active Feedback System to Control Synchrotron Oscillations in the Slc Damping Rings’

_ Initially the SLC Damping Rings accomplished Robinson instability damping by operating the RF accelerating cavities slightly detuned. In order to be able to run the cavities tuned and achieve damping for Robinson instability and synchrotron oscillations at injection an active feedback system has been developed. This paper describes the theoretical basis for the feedback system and the development of the hardware. Extensive measurements of the loop response including stored beam were performed. Overall performance of the system is also reported. Taking the derivative of (4) and substituting into (3) and grouping terms results in a homogeneous equation (5) with constant coefficients which describes a damped harmonic oscillator. The last term is the forcing function generated by the energy feedback. It is now obvious that the energy feedback-acts on the i term which determines the rate of damping.