Simulation of Transient Beam-Feedback Interaction and Application to Extraction of CNGS Beam from the SPS

For present and future high energy proton accelerators, such as the LHC, transverse feedback systems play an essential role in supplying the physics experiments with high intensity beams at low emittances. We developed a simulation model to study the interaction between beam and transverse feedback system in detail, bunch-by-bunch and turn-by-turn, considering the real technical implementation of the latter. A numerical model is used as the non linear behaviour (saturation) and limited bandwidth of the feedback system, as well as the transient nature at injection and extraction, complicates the analysis. The model is applied to the practical case of the CNGS beam in the SPS accelerator. This beam will be ejected from the SPS in two batches causing residual oscillations by kicker ripples on the second batch. This second batch continues to circulate for 2167 turns after the first batch has been extracted and oscillations are planned to be damped by the feedback system. The model can be extended to examine transient effects at injection (LHC), and coupled bunch instability effects can be included.