Initial Results of Simulation of a Damping System for Electron Cloud-Driven Instabilities in the CERN SPS

Single and multi-bunch instabilities on bunch trains driven by electron clouds have been observed in the CERN SPS for some years. In this paper, we present initial results to implement a damping system in a computer simulation of a single bunch vertical instability using the HEADTAIL code. The code simulates the interaction between a proton bunch and a uniform electron cloud that has built up inside of the beam pipe. In all simulations we use typical SPS parameter sets for three different values of the beam momentum : 26 GeV/c, 55 GeV/c and 120 GeV/c. The feedback is implemented as a corrective kick calculated from the vertical centroid of each slice of the electron bunch with a one turn delay. The bandwidth of the feedback is varied by filtering the slice information along the bunch. Initial results indicate that the instability can be damped with a minimum bandwidth of 300 MHz with a relatively high gain.