Instabilities simulations with wideband feedback systems: CMAD, HEADTAIL, WARP

Transverse mode coupling (TMCI) and electron cloud instabilities (ECI) pose fundamental limitations on the acceptable beam intensities in the SPS at CERN. This in turn limits the ultimate achievable luminosity in the LHC. Therefore, future luminosity upgrades foresee methods for evading TMCI as well as ECI. Proposed approaches within the LHC Injector Upgrade (LIU) project include new optics with reduced transition energy as well as vacuum chamber coating techniques. As a complementary option, high bandwidth feedback systems may provide instability mitigation by actively damping the intra-bunch motion of unstable modes. In an effort to evaluate the potentials and limitations of such feedback systems and to characterise some of the specifications, a numerical model of a realistic feedback system has been developed and integrated into available instabilities simulation codes. Together with the implementation of this new feedback system model, CMAD and HEADTAIL have been used to investigate the impact of different wideband feedback systems on ECI in the SPS. In this paper, we present some details on the numerical model of the realistic feedback system and its implementation as well as the results obtained from the simulation study using this model together with the instability codes.