Identification of Intra-Bunch Transverse Dynamics for Model Based Wideband Feedback Control at CERN Super Proton Synchrotron

Multi-input multi-output (MIMO) feedback design techniques can be helpful to stabilize intra-bunch transverse instabilities induced by electron-clouds or transverse mode couplings at the CERN Super Proton Synchrotron (SPS). These MIMO techniques require a reduced order model of intra-bunch dynamics. We estimate a linear reduced order MIMO models for transverse intra-bunch dynamics and use these models to design model based MIMO feedback controllers. The effort is motivated by the plans to increase currents in the SPS as part of the HL-LHC upgrade. Parameters of the reduced order models are estimated based on driven beam SPS measurements. We study different types of controllers. We test the model based designs using macro particle simulation codes (CMAD and HEADTAIL) and compare its performance with FIR filters tested during beam measurements of the feedback system in SPS machine development (MD) studies.