Identification of Intra-Bunch Dynamics using CERN SPS Machine Measurements ∗

Modern control techniques can be used to design feedback systems for stabilizing the intra-bunch dynamics in the presence of electron cloud (ECI) and transverse mode coupling (TMCI) instabilities. These techniques require reduced models of the bunch dynamics. We present a methodology to identify reduced order linear models representing single bunch dynamics using CERN SPS machine measurements. Vertical motion, in response to a wideband excitation signal, is sampled multiple times across the 5 ns bunch. The data and an observable canonical structure [1] are used to identify the dynamics, which is represented as a discrete time multi-input multi-output (MIMO) system. We focus on mode 0 (barycentric) and mode 1 (head-tail) data to identify a reduced order model. Results show that models clearly capture dominant dynamics and replicate machine measurements with corresponding central tune, damping value for each mode and correct separation between the modes