Identification of Intra-bunch Transverse Dynamics for Feedback Control Purposes at CERN Super Proton Synchrotron

We present methods for parameter estimation of intra-bunch transverse beam dynamics. The dynamics is represented via reduced order linear models. These models are useful in beam monitoring and in the design of feedback controllers to stabilize intra-bunch transverse instabilities. The effort is motivated by the plans to increase currents in the Super Proton Synchrotron as part of the HL-LHC upgrade where feedback methods could control instabilities and allow greater freedom in machine lattice parameters. Identification algorithms use subspace methods to compute a discrete multi-input multi-output (MIMO) representation of the nonlinear dynamics. We use macro particle simulation data (CMAD and HEADTAIL) and SPS machine measurements as the source of dynamics information for the identification of beam dynamics. Reduced models capture the essential dynamics of the beam motion or instability at a particular operating point, and can then be used analytically to design optimal feedback controllers. The robustness of the model parameters against noise and external excitation signals is studied, as is the effect of the MIMO model order on the accuracy of the identification algorithms.