SLAC, Menlo Park, California, USA
CERN, Geneva, Switzerland
Stanford University, Stanford, California, USA
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.
CERN, Geneva, Switzerland
SLAC, Menlo Park, California, USA
CERN, Geneva, Switzerland
The feedback control of intra-bunch instabilities driven by electron-clouds or strong head-tail coupling (transverse mode coupled instabilities TMCI) requires bandwidth sufficient to sense the vertical position and apply multiple corrections within a nanosecond-scale bunch. These requirements impose challenges and limits in the design and implementation of the feedback system. This paper presents model-based design techniques for feedback systems to address the stabilization of the transverse bunch dynamics. These techniques include in the design the effect of noise and signals perturbing the bunch motion. They also include realistic limitations such as bandwidth, nonlinearities in the hardware and maximum power deliverable. Robustness of the system is evaluated as a function of parameter variations of the bunch.