Identification of intra-bunch dynamics for model-based beam instability control for the CERN super proton synchrotron
Keywords: Aeronautics and Astronautics.

The intra-bunch transverse dynamics in circular accelerators can be driven unstable from mechanisms of electron clouds or transverse mode coupling for high intensity and high energy operations. Beam instabilities can be performance-limiting factors in machine operations for the Super Proton Synchrotron (SPS) and potentially for the High Luminosity Large Hadron Collider (HL-LHC) at CERN located in Geneva, Switzerland. Therefore, stability of transverse beam dynamics is necessary for healthy machine operations at the desired energy and intensity levels, and is especially important for future higher intensity operations anticipated in the HL upgrade to the LHC. An intra-bunch feedback control system is a potential solution to stabilize transverse dynamics. The feedback and dynamics group at the SLAC National Accelerator Laboratory developed a Wideband Feedback System (WBFS) and demonstrated control of intra-bunch motion for a range of machine operation conditions. This result was obtained using limited power and computational resources in a demonstration system at the CERN SPS. The WBFS uses a diagonal control architecture with Finite Impulse Response (FIR) filters as control logic. This is the first demonstration of successful intra-bunch dynamics control using a wideband system for a nanosecond-scale proton beam. Although this approach successfully demonstrated the use of a wideband feedback system with 500 MHz bandwidth at a 3.2 Gs/sec. sample rate, experimental and simulation studies suggest limitations for the diagonal control architecture with FIR filters in terms of uniform damping for multi-modal instabilities, ability to provide resistive damping phase for the band of frequencies of interest (a.k.a loop stability for higher order modes), and actuation saturation due to noise and disturbance for more demanding operational conditions. This dissertation presents a new model-based multi-input multi-output (MIMO) control approach to study and overcome some of the limitations of the diagonal control architecture. The main challenge in developing the model-based approach is to capture dominant dynamics using simplified analytical models. A discrete-time linear time invariant (LTI) reduced-order model structure is proposed for the intra-bunch dynamics. A subspace system identification based technique is developed to estimate the parameters of the models using experimental SPS and high-fidelity nonlinear simulation (HEADTAIL, CMAD) data. It is demonstrated that the reduced-order models capture dominant intra-bunch transverse dynamics for the small motion linear operating regime. These models are validated against experimental and high-fidelity simulation data, and are shown to be sufficient to design a model-based controller. Model-based controllers, particularly Linear Quadratic Gaussian (LQG) controllers, are designed using the identified linear reduced-order models. The new control architecture is implemented and a few LQG controllers are tested in the high-fidelity numerical particle tracking simulation. Stabilization of multiple intra-bunch modes is demonstrated. The performance of the new model-based control approach is studied and evaluated in a comparative study with the diagonal FIR control architecture.