Feedback System Design Techniques for Control of Intra-bunch Instabilities at the SPS

The feedback control of intra-bunch instabilities driven by electron-clouds or strong head-tail coupling 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. Different controllers are compared based on stability margins and equivalent noise gain between input-output of the processing channel. The controller design uses as example the bunch dynamics defined by the SPS ring including the Q20 optics.