SLAC, Menlo Park, California, USA
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 are used to identify the dynamics, which is represented as discrete time multi-input multi-output (MIMO) system. We focused 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 values for each mode and correct separation between modes.
SLAC, Menlo Park, California, USA
CERN, Geneva, Switzerland
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 correction fields to multiple se ctions of a nanosecond-scale bunch. These requirements impose challenges and limits in the design of the feedback channel. We present experimental measurements taken from CERN SPS machine development studies with an intra-bunch feedback channel prototype. The performance of a 3.2 GS/s digital processing system is evaluated, quantifying the effect of noise and limits of the feedback channel in the bunch stability as well as transient and steady state motion of the bunch. The controllers implemented are general purpose 16 tap FIR filters and the impact on the bunch stability of controller parameters are analyzed and quantified. These studies based on the limited feedback prototype are crucial to validate reduced models of the system and macro-particle simulation codes including the feedback channel. These models will allow us predicting the beam dynamics and controller limits when future wide-band hardware is installed in the final prototype to stabilize multiple bunches.
