Coupled-bunch instabilities excited by the interaction of the particle beam
with its surroundings can seriously limit the performance of circular particle
accelerators. These instabilities can be cured by the use of active feedback
systems based on sensors capable of detecting the unwanted beam motion and
actuators that apply the feedback correction to the beam. Advances in
electronic technology now allow the implementation of feedback loops using
programmable digital systems. Besides important advantages in terms of
flexibility and reproducibility, digital systems open the way to the use of
novel diagnostic tools and additional features. We first introduce
coupled-bunch instabilities, analysing the equation of motion of charged
particles and the different modes of oscillation of a multi-bunch beam, showing
how they can be observed and measured. Different types of feedback systems will
then be presented as examples of real implementations that belong to the
history of multi-bunch feedback systems. The main components of a feedback
system and the related issues will also be analysed. Finally, we shall focus on
digital feedback systems, their characteristics, and features, as well as on
how they can be concretely exploited for both the optimization of feedback
performance and for beam dynamics studies.Comment: 44 pages, contribution to the CAS - CERN Accelerator School: Advanced
Accelerator Physics Course, Trondheim, Norway, 18-29 Aug 201