Beam cavity interaction

We begin by giving a description of the rf generator-cavity-beam coupled system in terms of basic quantities. Taking beam loading and cavity detuning into account, expressions for the cavity impedance as seen by the generator and as seen by the beam are derived. Subsequently methods of beam-loading compensation by cavity detuning, rf feedback, and feed-forward are described. Examples of digital rf phase and amplitude control for the special case of superconducting cavities are also given. Finally, a dedicated phase loop for damping synchrotron oscillations is discussed.