RF system models for the CERN Large Hadron Collider with application to longitudinal dynamics

The LHC RF station-beam interaction strongly influences the longitudinal beam dynamics, both single bunch and collective effects. Non-linearities and noise generated within the Radio Frequency (RF) accelerating system interact with the beam and contribute to beam motion and longitudinal emittance blowup. Thus, the noise power spectrum of the RF accelerating voltage strongly affects the longitudinal beam distribution. Furthermore, the coupled-bunch instabilities are also directly affected by the RF components and the configuration of the Low Level RF (LLRF) feedback loops. In this work we present a formalism relating the longitudinal beam dynamics with the RF system configurations, an estimation of collective effects stability margins, and an evaluation of longitudinal sensitivity to various LLRF parameters and configurations