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

Abstract

The Large Hadron Collider rf station-beam interaction strongly influences the longitudinal beam dynamics, both single-bunch and collective effects. Nonlinearities 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.

Radio frequency noise effects on the CERN Large Hadron Collider beam diffusion

“…It was evident that the growth rate of the bunch length is strongly related to the accelerating voltage phase noise power spectral density around kf rev AE f s , as predicted in [1]. When the BPL is off, the noise power is dominated by a single contribution at f s , which depends strongly on the 400.8 MHz reference noise.…”

“…VIII includes an elementwise study of the rf feedback noise contributions. This paper follows the work previously presented by the authors in [1,3].…”

“…Through these initial measurements, it was evident that the growth rate of the bunch length is strongly related to the accelerating voltage phase noise power spectral density around kf rev AE f s , as predicted in [1]. For a more quantitative and accurate study, a first test to inject noise around f s was not conclusive as the BPL significantly modified the injected noise spectrum.…”

“…The theoretical formalism presented in [1] suggests that the noise experienced by the beam depends on the accelerating voltage phase noise power spectrum, aliased to a band between DC and the first revolution harmonic, due to the periodic sampling of the accelerating voltage V c by the beam. Additionally, the dependence of the rf accelerating voltage noise spectrum on the low level rf (LLRF) configurations has been predicted using time-domain simulations and models described in [2].…”

Longitudinal emittance blowup in the large hadron collider

“…A theoretical treatment of the beam diffusion in the LHC has been presented in Ref. [3]. Using this treatment, a comparison of the estimated and measured longitudinal emittance growth rates was presented in Ref.…”