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.
Highlights
The Large Hadron Collider (LHC) rf system consists of eight rf stations per beam
Each rf station includes an accelerating superconducting cavity, a 330 kW klystron, and the low level rf (LLRF) system consisting of the klystron polar loop and the impedance control feedback system
It should be noted that with this treatment, the individual noise sources with power spectrum density SNðfÞ can be shaped or colored noise sources. This is an advantage of this formalism over a similar analysis using the FokkerPlanck equation, which cannot be extended to colored noise sources, or to white noise sources shaped by the dynamics of the rf station, as discussed in [5,6]
Summary
The Large Hadron Collider (LHC) rf system consists of eight rf stations per beam. The rf system accelerates the beam during the ramp, compensates the small energy losses during coasting, and provides longitudinal focusing. Each rf station includes an accelerating superconducting cavity, a 330 kW klystron, and the low level rf (LLRF) system consisting of the klystron polar loop and the impedance control feedback system. Single-bunch longitudinal emittance growth as well as beam stability related to collective effects are examined in this paper Both of these longitudinal dynamics effects are strongly coupled to the effective impedance of the rf station and the configurations of the feedback loop. III a quantitative description of the relationship between the noise spectral density and the longitudinal beam emittance will be presented, as a function of the rf loop configuration and the system noise
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