Search

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.

The Positron-Electron Project II (PEP-II) B Factory collider ended the final phase of operation at nearly twice the design current and 4X the design luminosity. In the ultimate operation state, eight 1.2 MW radio-frequency (rf) klystrons and 12 accelerating cavities were added beyond the original implementation, and the two storage rings were operating with longitudinal instability growth rates roughly 5X in excess of the original design estimates. From initial commissioning there has been continual adaptation of the low level rf (LLRF) control strategies, configuration tools, and some new hardware in response to unanticipated technical challenges. This paper offers a perspective on the original LLRF and longitudinal instability control design, and highlights via two examples the system evolution from the original design estimates through to the final machine with 1.2×10^{34} luminosity. The impact of unanticipated signals in the coupled-bunch longitudinal feedback and the significance of nonlinear processing elements in the LLRF systems are presented. We present valuable “lessons learned” which are of interest to designers of next generation feedback and impedance controlled LLRF systems.

A dynamics simulation model is used to estimate limits of performance of the positron-electron project (PEP-II). The simulation captures the dynamics and technical limitations of the low level radio frequency (LLRF) system, the high-power rf components, and the low-order mode coupled-bunch longitudinal beam dynamics. Simulation results showing the effect of nonlinearities on the LLRF loops, and studies of the effectiveness of technical component upgrades are reported, as well as a comparison of these results with PEP-II measurements. These studies have led to the estimation of limits and determining factors in the maximum stored current that the low energy ring/high energy ring (LER/HER) can achieve, based on system stability for different rf station configurations and upgrades. In particular, the feasibility of the PEP-II plans to achieve the final goal in luminosity, which required an increase of the beam currents to 4 A for LER and 2.2 A for HER, is studied. These currents are challenging in part because they would push the longitudinal low-order beam mode stability to the limit, and the klystron forward power past a level of satisfactory margin. An acceptable margin is defined in this paper, which in turn determines the corresponding klystron forward power limitation.

A time domain dynamic modeling and simulation tool for beam-cavity interactions in the Low Energy Ring (LER) and High Energy Ring (HER) at the Positron-Electron Project (PEP-II) is presented. Dynamic simulation results for PEP-II are compared to measurements of the actual machine. The motivation for this tool is to explore the stability margins and performance limits of PEP-II radio-frequency (RF) systems at future higher currents and upgraded RF configurations. It also serves as a test bed for new control algorithms and can define the ultimate limits of the low-level RF (LLRF) architecture. The time domain program captures the dynamic behavior of the beam-cavity-LLRF interaction based on a reduced model. The ring current is represented by macrobunches. Multiple RF stations in the ring are represented via one or two macrocavities. Each macrocavity captures the overall behavior of all the 2 or 4 cavity RF stations. Station models include nonlinear elements in the klystron and signal processing. This enables modeling the principal longitudinal impedance control loops interacting via the longitudinal beam model. The dynamics of the simulation model are validated by comparing the measured growth rates for the LER with simulation results. The simulated behavior of the LER at increased operation currents is presented via low-mode instability growth rates. Different control strategies are compared and the effects of both the imperfections in the LLRF signal processing and the nonlinear drivers and klystrons are explored.