C. Rivetta

Selecting rf amplifiers for impedance controlled LLRF systems - nonlinear effects and system implications

Several high-current accelerators use feedback techniques in the accelerating RF systems to control the impedances seen by the circulating beam. [1, 2] These Direct and Comb Loop architectures put the high power klystron and LLRF signal processing components inside feedback loops, and the ultimate behavior of the systems depends on the individual sub-component properties. Imperfections and non-idealities in the signal processing leads to reduced effectiveness in the impedance controlled loops. In the PEP-II LLRF systems non-linear effects have been shown to reduce the achievable beam currents, increase low-mode longitudinal growth rates and reduce the margins and stability of the LLRF control loops. We present measurements of the driver amplifiers used in the PEP-II systems, and present measurement techniques needed to quantify the small-signal gain, linearity, transient response and image frequency generation of these amplifiers.

Analysis of the longitudinal low-order mode beam dynamics in PEP-II rings at high current beams

PEP-II plans to achieve the final goal in luminosity will require an increase of the beam currents to 4 A for LER and 2.2 A for HER. These magnitudes are challenging in part because they will push the longitudinal low-order mode (LOM) beam stability and the station stability to the limit. To analyze the behavior of both rings at high currents and to understand the limits in the longitudinal feedback systems, a simulation tool has been developed at SLAC. This tool is based on a reduced model of the longitudinal LOM dynamics of the beam interacting with the effective impedance presented by the RF stations. Simulations and measurements of the longitudinal beam behavior in both rings have been performed to understand the ultimate limits of the systems. These studies have defined the impact of control loop parameters in the longitudinal beam dynamics, identified the limiting behavior of RF devices affecting the optimal performance of the RF stations and quantified the behavior of the longitudinal LOM beam dynamics. Results of sensitivity to parameter variations in the beam dynamics and limits in the maximum current that LER/HER can achieve based on the longitudinal beam stability are reported in this paper.

Control of Intra-Bunch Vertical Motion in the SPS with GHz Bandwidth Feedback

A GHz bandwidth vertical beam feedback system has been in development at the CERN SPS for control of unstable vertical beam motion in single bunch and bunch train configurations. We present measurements and recent studies of stable and unstable motion for intensities up to 2 × 1011 p/bunch [1]. The system has been operated at 3.2 GS/s with 16 samples across a 5-ns RF bucket (4.2 ns 3σ bunch at injection) and experimental results confirm damping of intra-bunch instabilities in Q20, Q22 and Q26 optics configurations. Instabilities with growth rates of 1/200 turns are well-controlled from injection, consistent with the achievable gains for the 2 installed stripline kickers with 1 kW broadband power. Measurements from multiple studies in single-bunch and bunch train configurations show achieved damping rates, control of multiple intra-bunch modes, behavior of the system at injection (including interaction with the existing vertical damper) and final damped noise floor. The work is motivated by anticipated intensity increases from the LIU and HL-LHC upgrade programs [2], and has included the development of a new 1 GHz bandwidth slotline kicker structure and associated amplifier system. TRANSVERSE WIDEBAND INTRA-BUNCH FEEDBACK DEMONSTRATION SYSTEM A single-bunch wideband digital feedback system was initially commissioned at the CERN SPS in November 2012 [3]. Over time the system has has been extended to include control for trains of 64 bunches [4] and configured with two 500-MHz bandwidth stripline kickers, each powered with 500W of broadband RF power. Over time the system has been used to study single bunch and multi-bunch beams at the SPS in Q26, Q20 and most recently Q22 optics. The essential goals in al these studies is to try to quantify the behavior of the feedback in terms of damping intra-bunch motion from impedance mechanisms, TMCI, or Ecloud mechanisms. ∗ Work supported by the U.S. Department of Energy under contract # DE-AC02-76SF00515, the US LHC Accelerator Research (LARP) program, the CERN LHC Injector Upgrade Project (LIU) and the US-Japan Cooperative Program in High Energy Physics. Figure 1: Vertical motion signal showing 16 samples across the bunch for 20,000 turns. Positive feedback is applied from turns 3500 6500, there is no feedback applied after turn 6500. The bunch motion is excited and continues without being damped.

Recent Upgrades to the CERN SPS Wideband Intra-bunch Transverse Feedback Processor

BACKGROUND One possible limitation of high luminosity operation for the LHC is electron cloud induced instabilities (ECI) and transverse mode coupled bunch instabilities (TMCI) in the SPS [1]. Such instabilities increase with higher beam intensities and can ultimately limit luminosity in the LHC. Several schemes are being pursued [2] to mitigate this effect: changes to the SPS lattice, vacuum chamber coating and active feedback control. The last item has been the focus of our work. To develop a practical feedback control system, a research and development effort has been undertaken between CERN and SLAC. This effort is multifaceted and involves beam and system dynamics simulation and modelling, technology development and machine measurements. The technology development portion has produced a wide bandwidth 4GSa/s transverse feedback demonstration or “demo” system. Machine development studies involving single bunch beam dynamics have given encouraging results: control of low-order intrabunch (head-tail) mode instabilities has been shown [3]. Building on this, our efforts continue with further refinement of the models and development of advanced control algorithms; both driving improvements to the feedback demonstrator system. The overall demo system has already undergone multiple improvements [4]. Focusing on the feedback processor itself, we outline several upgrades already performed and others in progress or being planned. SYSTEM OVERVIEW The transverse feedback demo system is shown in Figure 1. Vertical motion of the beam is sensed by a stripline Beam Position Monitor (BPM) pickup. Preprocessing occurs in the Analog Front End, where an RF hybrid produces the displacement signal, from the four pickup signals. This signal is then amplified, filtered and equalized before being passed to the feedback processor.

Instabilities simulations with wideband feedback systems: CMAD, HEADTAIL, WARP

Transverse mode coupling (TMCI) and electron cloud instabilities (ECI) pose fundamental limitations on the acceptable beam intensities in the SPS at CERN. This in turn limits the ultimate achievable luminosity in the LHC. Therefore, future luminosity upgrades foresee methods for evading TMCI as well as ECI. Proposed approaches within the LHC Injector Upgrade (LIU) project include new optics with reduced transition energy as well as vacuum chamber coating techniques. As a complementary option, high bandwidth feedback systems may provide instability mitigation by actively damping the intra-bunch motion of unstable modes. In an effort to evaluate the potentials and limitations of such feedback systems and to characterise some of the specifications, a numerical model of a realistic feedback system has been developed and integrated into available instabilities simulation codes. Together with the implementation of this new feedback system model, CMAD and HEADTAIL have been used to investigate the impact of different wideband feedback systems on ECI in the SPS. In this paper, we present some details on the numerical model of the realistic feedback system and its implementation as well as the results obtained from the simulation study using this model together with the instability codes.