Dieter Lens

Predictive control for longitudinal beam dynamics in heavy ion synchrotrons

We present a design of a predictive control scheme for longitudinal beam dynamics in heavy ion synchrotrons. Specifically, we consider a linear-quadratic model predictive control (MPC) approach, whereby the quadratic program is solved via a fast gradient method. Furthermore, we investigate whether the fast gradient method allows for real-time feasible implementation of the proposed approach on a field programmable gate array (FPGA). Our results indicate that sampling rates in the order of 1MHz are achievable.

Damping of longitudinal modes in heavy-ion synchrotrons by RF-feedback

The stability of RF (radio frequency) control systems is an essential part of particle accelerator technology. In accelerators, such as heavy-ion synchrotrons, RF feedback systems are used to damp longitudinal oscillation modes of the particle beam. Longitudinal modes have been analyzed in detail by accelerator physicists and there exists a closed theory that describes most of the observed phenomena in synchrotrons. However, from the point of view of the control engineer who wants to design the RF controls, there is a lack of convenient models to study the RF control loop dynamics analytically. Recently, it was shown that the interaction of the RF and the first two longitudinal modes can be described by a bilinear model. In this paper, it is shown that the measurement of the first harmonic of the beam current signal is sufficient to calculate the model output vector. This result is used to design nonlinear controls for the second longitudinal oscillation mode. The control design is based on the sumof- squares decomposition. The controls are compared using particle tracking simulations.

A Digital Beam-Phase Control System for a Heavy-Ion Synchrotron With a Dual-Harmonic Cavity System

As it is planned to switch the heavy-ion synchrotron SIS18 from single- to dual-harmonic cavity operation after construction of the new Facility for Antiproton and Ion Research (FAIR), its closed-loop control system for the damping of coherent longitudinal oscillations needs an appropriate adjustment. To damp dipole oscillations, the phase shift, applied by the control system to the first cavity voltage (running with harmonic number h1) has to be doubled for the second cavity (running with double frequency and harmonic number h2 = 2 · h1). Furthermore, the dipole oscillation frequency can no longer be estimated by linearization of the applied voltage like it is done in a single-harmonic cavity setting. In a dual-harmonic cavity setting as it is presented here, the dipole oscillation frequency depends nonlinearly on the bunch length. The control loop is closed by a digital signal processor, an optical splitter, and direct digital synthesizers. This paper describes the control loop and its theoretical background, and presents measurement results. In addition, simulation results and theoretical predictions are given, which are all in good agreement. Furthermore, optimal filter parameter settings are derived.

Progress in damping of longitudinal beam oscillations during acceleration

In the FAIR synchrotrons, coherent longitudinal oscillations of the bunched beam will have to be damped by dedicated feedback systems. While the damping for coasting beam energy has been successfully verified in SIS18 by several experiments (cf. e.g. [1]), the damping of these modes during the acceleration process poses additional challenges. The main technological issues are discussed and a progress status is given. For details on the longitudinal feedback system for FAIR with bunch-by-bunch feedback, we refer to [2].

Comparison of filter designs for a digital beam-phase feedback system in a Heavy-Ion Synchrotron

The bunched particle beam in a synchrotron can perform various longitudinal oscillation modes of which the dipole mode occurs most frequently. Although naturally damped by Landau damping, these oscillations can become unstable if driven accordingly. In any case Landau damping is accompanied by filamentation of the bunch which leads to rms emittance blow up and thus reduces the beam quality. Therefore a beam-phase feedback is used to damp dipole oscillations. At GSI Helmholtzzentrum für Schwerionenforschung GmbH the feedback is designed as an FIR filter [1]. However, the feedback performance may be improved using a matched filter instead of the current filter setting as is demonstrated in this work by comparing the different filter designs.

Cavity Impedance Reduction Strategies During Multi Cavity Operation in the SIS100 High Intensity Hadron Synchrotron

The planned SIS100 heavy ion synchrotron at the GSI Helmholtzzentrum für Schwerionenforschung will possess twenty ferrite accelerating cavities in its final stage of extension. As at injection and at flat top during slow extraction of the planned acceleration cycles the RF voltage will be relatively low, not all cavities will be active in this part of operation. It is important to analyse the impact of the inactive cavities on the overall RF voltage and subsequently their implication on the longitudinal particle dynamics. Classical approaches for reducing the beam impedance consist of active detuning of the cavities to pre-described parking frequencies. The fact that two out of ten buckets have to stay empty in all SIS100 scenarios is of particular interest as additional frequency components appear in the excitatory beam current, which have to be considered when the cavity is detuned. Therefore multi-cavity particle tracking simulations, consisting of twenty cavities and their attached LLRF control systems, are carried out in order to analyse different possibilities to minimize the impact on the beam dynamics and emittance growth.

Tuning of 3-Tap Bandpass Filter during Acceleration for Longitudinal Beam-Stabilization at FAIR

During acceleration in the heavy-ion synchrotrons SIS18/SIS100 at GSI/FAIR longitudinal beam oscillations are expected to occur. To reduce longitudinal emittance blow-up, dedicated LLRF beam feedback systems are planned. To date, damping of longitudinal beam oscillations has been demonstrated in SIS18 machine experiments with a 3-tap filter controller (e.g. [1]), which is robust in regard to control parameters and also to noise. On acceleration ramps the control parameters have to be adjusted to the varying synchrotron frequency. Previous results from beam experiments at GSI indicate that a proportional tuning rule for one parameter and an inversely proportional tuning rule for a second parameter is feasible, but the obtained damping rate may not be optimal for all synchrotron frequencies during the ramp. In this work, macro-particle simulations are performed to evaluate, whether it is sufficient to adjust the control parameters proportionally (inversely proportionally) to the change in the linear synchrotron frequency, or if it is necessary to take more parameters, such as bunch-length and synchronous phase, into account to achieve stability and a considerable high damping rate for excited longitudinal dipole beam oscillations. This is done for singleand dual-harmonic acceleration ramps.

Verification of the longitudinal feedback topology in SIS18

To damp oscillations of bunched beams, SIS100 will be equipped with a bunch-by-bunch (BxB) longitudinal feedback system (LFB). This helps to stabilize the beam, to keep longitudinal emittance blow up low and to minimize beam losses. The proposed LLRF topology of the closed loop system is, in some aspects, similar to the beam phase control system [1]. The difference and challenge is mainly the BxB signal processing followed by the generation of a correction voltage in dedicated feedback cavities. The adapted topology was verified at SIS18 during a beam time in 2014 using LLRF prototype subsystems and the two ferrite acceleration cavities.

Closed-Loop Control

In this chapter, an introduction to the basics of continuous-time feedback systems is given. For more detailed treatments, the reader is referred to textbooks such as [1–5]. A simple amplitude control loop serves as an example in the following sections. The concepts presented here, however, may also be applied to more advanced control loops (cf. [6, 7]). The RF control loops are often called low-level RF (LLRF) systems to distinguish them from the high-power parts.

Ansätze zur modellprädiktiven Regelung der longitudinalen Strahldynamik in Synchrotronen

Zusammenfassung Die Stabilisierung der longitudinalen Strahldynamik in Hadronensynchrotronen ist ein anspruchsvolles Regelungsproblem, da die erforderlichen Abtastzeiten des Regelkreises im Bereich von wenigen Mikrosekunden bis hin zu einigen hundert Nanosekunden liegen. In diesem Beitrag wird untersucht, ob modellprädiktive Verfahren für die Regelung der longitudinalen Strahldynamik eingesetzt werden können. Durch eine geeignete Problemformulierung und effiziente numerische Algorithmen kann das Optimierungsproblem hinreichend schnell auf einem High-End-FPGA gelöst werden. Simulationen für das Synchrotron SIS18 verdeutlichen, dass deutliche Performanzgewinne erreicht werden können.