Harald Klingbeil

An FPGA-Based Linear All-Digital Phase-Locked Loop

In this paper, an all-digital phase-locked loop (ADPLL) is presented, and it is implemented on a field-programmable gate array. All components like the phase detector (PD), oscillator, and loop filter are realized as digital discrete-time components fed from analog-to-digital converters. The phase detection is realized by generating first an analytic signal using a compact implementation of the Hilbert transform and then computing the instantaneous phase with the CORDIC algorithm. A phase-unwrap component was realized, which extends the linear range of the PD, so that the linear model is valid in the full frequency range. This property leads to a constant lock-in time for arbitrary frequency changes. An analytic solution for the lock-in frequency range and the stability range including processing delays is given. All relations to design an ADPLL of the presented structure are derived. A detailed example application of an ADPLL designed as an offset local oscillator is given.

A Digital Beam-Phase Control System for Heavy-Ion Synchrotrons

A closed-loop control system for damping undesired longitudinal oscillations of particle bunches in heavy-ion synchrotrons is presented. The system is based on technologies like digital signal processors (DSPs), modern field programmable gate arrays (FPGAs), and direct digital synthesis (DDS). After describing the technological challenges, the design of the system is presented, and some theoretical background is given. Finally, measurement results are presented which are in good agreement with simulations and theoretical predictions.

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.

Bandwidth Requirement Determination for a Digitally Controlled Cavity Synchronisation in a Heavy Ion Synchrotron Using Ptolemy II

This paper describes a high-level simulation model and its application to determine bandwidth requirements for the hardware implementation of a digital control system. The simulation model is based on Ptolemy II and describes a heavy-ion synchrotron and its control systems for resonance frequency, beam phase, and cavity synchronisation. Simulations are used to verify the suitability of the chosen system structure and to obtain minimum update rates for the coefficients of the adaptive digital controllers. These update rates translate into bandwidth requirements for a fiber optical network connecting the different controller subsystems. Our modelling approach as well as our method to determine the low-level requirements are described in detail and simulation results are presented and discussed.

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.

Beam Loss and Longitudinal Emittance Growth in SIS

Beam losses of several percent occur regularly in SIS. The onset occurs during the RF capture of the beam. Previous studies have revealed that the losses can come from the RF bucket at the start of acceleration being over filled due to the longitudinal bucket acceptance being too small, or due to the mismatch between the mean energy from the UNILAC and synchronous energy of the SIS. The beam losses as measured by a DC beam transformer however show in addition to the sharp initial drop, for the above reasons, a much slower decay in the beam intensity. The speculated cause comes from the incoherent transverse tune shift of the bunched beam, which forces particles into transverse resonant conditions. The longitudinal emittance growth is also another important issue for SIS. Past measurements from Schottky‐noise pick‐ups have shown a factor of 3–5 increase in the longitudinal emittance depending on the extraction energy; a large factor when compared against expectations from theory. These factors were calcula...

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.

Kraftwirkungen statischer Felder

In diesem Kapitel werden grundlegende Kraftberechnungsmethoden in der elektromagnetischen Feldtheorie diskutiert. Die Ausfuhrungen sind auf den einfachen Fall der Statik sowie auf starre Korper beschrankt. Zunachst wird diskutiert, wie man mithilfe virtueller Verruckungen Krafte berechnen kann, die auf starre Korper wirken. Anschliesend werden ausgehend von den Formeln fur die Lorentzkraft und die Coulombkraft Kraftdichten eingefuhrt, um eine Kraftebilanz herzuleiten, die auf dem Maxwell’schen Spannungstensor basiert. Als Anwendungsbeispiel fur den Maxwell’schen Spannungstensor dient die Berechnung der Kraft, die zwischen einer Punktladung und einem dielektrischen Halbraum wirkt, vor dem sie platziert ist.