Modeling Longitudinal Oscillations of Bunched Beams in Synchrotrons

Longitudinal oscillations of bunched beams in synchrotrons have been analyzed by accelerator physicists for decades, and a closed theory is well-known [1]. The first modes of oscillation are the coherent dipole mode, quadrupole mode, and sextupole mode. Of course, these modes of oscillation are included in the general theory, but for developing RF control systems, it is useful to work with simplified models. Therefore, several specific models are analyzed in the paper at hand. They are useful for the design of closed-loop control systems in order to reach an optimum performance with respect to damping the different modes of oscillation. This is shown by the comparison of measurement and simulation results for a specific closed-loop control system.Comment: 14 pages, 14 figure

Theoretical Foundations of Synchrotron and Storage Ring RF Systems

This is an open access book. This course-tested text is an ideal starting point for engineers and physicists entering the field of particle accelerators. The fundamentals are comprehensively introduced, derivations of essential results are provided and a consistent notation style used throughout the book allows readers to quickly familiarize themselves with the field, providing a solid theoretical basis for further studies. Emphasis is placed on the essential features of the longitudinal motion of charged particle beams, together with the corresponding RF generation and power amplification devices for synchrotron and storage ring systems. In particular, electrical engineering aspects such as closed-loop control of system components are discussed. The book also offers a valuable resource for graduate students in physics, electronics engineering, or mathematics looking for an introductory and self-contained text on accelerator physics

Theoretical foundations of synchrotron and storage ring RF systems

This course-tested text is an ideal starting point for engineers and physicists entering the field of particle accelerators. The fundamentals are comprehensively introduced, derivations of essential results are provided, and a consistent notation style used throughout the book allows readers to quickly familiarize themselves with the field, providing a solid theoretical basis for further studies.   Emphasis is placed on the essential features of the longitudinal motion of charged particle beams, together with the corresponding RF generation and power amplification devices for synchrotron and storage ring systems. In particular, electrical engineering aspects such as closed-loop control of system components are discussed.   The book also offers a valuable resource for graduate students in physics, electronics engineering, or mathematics looking for an introductory and self-contained text on accelerator physics

Development of an ERL RF Control System

The Mainz Energy-recovering Superconducting Accelerator (MESA), currently under construction at Johannes Gutenberg-Universität Mainz, requires a newly designed digital low-level radio frequency (LLRF) system. Challenging requirements have to be fulfilled to ensure high beam quality and beam parameter stability. First, the layout with two recirculations and the requirements will be shown from an LLRF point of view. Afterwards, different options for the control system are presented. This includes the generator-driven system, the self-excited loop and classical PID controller as well as more sophisticated solutions

Longitudinal Beam Stabilization at FAIR by Means of a Derivative Estimation

During acceleration in SIS18/SIS100 at GSI/FAIR longitudinal beam-oscillations are expected to occur. To reduce emittance blow-up, dedicated LLRF beam feedback systems are planned. To date longitudinal beam oscillations have been damped in machine experiments with a finite-impulse-response (FIR) filter controller with 3 filter taps. An alternative approach implementing the FIR filter as a derivative estimator controller is simulated and tested. This approach shares the same controller topology and can therefore be easily integrated in the system. It exploits the fact that the sampling rate of the feedback hardware is considerably higher than the frequency of the beam oscillations. It is therefore capable of damping oscillations without overshoot within one oscillation period

Impact of Simplified Stationary Cavity Beam Loading on the Longitudinal Feedback System for SIS100

The main synchrotron SIS100 of the Facility for Antiproton and Ion Research (FAIR) will be equipped with a bunch-by-bunch feedback system to damp longitudinal beam oscillations. In the basic layout, one three-tap finite impulse response (FIR) filter will be used for each single bunch and oscillation mode. The detected oscillations are used to generate a correction voltage in dedicated broadband radio frequency (RF) cavities. The digital filter is completely described by two parameters, the feedback gain and the passband center frequency, which have to be defined depending on the longitudinal beam dynamics. In earlier works, the performance of the closed loop control with such an FIR-filter was analyzed and compared to simulations and measurements with respect to the damping of coherent dipole and quadrupole modes, the first modes of oscillation. This contribution analyzes the influence of cavity beam loading on the closed loop performance and the choice of the feedback gain and passband center frequency to verify future high current operation at FAIR

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 blowup, 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 single- and dual-harmonic acceleration ramps

A Method to Obtain the Frequency of the Longitudinal Dipole Oscillation for Modeling and Control in Synchrotrons with Single or Double Harmonic RF Systems

In a heavy-ion synchrotron the bunched beam can perform longitudinal oscillations around the synchronous particle (single bunch dipole oscillation, SBDO). If disturbances/instabilities exciting the SBDO exceed the rate of Landau damping, the beam can become unstable. Furthermore, Landau damping is accompanied by an increase of the beam emittance which may be undesired. Thus, control efforts are taken to stabilize the beam and to keep the emittance small. It is known that for a single harmonic cavity and a small bunch the SBDO oscillates with the synchrotron frequency if the oscillation amplitudes are small. For a larger bunch or a double harmonic RF systems that introduces nonlinearities, this is no longer valid. This work shows how the frequency of the SBDO can be determined in general. As a result, the SBDO can again be modeled as a harmonic oscillator with an additional damping term to account for Landau damping. This model can be used for feedback designs which is shown by means of a simple example. As the frequency of the SBDO and the damping rate depend on the size of the bunch in phase space, it is shown how this information can be obtained from the measured beam current

Input Signal Generation for Barrier Bucket RF Systems at GSI

At the GSI facility in Darmstadt, Germany, Barrier Bucket RF systems are currently designed for the SIS 100 synchrotron (part of the future FAIR facility) and the Experimental Storage Ring (ESR). The purpose of these systems is to provide single sine voltage pulses at the cavity gap. Due to the high requirements regarding the gap signal quality, the calculation of the pre-distorted input signal plays a major role in the system development. A procedure to generate the input signal based on the dynamic properties in the linear region of the system has been developed and tested at a prototype system. It was shown that this method is able to generate single sine gap signals of high quality in a wide voltage range. As linearity can only be assumed up to a certain magnitude, nonlinear effects limit the quality of the output signal at very high input levels. An approach to overcome this limit is to extend the input signal calculation to a nonlinear model of the system. In this contribution, the current method to calculate the required input signal is presented and experimental results at a prototype system are shown. Additionally, first results in the nonlinear region are presented

Test Setup for Automated Barrier Bucket Signal Generation

For sophisticated beam manipulation several ring accelerators at FAIR and GSI like the main synchrotron SIS100 and the ESR will be equipped with barrier bucket systems. Hence, the associated LLRF has to be applicable to different RF systems, with respect to the cavity layout and the power amplifier used, as well as to variable repetition rates and amplitudes. Since already the first barrier bucket pulse of a long sequence has to meet certain minimum demands, an open-loop control on the basis of calibration data is foreseen. Closed-loop control is required to improve the signal quality during a sequence of pulses and to adapt to changing conditions like temperature drifts. A test setup was realized that allows controlling the signal generator, reading out the oscilloscope as well as processing the collected data. Frequency and time domain methods can be implemented to approach the dynamics of the RF system successively and under operating conditions, i.e. generating single sine pulses. The setup and first results from measurements are presented as a step towards automated acquisition of calibration data and iterative improvement of the same