Coupled-bunch instabilities excited by the interaction of the particle beam with its surroundings can seriously limit the performance of circular particle accelerators. These instabilities can be cured by the use of active feedback systems based on sensors capable of detecting the unwanted beam motion and actuators that apply the feedback correction to the beam. Advances in electronic technology now allow the implementation of feedback loops using programmable digital systems. Besides important advantages in terms of flexibility and reproducibility, digital systems open the way to the use of novel diagnostic tools and additional features. We first introduce coupledbunch instabilities, analysing the equation of motion of charged particles and the different modes of oscillation of a multi-bunch beam, showing how they can be observed and measured. Different types of feedback systems will then be presented as examples of real implementations that belong to the history of multi-bunch feedback systems. The main components of a feedback system and the related issues will also be analysed. Finally, we shall focus on digital feedback systems, their characteristics, and features, as well as on how they can be concretely exploited for both the optimization of feedback performance and for beam dynamics studies.

/pdf/multi-bunch-feedback-systems-3oisonrbna.pdf

Multi-bunch Feedback Systems

Coupled-bunch instabilities excited by the interaction of the particle beam with its surroundings can seriously limit the performance of circular particle accelerators. These instabilities can be cured by the use of active feedback systems based on sensors capable of detecting the unwanted beam motion and actuators that apply the feedback correction to the beam. Advances in electronic technology now allow the implementation of feedback loops using programmable digital systems. Besides important advantages in terms of flexibility and reproducibility, digital systems open the way to the use of novel diagnostic tools and additional features. We first introduce coupled-bunch instabilities, analysing the equation of motion of charged particles and the different modes of oscillation of a multi-bunch beam, showing how they can be observed and measured. Different types of feedback systems will then be presented as examples of real implementations that belong to the history of multi-bunch feedback systems. The main components of a feedback system and the related issues will also be analysed. Finally, we shall focus on digital feedback systems, their characteristics, and features, as well as on how they can be concretely exploited for both the optimization of feedback performance and for beam dynamics studies.

https://e-publishing.cern.ch/index.php/CYRSP/article/download/525/386

The common approach to achieve the high luminosity needed for high precision measurements adopted by the particle factories now under construction consists in storing high current e{sup +}e{sup -} beams distributed in many bunches in separate rings. The beams are brought together to collide at one interaction point. An inconvenience of this strategy is that the performances can be seriously limited by unstable coupled-bunch oscillations excited by transients or noise and sustained by long-lasting parasitic resonating modes (high order modes-HOM) in the vacuum chamber, mainly in the RF cavities. Minimization of the HOM content and broad-band feedback systems together with the reduction of the driving transients are the complementary cures to this kind of disease. This paper introduces the subject with some examples and special emphasis on bunch-by-bunch feedback systems.

/pdf/multibunch-instabilities-and-cures-226noys84p.pdf

Multibunch Instabilities and Cures

The DSP-based bunch-by-bunch feedback system installed in the PEP-II high-energy ring (HER) has been used to damp instabilities induced by unwanted higher-order modes (HOMs) at beam currents up to 605 mA during commissioning. Beam pseudospectra calculated from feedback system data indicate the presence of coupled-bunch modes that coincide with a previously observed cavity mode (0-M-2). Bunch current and synchronous phase measurements are also extracted from the data. These measurements reveal the impedance seen by the beam at revolution harmonics. The impedance peak at 3×frev indicates incorrect parking of the idle cavities, and explains the observed instability of mode 3. Bunch synchrotron tunes are calculated from lorentzian fits to the data. Bunch-to-bunch tune variation due to the cavity transient is shown to be large enough to result in Landau damping of coupled-bunch modes.

/pdf/commissioning-experience-from-pep-ii-her-longitudinal-36rvfx26p6.pdf

Commissioning experience from PEP-II HER longitudinal feedback

Bunch-by-bunch beam parameters monitor is a very useful tool for accelerator operation and optimization. An in situ bunch-by-bunch three-dimensional position and charge measurement system has been developed at the Shanghai Synchrotron Radiation Facility. Signals from beam position monitors carry almost full beam information, a broadband digital receiver can retain most information. Therefore, a four-channel wideband oscilloscope is employed to capture the signals from all electrodes of the beam position monitor. Correlation coefficient-based methods are used to extract these bunch-by-bunch parameters synchronously. We evaluated the performance of this bunch-by-bunch information extraction method, the measurement uncertainty of longitudinal phase is less than 0.2 ps, the uncertainty of transverse position is less than $10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and the charge uncertainty is 0.3% under the condition that the bunch charge is 600 pC. Thanks to the great performance of the new system, it is accurate enough to study the transient state during injection. In addition, an in situ wakefield measurement system is planned to be established based on this system.

https://link.aps.org/pdf/10.1103/PhysRevAccelBeams.24.032802

Bunch-by-bunch three-dimensional position and charge measurement in a storage ring

The operation of a longitudinal multibunch damping system using digital signal processing (DSP) techniques is shown via measurements from the Lawrence Berkeley Laboratory (LBL) Advanced Light Source (ALS) The feedback system (developed for use by PEP-II, ALS, and DAɸNE) uses a parallel array of signal processors to implement a bunch-by-bunch feedback system for sampling rates up to 500 MHz The programmable DSP system allows feedback control as well as accelerator diagnostics A diagnostic technique is illustrated which uses the DSP system to excite and then damp the beam The resulting 12-ms time domain transient is Fourier analyzed to provide the simultaneous measurement of growth rates and damping rates of all unstable coupled-bunch beam modes

/pdf/observation-control-and-modal-analysis-of-longitudinal-7317e9bzeg.pdf

Observation, control, and modal analysis of longitudinal coupled-bunch instabilities in the ALS via a digital feedback system

The operation of a longitudinal multi-bunch damping system using digital signal processing techniques is shown via measurements from the LBL Advanced Light Source. The feedback system (developed for use by PEP-II, ALS and DA NE) uses a parallel array of signal processors to implement a bunch by bunch feedback system for sampling rates up to 500 MHz. The programmable DSP system allows feedback control as well as accelerator diagnostics. A diagnostic technique is illustrated which uses the DSP system to excite and then damp the beam. The resulting 12 ms time domain transient is Fourier analyzed to provide the simultaneous measurement of growth rates and damping rates of all unstable coupled-bunch beam modes.

Observation, Control and Modal Analysis of Coupled-Bunch Longitudinal Instabilities

A bunch-by-bunch longitudinal feedback system has been designed and built to control coupled-bunch instabilities in the PEP-I1 machine. A prototype system has been installed at the Advanced Light Source at LBNL. Programmable DSPs allow longitudinal feedback processing in conjunction with data acquisition or instrumentation algorithms. Here we describe techniques developed for different beam and system diagnostics, such as measurements of the modal growth and damping rates and measurements of the bunch-by-bunch currents. Results from the Advanced Light Source are presented to illustrate these techniques.

Ultibuncw longitudinal insta ilities and beam diagnostics using a dsp-based feedback system

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Observation, control, and modal analysis of longitudinal coupled-bunch instabilities in the ALS via a digital feedback system

Observation, Control and Modal Analysis of Coupled-Bunch Longitudinal Instabilities

Ultibuncw longitudinal insta ilities and beam diagnostics using a dsp-based feedback system