CERN Yellow Reports: Conference Proceedings
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Review of impedance-induced instabilities and their possible mitigation techniques
In this paper, some important impedance-induced insta- bilities are briefly described for both the longitudinal and transverse planes. The main tools used nowadays to predict these instabilities and some considerations about possible mitigation techniques are also presented.
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Space charge effects for transverse collective instabilities in circular machines
Fifty years ago, the first significant publication was presented on transverse collective instabilities of spacecharge-dominated beams in circular machines; it was a CERN preprint of G. Merle and D. Möhl “The stabilizing influence of nonlinear space charge on transverse coherent oscillations”. A relatively simple equation of motion was suggested there as something obvious. Although it was, strictly speaking, neither obvious nor even quite correct, as further studies have shown, it played and continues to play an extraordinarily important role. Thus, this anniversary adds a special flavor to the request of the workshop organizers to review the main results in this area of beam dynamics. Purporting to fulfill that, this paper is divided in two sections, on coasting and bunched beams respectfully. We rather rarely deal with coasting beams in circular machines, but still they deserve a special attention not only for themselves, but also as relatively simple configurations to start from and get some key ideas. This set of ideas includes a concept of rigid slices and strong space charge as its justification. Also, it includes inter-play of Landau damping (LD), space charge (SC) and octupoles, showing the importance of their polarity, in particular. These ideas, common for coasting and bunched beams, are presented in Sec. II and used in Sec. III. In the latter section, SC-modification of the transverse mode coupling instability (TMCI) is discussed, including paradoxes which were resolved in a discovery of convective instabilities. The goal of this paper is to present, in a compact way, the main results in the area of beam dynamics, specified by the subject, where both SC and wake field are important. To a certain degree, such a task cannot be free from some subjectivity and arbitrariness, and I beg pardon of those colleagues who will find some valuable results underrepresented or not presented at all.
Review of instabilities with ions or/and electrons and possible mitigations
The presence of ions and electrons from gas ionization, photoemission or secondary emission is unavoidable in the vacuum chambers of high intensity accelerators and storage rings. Under suitable conditions, these ions and electrons can accumulate and drive the beams unstable. In this contribution, the mechanisms behind and the main conditions for ion and electron accumulation in the bunched beams are summarized. The characteristics of the induced instabilities, as well as common modelling techniques and mitigation strategies are reviewed. The possible interplays between ions and electrons are also discussed.
Review of instabilities with beam-beam effects and possible mitigations
In circular colliders the two counter rotating beams interact electromagnetically at various locations along the ring, where sharing a common beam pipe, and at the interaction regions via the so called beam-beam force. These interactions are of different nature, long-range or head-on and they represent a very important non-linear force acting on the particle beams. When mitigating impedance driven instabilities the impact of beam-beam effects has to be accounted for, since these effects change many of the optical properties and particle dynamics with very important impacts to the stability conditions. Since the beam-beam force can change single particle properties as well as coherent beam oscillations they need to be added in all their aspects to the study of mitigation methods for coherent impedance driven instabilities. The beam-beam effects can help mitigating but can be detrimental in enhancing the coherent motion. Several observations from past colliders have shown the impact of beam-beam effects on beam stability but more recently the Large Hadron Collider (LHC) has given the possibility to experimentally probe the impact of these interactions on the beam stability due to the constant appearance of instabilities. A very dense experimental and theoretical campaign has been motivated to better understand their role in the instability picture. In this paper the main contributions to beam stability and mitigations coming from beam-beam effects are explained with direct observations and experimental evidences from the LHC. The challenges arising from the higher energy reach of future colliders has also boosted at a study level the development of alternative mitigating methods and a new strategy for the design of future accelerators with conventional mitigation techniques.
Operational experience of beam stability control
The CERN accelerator complex, as well as other accelerator facilities world-wide, produce a large variety of particle beams for use in experiments. The beam quality is of prime importance and can be characterised by many parameters, such as beam or bunch intensity, longitudinal and transverse beam size, time structure, etc. Certain combinations of these beam parameters, along with the machine characteristics such as impedance, can lead to challenging configurations that can drive the particle beams unstable, potentially leading to degradation of the beam quality and particle losses around the circumference of the accelerator. These losses result in activation of the accelerator components and therefore prolong the cooldown time to allow for hands-on preventive and corrective maintenance, hence reducing the beam time available for physics. Beam stability control is therefore of major importance for the operation of accelerators and can be obtained through distinct means for different accelerators and beam characteristics. This paper outlines the principal operational instability observations and mitigations applied for the CERN accelerator complex, complemented with approaches used in some other accelerator laboratories around the world. An attempt is made to illustrate the interplay between the beam dynamics experts and the operations teams.
Stability diagrams allow one to determine whether a system is stable due to the presence of incoherent tune spread in a beam, a phenomenon known as Landau damping. This paper presents an overview of the mathematical foundations that underpin stability diagrams. I first describe stability diagrams as a mapping between two complex planes: the space of eigenvalues of the underlying Vlasov equation, and a space that can most easily be described as the product of beam current and an effective impedance. I go on to describe the circumstances when the Vlasov description of impedance-driven instabilities can or can not be formulated to construct a stability diagram. Finally I outline how this is applied to impedance-driven collective effects in particle accelerators.
In these proceedings we sketch a general theory for Landau damping in the transverse plane, in the particular case of beam-coupling impedance with linear (octupolar) detuning as the source of tune spread. Using a Hamiltonian formalism and perturbation theory, we will go beyond the traditional stability diagram approach to obtain the general non-linear determinant equation that leads to modes determination. Limiting cases are studied, and preliminary results of the full formalism are obtained in an attempt to generalize the concept of stability diagram.
Landau damping in the longitudinal plane
Loss of Landau damping in the longitudinal plane can limit the performance of an accelerator and lead to particle losses via undamped bunch oscillations or to single- and multi-bunch instabilities. The threshold for loss of Landau damping for a single bunch is usually defined by comparing the position of the coherent bunch oscillation frequency with respect to the incoherent synchrotron frequency spread. Different ways of calculating this threshold are presented and compared, using the LHC as an example. Loss of Landau damping in longitudinal plane can be cured by increasing the synchrotron frequency spread, either through controlled emittance blow-up or the installation of an additional, higher- harmonic RF system.
Advanced Landau damping with radio-frequency quadrupoles or nonlinear chromaticity
Landau damping is a powerful mechanism to suppress impedance-driven coherent instabilities in circular accelerators. In the transverse planes it is usually introduced by means of magnetic octupoles. We will discuss a method to generate the required incoherent betatron frequency spread through detuning with the longitudinal rather than the transverse amplitudes. The approach is motivated mainly by the high-brightness, low transverse emittance beams in future colliders where detuning with the transverse amplitudes from magnetic octupoles becomes significantly less effective. Two equivalent methods are under study: a radio-frequency quadrupole cavity and the nonlinear chromaticity. The underlying beam dynamics mechanisms are explained based on a recently extended Vlasov theory and relevant results are discussed for dierent longitudinal beam distributions under specific approximations. Finally, the analytical studies are benchmarked against numerical simulations employing a circulant matrix and a macroparticle tracking model.
On Landau damping restoration with electron lenses in space-charge dominated beams
It is shown that the Lorentz forces of a low-energy, magnetically stabilized electron beam, or “electron lens”, can introduce transverse nonlinear focusing sufficient for Landau damping of transverse beam instabilities in accelerators. Unlike other nonlinear elements, the electron lens can provide the frequency spread mainly at the desirable range of particle amplitudes, thus permitting to avoid the beam lifetime degradation.
Many years have passed since the invention of BNS damping, but it still attracts wide attention of accelerator physicists to implement this method in classical accelerators and future high gradient acceleration technique. In this article we recall initial background principles of the development of BNS damping.
Mitigation of collective effects by optics optimisation
This paper covers recent progress in the design of optics solutions to minimize collective effects such as beam instabilities, intra-beam scattering or space charge in hadron and lepton rings. The necessary steps are reviewed for designing the optics of high-intensity and high-brightness synchrotrons but also ultra-low emittance lepton storage rings, whose performance is strongly dominated by collective effects. Particular emphasis is given to proposed and existing designs illustrated by simulations and beam measurements.
Transverse beam instabilities and linear coupling in the LHC
Transverse beam instabilities had been observed in the LHC when the tunes were moving closer together (Laslett tune shift at injection) or when the coupling was known to be large (the beam measurement of the closest tune approach, |C-| showed an increase to approximately the tune separation). This knowledge, in addition to the examples of transverse beam instabilities seen during the energy ramp at the HERA proton ring, hinted at a link between linear coupling and transverse stability. Linear coupling had been used in the Proton Synchrotron (PS) at CERN to stabilise a strong horizontal instability by coupling into the vertical plane. This was possible due to a sharing of the instability rise times between the two planes. These two sets of observations are seemingly in contradiction to each other. This provided the motivation for a study into how linear coupling plays a role in transverse beam stability in the LHC.
Coping with longitudinal instabilities using controlled emittance blow-up
Controlled emittance blow-up is a widely-spread method to mitigate beam instabilities in accelerators. This paper summarises the different methods used to generate and apply RF phase noise or RF phase modulation in the RF systems of the CERN synchrotrons. It also details machine by machine when and how different methods are used.
Suppression of the fast beam-ion instability by tune spread in the electron beam due to beam-beam effects
The fast beam-ion instability (FII) is caused by the interaction of an electron bunch train with the residual gas ions. The ion oscillations in the potential well of the electron beam have an inherent frequency spread due to the nonlinear profile of the potential. However, this frequency spread, and associated with it Landau damping, typically is not strong enough to suppress the instability. In this work, we develop a model of FII that takes into account the frequency spread in the electron beam due to the beam-beam interaction in an electron-ion collider. We show that with a large enough beam-beam parameter the fast ion instability can be suppressed. We estimate the strength of this effect for the parameters of the eRHIC electron-ion collider.
Beam loading compensation for optimal bunch lengthening with harmonic cavities
Emittance growth and short beam lifetime due to intra-beam scattering in extremely low emittance storage rings can be mitigated if harmonic RF cavities are used for the purpose of lengthening the longitudinal bunch size. The “flat potential condition” can be achieved with harmonic cavities, lengthening the bunch by a factor of ~5. However, the performance is limited by the transient beam-loading effect in the RF cavities, which is induced by gaps in the ring fill pattern. As a counter-measure of this effect, we have proposed the active compensation techniques by using a single kicker cavity having a bandwidth of several times the revolution frequency. The transient effect can be compensated when the kicker cavity voltage is determined to suppress bunch phase shifts along the train.
Suppression of the longitudinal coupled bunch instability in DAΦNE in collision with a crossing angle
In DAΦNE, the Frascati e+/e– collider operating since 1998, an innovative collision scheme, the crab waist, has been successfully implemented during the years 2008<span style="caret-color: #000000; color: #000000; font-family: source-serif-pro, serif; font-size: 17.81599998474121px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">–09. During operations for the Siddharta experiment an unusual synchrotron oscillation damping effect induced by beam-beam collisions has been observed. Indeed, when the longitudinal feedback is off, the positron beam becomes unstable with currents above 200–300 mA due to coupled bunch instability. The longitudinal instability is damped by colliding the positron beam with a high current electron beam (of the order of 2 A). A shift of about –600 Hz in the residual synchrotron sidebands is observed. Precise measurements have been performed by using both a commercial spectrum analyzer and the diagnostic capabilities of the longitudinal bunch-by-bunch feedback. The damping effect has been observed in DAΦNE for the first time during collisions with the crab waist scheme. Our explanation, based both on theoretical consideration and modelling simulation, is that beam collisions with a large crossing angle produce longitudinal tune shift and spread, providing Landau damping of synchrotron oscillations.
RF scheme to mitigate longitudinal instabilities in the SPPC
A large collider project CEPC-SPPC is under study with a global effort and a leading role from IHEP, with CEPC (Circular Electron-Positron Collider, Phase I) to probe Higgs physics and SPPC (Super Proton-Proton Collider, Phase II) to explore new physics beyond the Standard Model. The key design goal for SPPC is to reach 75 TeV in center-of-mass energy with a circumference of 100 km. As an important part of the SPPC conceptual study, the study on the longitudinal dynamics at SPPC has been conducted, with a focus on the RF scheme to meet the requirements for luminosity and mitigate the relevant instabilities. The longitudinal instability bottleneck associated with the longitudinal dynamics is the loss of Landau damping. To mitigate the beam instabilities, a higher harmonic RF system (800 MHz) together with the basic RF system (400 MHz) to form a dual-harmonic RF system is found helpful, which also increases the luminosity by producing shorter bunches. The preliminary results indicate that longitudinal impedance threshold can be increased.
Mitigation of space charge effects using electron column at IOTA ring
We investigate a novel method to mitigate space charge effects of high intensity proton beams propagating in circular accelerators by means of trapping and controlling electrons generated from beam-induced residual gas ionization. This compensation method uses Coulomb repulsion force between a proton beam and electrons to mitigate self-space charge effects of the beam if it passes through a plasma column. The transverse electron-proton (e-p) instability in the plasma column is well controlled by the longitudinal magnetic field of a solenoid magnet and the bias voltages on electrodes. In this report, we will show simulation results how to control distributions of electrons and ions as well as that of the proton beam inside the column.
Beam transfer function and stability diagram in the Large Hadron Collider
Predictions of transverse instability thresholds in the LHC are based on the computation of Landau damping by calculating the stability diagram (SD). However any modification of the tune spread and/or particle distribution modifies the expected Landau damping in the beams. The beam transfer function (BTF) provides direct measurements of the Landau damping and can be used to understand the limitations of the models.
We describe a proof-of-principle test to measure Landau damping in a hadron ring using a destabilizing transverse feedback acting as a controllable source of beam coupling impedance. The test was performed at the Large Hadron Collider and stability diagrams for a range of its Landau octupole strengths have been measured for its injection energy of 450 GeV. In the future, the procedure could become an accurate way of measuring stability diagrams throughout the machine cycle.
The spectrum of a quadrupolar pick-up gives access to coherent second-order modes of a beam in a non-invasive way. The signature of bunched beams not only features the first-order and second-order dipolar modes, but also most notably (1.) bands of even envelope modes, (2.) odd (skew) envelope modes and (3.) coherent dispersion modes. The odd (skew) envelope modes can provide information on linear coupling and mismatch thereof. The tunes of even envelope modes and the coherent dispersion modes shift significantly with space charge and can thus provide a measurement thereof. The paper presents measurements of the various modes at the CERN Proton Synchrotron, demonstrates how the spectral amplitudes depend on the mismatch conditions, and suggests a new, alternative way to quantify space charge at high brightness conditions via the coherent dispersion mode.
Diagnostics of longitudinal bunch instabilities at KARA
KARA, the Karlsruhe Research Accelerator, can be operated in different modes, including a short-bunch mode. During this mode, where the dispersion is stretched in order to reduce the momentum-compaction factor, micro-bunching instability can occur. At KARA, several measurement setups and techniques are used to investigate this instability further with the long-term perspective to suppress and control it. In this contribution, we give an overview about the different setups and the results achieved during the past years.
Impedance localization and identification
The beam coupling impedance represents one of the sources of potential beam instabilities in particle accelerators. The localization of large coupling impedance sources is therefore very important in order to focus the efforts for mitigation measures when these are needed. In this work we will focus on the common methods adopted to quantify the transverse impedance of a particle accelerator both from the global and the local point of views. This activity can be performed in both bunched and coasting beams following different strategies.
Source of horizontal instability at the CERN Proton Synchrotron Booster
The CERN Proton Synchrotron Booster (PSB) has been known to suffer from horizontal instabilities since its early operation. These instabilities appear at specific beam energies and range of working points. The source of the instability and the reason why the instabilities appear at specific energies remained unidentified. In routine operation, the instabilities have not been limiting the performance reach thanks to the horizontal feedback system. Recently, the interest in these instabilities has been sparked by the on-going LHC Injectors Upgrade (LIU) program, as well as, the Physics Beyond Colliders (PBC) study group. Their systematic characterization has been carried out through measurements. Macroparticle simulations and analytical modeling have been applied to explain the measurements and the dependence on the kinetic energy. Finally, the extraction kicker has been unambiguously identified as the source of the instability.
During Long Shutdown 2 (2019<span style="caret-color: #4d5156; color: #4d5156; font-family: arial, sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration: none; display: inline !important; float: none;">–2020) the transverse observation system (ADTObsBox) in the LHC will undergo a substantial upgrade. The purpose of this upgrade is to allow for true low latency, online processing of the 16 data-streams of transverse bunch-by-bunch, turn-by-turn positional data provided by the beam position monitors in transverse feed-back system in the LHC (ADT). This system makes both offline and online analysis of the data possible, where the emphasis will lie on online analysis, something that the older generation was not designed to provide. The new system provides a platform for real-time analysis applications to directly capture the data with minimal latency while also providing a heterogeneous computing platform where the applications can utilize CPUs, GPUs and dedicated FPGAs. The analysis applications include bunch-by-bunch transverse instability analysis which will profit from significant reduction of latency.
Reliable monitoring of the longitudinal beam quality is essential for a safe and effcient operation of any high intensity accelerator. The definition of beam quality criteria vary from one machine to the other, depending on the beam and machine parameters. In this paper, the most commonly used concepts of longitudinal beam quality monitoring are addressed with emphasis given on the applications in the circular accelerators at CERN.
Design optimization and impedance sources in Low Emittance Rings (LERs)
There is a clear trend today that future ultra-low emittance rings adopt vacuum chambers with a significantly reduced radius of aperture. A big effort would be needed to keep the machine impedance on the same level as before.
Low impedance design with example of kickers (including cables) and potential of metamaterials
Unmatched terminations of single elements were recently identified to be responsible for beam instabilities in the CERN PSB and LEIR machines. Impedance models are needed to estimate the impedance of similar devices and to assess potential intensity limitations. A circuital model that includes the effect of coupling to cables on the beam coupling impedance will be discussed. Moreover, examples of low impedance design with special emphasis on the mitigation of the impedance of ferrite kickers (e.g. longitudinal serigraphy) will be presented and guidelines for optimized impedance design will be provided. Finally, the potential of metamaterials for impedance mitigation will be discussed.
Low-impedance beam screen design for future hadron colliders
In future hadron colliders with collision energies greater than the energy of the Large Hadron Collider (LHC), the beamscreen becomes an increasingly important source of beam coupling impedance. This may lead to coherent beam instabilities, especially in the transverse plane, and potentially a failure to reach the desired beam intensity. Here we discuss design choices affecting the beamscreen impedance in the proposed Future Circular Collider (FCC-hh). We consider the resistive impedance of the copper walls and their high-temperature superconductor alternative, the impedance due to the surface treatment for electron cloud suppression, and the geometric impedance of the pumping holes and the interconnects.
The LHC at CERN is equipped with a sophisticated collimation system, aimed at protecting superconducting magnets against quenches in case of losses from the circulating beams. The collimation system is one of the major contributors to the machine impedance at top energy. A relevant hardware upgrade of the system will take place in the context of the High Luminosity LHC (HL-LHC) project; one of the main objectives is to make stabilisation of the brighter HL-LHC beams reachable within the capabilities of the Landau octupoles. In fact, a relevant fraction of the carbon–based collimators will be exchanged with new ones, the jaws of which are made of materials more optimised in terms of impedance; hence, the footprint of the collimation system will be significantly reduced. The present contribution gives an overview of the baseline low-impedance upgrade of the LHC collimation system as foreseen by the HL-LHC project and the expected impact on impedance. Additional options that could further improve the footprint of the collimation system on the machine impedance are briefly summarised.
The ability of a low secondary electron yield coating to mitigate detrimental electron cloud effects potentially affecting accelerators’ performances has been convincingly validated. The interference of such coatings with other properties required to accelerator constructive materials (i.e. vacuum compatibility, magnetic permeability, high surface conductivity, etc.) is of great concern and has recently attracted a lot of interest and studies. For instance, the severe impedance budget constraint requires the highest conductivity in the surface layers within the skin depth (typically some μm) characteristic of the e.m. interaction. It is therefore of uttermost importance to define the minimum thickness one overlayer should have in order to be an eective electron cloud mitigator and minimize its impact to surface conductivity. To this purpose, XPS and secondary electron spectroscopy have been simultaneously applied to the prototypical system formed by increasing coverages of amorphous Carbon (a-C) deposited on atomically clean Cu. XPS has been successfully used to qualify and quantify the a-C thickness, rendering possible a detailed coverage dependent study. A significantly thin a-C layer, of about 5 to 7 nm, is surprisingly enough to lower the secondary emission properties of the whole system below 1. This observation opens up the possibility to develop, on industrial scale, thin enough electron cloud mitigators that will not affect impedance issues.
Electron cloud mitigation with laser ablated surface engineering technology
Parameters of the high intensity accelerators with positively charged beams could be compromised by electron cloud (e-cloud) effect. One of the most efficient mitigation method is providing the beam vacuum chamber walls with low secondary electron yield (SEY). A discovery of low SEY surfaces produced with laser bblated surface engineering (LASE) brought a new technological solution for e-cloud mitigation. This paper highlights the main results obtained since its discovery in 2014.
Vlasov eigenfunction analysis of space-charge and beam-beam effects
Space-charge and beam-beam interaction affect both incoherent and coherent motion of particles potentially leading to instabilities and deterioration of the beam parameters. An overview of these phenomena will be given with an emphasis on the observable spectral characteristics and the mitigation methods of their harmful effects.
Active methods of suppressing longitudinal multi-bunch instabilities
Longitudinal multi-bunch instabilities limit the beam intensity and quality reach of hadron synchrotrons. In case the impedance source driving the instability is well known, for example an RF cavity, active feedback can be set up locally to reduce its effect on the beam. For multi-bunch instabilities excited by other impedances, global feedback systems are needed. A combination of both types is required to produce the high intensity beam for the future High-Luminosity LHC (HL-LHC) in the CERN Proton Synchrotron (PS). All RF cavities at 10 MHz, 20 MHz, 40 MHz and 80 MHz involved in the generation of LHC-type beams are equipped with direct, wideband feedback. To achieve an impedance reduction beyond their electrical stability limit, they are complemented by local 1-turn delay and multi-harmonic feedback systems. Additionally, a global coupled-bunch feedback loop operating in the frequency domain with a Finemet cavity as longitudinal wideband kicker damps all possible dipole oscillation modes. Beam measurements in the PS are presented, highlighting the key contributors needed to stabilize the highest intensity beams for the LHC.
Damping rate limitations for transverse dampers in large hadron colliders
The paper focuses on two issues important for the design and operation of bunch-by-bunch transverse damper in a very large hadron collider, where fast damping is required to suppress beam instabilities and noise induced emittance growth. The first issue is associated with kick variation along a bunch that affects the damping of head-tail modes. The second issue is associated with effect of damper noise on the instability threshold. The paper accounts for developments motivated by the discussions at this conference and carried out after it.
Implementation of transverse dampers in beam stability analyses
Collective effects in high intensity, high energy particle accelerators and colliders are becoming increasingly important as performance is continuously pushed to the limits. The mitigation of collective effects, in particular coherent beam instabilities, relies heavily on transverse feedback systems. The dimensioning of these feedback systems (i.e. power, bandwidth, pickup and kicker distribution) are key to the systems performance and its effectiveness in combating collective effect limitations. Consequently, their realistic modeling in computer simulation codes is also highly important. In this paper we will briefly outline recent developments in advanced modeling of transverse feedback systems in collective eects using the example of macroparticle simulation codes developed at CERN.
Interplay of transverse damper and head-tail instability
Transverse head-tail instability is a major limitation for the single-bunch beam current in circular accelerators. Beam-based feedback is one of the potential tools to suppress this type of instability. The feedback systems (transverse dampers) provide active suppression of the beam oscillations by electromagnetic fields, the amplitude of which is calculated in real time from the measured beam position. The effciency of the transverse dampers in combination with various chromaticity settings is discussed.
Destabilising effect of resistive transverse dampers
A resistive transverse damper is needed for multi-bunch operation in a machine like the CERN LHC and it is very efficient as it considerably reduces the necessary amount of nonlinearities (from octupoles) needed to reach beam stability through Landau damping. However, a resistive transverse damper also destabilizes the single-bunch motion below the transverse mode coupling instability (TMCI) intensity threshold (for zero chromaticity), introducing a new kind of instability, which has been called “ISR instability” (for Imaginary tune Split and Repulsion). The purpose of this contribution is to explain in detail this new instability mechanism and its mitigation.
Feedback design for control of the micro-bunching instability based on reinforcement learning
The operation of ring-based synchrotron light sources with short electron bunches increases the emission of coherent synchrotron radiation in the THz frequency range. However, the micro-bunching instability resulting from self-interaction of the bunch with its own radiation field limits stable operation with constant intensity of CSR emission to a particular threshold current. Above this threshold, the longitudinal charge distribution and thus the emitted radiation vary rapidly and continuously. Therefore, a fast and adaptive feedback system is the appropriate approach to stabilize the dynamics and to overcome the limitations given by the instability. In this contribution, we discuss first efforts towards a longitudinal feedback design that acts on the RF system of the KIT storage ring KARA (Karlsruhe Research Accelerator) and aims for stabilization of the emitted THz radiation. Our approach is based on methods of adaptive control that were developed in the field of reinforcement learning and have seen great success in other fields of research over the past decade. We motivate this particular approach and comment on different aspects of its implementation.
Coherent and incoherent space charge resonance effects
The question of interplay of coherent and incoherent space charge driven resonances and of their Landau damping has found some interest in beam dynamics of modern high-intensity synchrotrons. We revisit the theoretical and simulation models describing coherent half-integer parametric resonances, analyze their Landau damping in 2D beams on the basis of simulated tune spectra and conclude that above second order (envelope modes) they play no role in realistic, Gaussian-like beam models. We also analyze incoherent resonance effects in the beam core regions and find that their role has been underestimated in part of the literature, in particular with regard to the very long-term beam evolution as in synchrotrons. We conclude that for such time scales more careful analysis of realistic simulation models is needed to support synchrotron design and evaluation of experiments.
Space charge effects on Landau damping from octupoles
Octupole magnets are the cornerstone of the collective instability mitigation in many hadron synchrotrons, including the future SIS100 synchrotron of the FAIR project. The betatron tune shifts, and the tune spread, linearly increase with the octupole magnet current, and enhance Landau damping. On the other hand, a strong octupole field, as a nonlinearity, can reduce the dynamic aperture. This can put a restriction for the allowable octupole magnet power. Thus, a good understanding of the octupole magnet usage for Landau damping of the collective instabilities is important. The direct space-charge can produce comparable or stronger tune shifts than the octupoles. Thus the effects of space-charge should be taken into account in a study for Landau damping due to octupoles. Space-charge can have manifold effects on Landau damping. Space-charge can cause loss of Landau damping, it can provide Landau damping, it changes the incoherent tune distribution and thus changes Landau damping in the beam. The bunched beams are considered in this work, with the focus on the head-tail instability. Head-tail modes are eigenmodes of the transverse collective bunch oscillations. Unstable head-tail modes are a major concern for high-intensity operation in ring accelerators. We consider unstable head-tail modes with different mode indices k, with the non-rigid bunch oscillations due to a finite chromaticity, even the lowest-order mode k = 0. In the next section we review some properties of Landau damping in coasting beams and in bunches, the effects of octupoles and space-charge. For this discussion we consider two dispersion relations. The particle tracking simulations and the stability study method are described, followed by the results for the beam stability due to octupoles with space-charge of different strength. The results and the conclusions are discussed with the consideration of the incoherent tune distributions.
Electron cloud effects in positron storage rings
This is a review of electron cloud effects/instabilities observed in positron storage rings. Coupled bunch and fast head-tail instabilities caused by an electron cloud have been studied for a long time, and the agreement of experiments and simulations/theory is almost perfect in positron storage rings. Mitigation of the instabilities based on the experiments and simulations have improved the accelerator performance drastically. It is essential to mitigate the instabilities in the present and future positron and proton rings.
Incoherent electron cloud effects in the Large Hadron Collider
During the operation of the Large Hadron Collider in 2018, the majority of physics data was collected with a beam energy of 6.5 TeV, a bunch spacing of 25 ns and with β-functions in the high luminosity interaction points equal to 30 cm. In this configuration, it was found through several experimental measurements that electron cloud induces a significant degradation of the beam lifetime. This contribution reviews the available experimental observations, showing in particular the role played by the e-cloud located in regions around the interaction points, where the two beams share the same vacuum chamber. Recent developments toward a reliable numerical simulation of these incoherent effects driven by electron cloud are also presented.
Impact of coherent and incoherent beam-beam effects on the beams stability
Various coherent instability mechanisms involving colliding beams are described together with techniques for their mitigation. They are illustrated with some examples based mostly on the recent experience at the Large Hadron Collider.
Noise and possible loss of Landau damping through noise excited wakefields
The effect of transverse Landau damping in circular hadron colliders depends strongly on the bunch distribution. The bunches are often assumed to be Gaussian in the transverse dimensions, as it fits well to measurements and it is the expected effect of intra-beam scattering. However, a small change of the distribution can cause a loss of stability. We study the effect that external noise excites the transverse motion of the beam, which produces wakefields, which act back on the beam and cause a diffusion of incoherent particles. The diffusion is narrow in frequency space, and thus also in action space. Macroparticle simulations have shown a similar change of the distribution, which is only detectable in action space, not projected in position space. The narrow diffusion efficiently drills a hole in the stability diagram, at the location of the unstable mode, eventually leading to an instability. The advised mitigation technique is to reduce the drilling rate by operating with a stability margin.
Mitigation of coherent beam instabilities (MCBI) for CERN LIU and HL-LHC
The high-luminosity upgrade of the Large Hadron Collider (HL-LHC) will meet its future yearly integrated luminosity target by means of performance improving upgrades of the LHC itself as well as by receiving significantly higher beam current and brightness from its injectors. The implications of the pushed beam parameters are twofold. On one side, all the accelerators of the LHC injection chain will have to be upgraded to produce the desired beam parameters. For this purpose, the LHC Injectors Upgrade (LIU) program has been established to implement all the needed modifications for meeting the required beam specifications. These upgrades will target the mitigation of coherent beam instabilities and space charge in the injectors, which will allow lifting their existing intensity and brightness limitations to the desired extent. On the other side, the LHC will have to be able to accept the new beam parameters and exploit them at best to produce the integrated luminosity target. This will mainly require control of impedance driven instabilities, beam-beam effects and electron cloud in the LHC itself. In this paper, we will focus on proton beams by describing the identified performance limitations of the LHC and its injectors, as well as the actions envisioned to overcome them.
Mitigation of coherent beam instabilities in linear colliders and FCC-hh
Collective instabilities play an important role in projects as diverse as FCC-hh and CLIC and drive some of the choices. In the paper a few examples are shown where the instabilities were mitigated by design choices and the resulting impact on the collider cost and power consumption is highlighted.
Mitigation of the impedance-related collective effects in FCC-ee
In order to achieve a high luminosity in the electron-positron Future Circular Collider (FCC-ee), very intense multi-bunch beams with low emittances are accumulated in two separate rings and collide in two interaction regions exploiting the crab waist collision scheme. In order to preserve beam quality and to avoid collider performance degradation a careful study of beam collective effects is required. In this paper we overview impedance related coherent beam effects and instabilities potentially dangerous for FCC-ee and discuss measures and techniques for their mitigation.
Mitigation of coherent beam instabilities in CEPC
The collective beam instabilities are potential restrictions in the Circular Electron Positron Collider (CEPC) to achieve high luminosity performance. These instabilities can induce beam quality degradation or beam losses. Different strategies used to mitigate these effects are discussed. The impedances of the dominant contributors are carefully designed and optimized to either reduce the parasitic power dissipation or increase the beam instability threshold. The bunch filling patterns are also optimized to fight the beam ion instability, the electron cloud build-up and the transient beam loading effect.
The luminosity performance for an electron-ion collider demands high-current operation for both the electron and ion beams, for a wide range of collision energies. This poses many challenges on the beam stability with regard to collective effects. In this paper, we present preliminary estimations of coherent instabilities for both of the EIC designs, i.e. JLEIC and eRHIC. Mitigation mechanisms or schemes envisioned for suppression of the instabilities are also discussed.
Status of negative momentum compaction operation at KARA
For future synchrotron light sources different operation modes are of interest. Therefore various modes are currently being tested at the Karlsruhe Research Accelerator (KARA) including optics for a negative momentum compaction factor. These optics have been calculated and are under commissioning at KARA. Additionally, studies about expected collective effects in this regime are being performed, including the head-tail and microbunching instabilities. In this contribution we will present the status of operation in the negative momentum compaction regime and discuss expected collective effects that will be studied in this context.
Time domain measurements of the sub-THz response of different coatings for beam pipe walls
Modern accelerators and light sources often require special treatment of the vacuum chamber surface in order to avoid undesirable effects and maximize machine performance. Coatings with Non Evaporable Getter compounds and amorphous Carbon have been extensively tested and used with very effective results since they allow to reduce the secondary electron emission from pipe walls and therefore the relevant beam instability. An electromagnetic characterization of such coatings is therefore fundamental to build a reliable impedance model. We present here a method based on time domain measurements of an electromagnetic wave passing through a tailored waveguide, where the material under test is deposited on a planar slab. This configuration allows an easy measure of samples having a homogeneous coating thickness and a reasonable area, with parameters chosen in order to have a good signal-to-noise ratio, avoiding at the same time problems due to peel-off and blistering during deposition. The study on the electromagnetic response is performed in the frequency range from 0.1 to 0.3 THz, corresponding to the first transverse electric (TE) mode propagation inside the designed waveguide.
Wake fields evaluation for beam collimators and the 60 pc electron beam at the compact ERL at KEK
In high-intensity particle accelerators, unwanted transverse and longitudinal wakefields arise when the high- charge particle beam passes through the narrow chambers or locations with small transverse apertures, such as collimator jaws. The transverse wake field may affect the beam emittance and the longitudinal wake field can cause the energy loss and the energy spread. In the present study we investigated the collimator’s impact to the beam performance. In this paper, we have shown numerical, analytical and measurement results on the collimator’s wakefields that will be important for the next step operation. Thus, considering future cERL upgrade to the IR-FEL, a possibility of consequent degradation of the FEL performance should be taken into account. The correspondent power loss was obtained as 13.7 W (81.25 MHz, 5 mA, 2 ps).
CLIC-DR electron cloud build up simulations
This study investigates impact of beam pipe material and external magnetic field on electron cloud build up mechanism. The machine parameters are in the scope of CLIC damping rings. Two dierent filling schemes for 0.5 and 1 ns bunch spacings are considered. VSim Plasma Discharges and Plasma Acceleration package is employed to perform 2D electrostatic particle in cell simulations such that the space charge eect and Furman-Pivi secondary emission yield model are included in the computations. It is illustrated that the build up time varies due to bunch spacing while the external magnetic field influences the number of electrons generated by initial seeds. The evolution of generated secondary electrons due to bunch passes and the corresponding energy levels are presented in details.
Consequences of longitudinal coupled-bunch instability mitigation on power requirements during the HL-LHC filling
During the filling of the Large Hadron Collider (LHC), it is desirable to keep the RF cavity voltage constant both in amplitude and phase to minimize the emittance blow-up and injection losses. To have a constant voltage and to minimize power consumption, a special beam-loading compensation scheme called half-detuning is used in the LHC, for which the cavity fundamental resonant frequency needs to be de-tuned from the RF frequency by an appropriate value. This, however, can result in fast coupled-bunch instabilities caused by the asymmetry of the fundamental cavity impedance. To mitigate them, a fast direct RF feedback and a one-turn delay feedback are presently used in the LHC. The semi-analytical model that describes the dynamics of the Low-Level RF system in the LHC shows that, depending on the mitigation scenario, the required transient RF power during injection could significantly exceed the steady-state value. This means that for High-Luminosity LHC (HL-LHC) beam intensities, one can potentially reach the limit of available RF power. In this paper, the model is described, and benchmarks with LHC measurements are presented. We also shortly revisit the damping requirements for the longitudinal coupled-bunch instability at injection energy, to find a compromise between longitudinal stability and RF power requirements for the HL-LHC beam.
Synchronous phase shift measurements for evaluation of the longitudinal impedance model at the CERN SPS
The High Luminosity LHC (HL-LHC) requires 2.3 <span style="caret-color: #4d5156; color: #4d5156; font-family: arial, sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration: none; display: inline !important; float: none;">× 1011 protons per bunch (ppb) at LHC injection. For the SPS, the injector to the LHC, this goal requires a doubling of the injected intensity to 2.6 <span style="caret-color: #4d5156; color: #4d5156; font-family: arial, sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration: none; display: inline !important; float: none;">× 1011 ppb. Longitudinal instabilities were observed in the SPS for intensities below the required 2.6 <span style="caret-color: #4d5156; color: #4d5156; font-family: arial, sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration: none; display: inline !important; float: none;">× 1011 ppb. Identifying, and ultimately mitigating, the impedance sources driving the instabilities requires an accurate impedance model. Here, we report on measurements of the synchronous phase shift with intensity and corresponding energy loss at the SPS injection. Using the loss factor to compute the energy loss from the measured bunch spectrum and the SPS impedance model leads to significant disagreements with measurements. This issue is investigated for the simplified case of a single resonator. However, simulating matched bunches using the SPS impedance model yields better agreement with measurements.
Identification of impedance sources responsible for longitudinal beam instabilities in the CERN PS
Longitudinal instabilities in the CERN PS are an important limitation to obtain the expected beam intensity and longitudinal emittance at the PS extraction in the framework of the LHC Injector Upgrade (LIU) project. The observed coupled-bunch instabilities lead to dipolar and quadrupolar oscillations, as well as to an uncontrolled longitudinal emittance blow-up for proton beams. A microwave instability observed with ion beams develops quickly at transition crossing. To identify the potential impedance sources of these instabilities, two strategies were adopted. Firstly, beam measurements were performed for dierent impedance configurations, i.e. by partially detuning the main RF cavities. Secondly, a thorough survey of the machine elements together with the RF studies allowed to refine the PS impedance model in order to find potentially missing contributions. Measurements were compared with particle simulations using the updated impedance model of the PS. Although the source of the dipolar coupled-bunch instability was already identified in the past, this study led to an identification of the impedance sources driving other types of longitudinal instabilities.
Vlasov solvers and simulation code analysis for mode coupling instabilities in both longitudinal and transverse planes
Two Vlasov solvers for the longitudinal and transverse planes are used to study the frequency shift of coherent oscillation modes and possible mode coupling instability for the two cases of a proton bunch interacting with either a constant inductive or a broad-band resonator impedance. In parallel to this approach, a new method to study the coherent frequency shift from the results of simulation codes is presented. Comparisons between the two methods are discussed, as well as simple analytical formulae (valid in the “long-bunch” regime), which clearly reveal how to mitigate these instabilities.
Systematic studies of the microbunching and weak instability at short bunch lengths
At KARA, the Karlsruhe Research Accelerator of the Karlsruhe Institute of Technology synchrotron, the so-called short-bunch operation mode allows the reduction of the bunch length down to a few picoseconds. The microbunching instability resulting from the high degree of longitudinal compression leads to fluctuations in the emitted terahertz radiation. For highly compressed bunches at KARA, the instability occurs not only in one but in two different bunch-current ranges that are separated by a stable region. The additional region of instability is referred to as short-bunch-length bursting or weak instability. We will present measurements of the threshold currents and fluctuation frequencies in both regimes. Good agreement is found between the measurement and numerical solutions of the Vlasov-Fokker-Planck equation. This contribution is based on the PRAB paper Phys. Rev. Accel. Beams 22, 020701.
This paper deals with the problem of defining the wakefunction for two counter-moving charges, i.e. two charges moving in opposite direction. In this case, the distance between the charges cannot be considered constant. From the counter-moving wakefunction the counter-moving wakepotential is derived. An example of this kind of wakepotential for a lossless pill-box cavity is obtained analitically and compared with numerical simulations.
Physics modelling and numerical simulation of beam-ion interaction in HEPS
The beam-ion interaction is one of the potential limitations of beam performance in ultra-low emittance electron rings. The High Energy Photon Source (HEPS), under construction in Beijing, is one example for which the beam-ion effect has to be carefully evaluated. In this paper, we will introduce the beam-ion interaction models applied in HEPS. Based on these models, a new numerical simulation code is developed. Currently, the code includes modules such as ionization, beam-ion interaction, synchrotron radiation damping, quantum excitation, bunch-by-bunch feedback etc. Settings such as weak-strong, strong-strong and arbitrary number of interaction points can be launched in the code. It will be shown that the beam instability excited by the beam-ion interaction can be effectively suppressed by the bunch-by-bunch feedback system.
Implementation of RF modulation in Booster for mitigation of the collective effects in the transient process after the swap-out injection
On-axis swap-out injection is a promising injection scheme for the diraction-limited storage rings with small dynamic apertures. However, some previous studies have shown that the initial mismatch in the longitudinal phase space may lead to transverse collective instability before approaching the equilibrium state, especially in the high bunch charge situation. We present our study of mitigating the collective eects in the transient process after injecting beam into storage rings by implementing RF modulation technique in booster. Both bunch lengthening and the increase of energy spread could be observed in the extracted bunch from booster. The reduction of particle loss in the transient process after the swap-out injection is demonstrated via simulations.
Measurements and damping of the ISIS head-tail instability
ISIS is the pulsed spallation neutron and muon source at the Rutherford Appleton Laboratory in the UK. Operation centres on a rapid cycling proton synchrotron (RCS) which accelerates 3 × 1013 protons per pulse from 70 MeV to 800 MeV at 50 Hz, delivering a mean beam power of 0.2 MW. Research and development at ISIS are focused on key aspects of high intensity operation with a view to increasing beam intensity on target, understanding loss mechanisms and identifying viable upgrade routes. At present, the main limitation on beam intensity at ISIS is beam loss associated with the head-tail instability. This paper presents new measurements of the head-tail instability in both RCS and storage ring modes whilst highlighting the differences between these and theoretical predictions. Macro-particle simulations of the instability are shown in comparison with experimental data. Finally, preliminary tests of an active transverse feedback system to damp the instability are also presented.
Study of collective effects in the CERN FCC-ee top-up Booster
The CERN FCC-ee top-up booster synchrotron will accelerate electrons and positrons from an injection energy of 20 GeV up to an extraction energy between 45.6 GeV and 182.5 GeV depending on the operation mode. These accelerated beams will be used for the initial filling of the high-luminosity FCC-ee collider and for keeping constant the beam current over time using continuous top-up injection. Due to the high-intensities of the circulating beams, collective effects may represent a limitation in the top-up booster. In this work we present a first evaluation of the impedance model and the effects on beam dynamics. Methods to mitigate possible instabilities will be also discussed.
Electron lenses provide an incoherent betatron tune spread for Landau damping of transverse coherent beam instabilities. We investigated the eect of the transverse electron beam size and shape for Landau damping with an electron lens. Another point of interests is Landau damping provided by a pulsed electron lens with homogeneous transverse beam profile. This type of electron lens is developed for space-charge compensation in SIS18.
Tailored metamaterial-based absorbers for high order mode damping
In modern particle accelerators, satisfying the desired beam properties (high currents, high luminosities, etc.) increasingly implies limiting the total beam coupling impedance, which depends on the machine and the parameters of the circulating beams. A number of different reduction techniques have been proposed during the years depending on the specific applications, ranging from higher order modes (HOM) damping to solutions entailing high electrical-conductivity coatings of the pipe. This paper investigates the use of metamaterial-based absorbers for sensibly reducing or nearly cancelling the HOM contribution to the impedance. We design and fabricate sub-wavelength two-dimensional metallic resonant structures based on the split ring resonator (SRR) geometry that can be employed as mode dampers in accelerating structures. Experimental results inside a pillbox cavity well agree with full wave electromagnetic simulations. In this work we present the first results on a SRR geometry tailored for LHC collimators. We show how metamaterials can be a valid alternative for impedance mitigation in experimental devices commonly operating along a particle beam line.
TMCI, why is the horizontal plane so different from the vertical one?
Based on the recent work of R. Lindberg on transverse collective instabilities it was observed that if the ratio of quadrupolar to dipolar impedance <span style="caret-color: #4d5156; color: #4d5156; font-family: arial, sans-serif; font-size: 14px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: left; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration: none; display: inline !important; float: none;"> ρ is equal to -1 there is no TMC-instability. This relationship is actually fulfilled by resistive wall (RW)-impedance on the horizontal plane in case of a flat vacuum chamber. HEADTAIL simulations were carried out to check if this observation can be confirmed. Additionally the effect of radial modes on the TMC-instability was studied.
A general overview of the MCBI 2019 ICFA Mini-Workshop
After the ICFA Mini-Workshop on “Electromagnetic Wake Fields and Impedances in Particle Accelerators" (organised by Vittorio Vaccaro, Maria Rosaria Masullo and Elias Métral) held in Erice (Sicily) from 24 to 28 April, 2014, and the ICFA Mini-Workshop on "Imped- ances and Beam Instabilities in Particle Accelerators" (organised by Giovanni Rumolo, Maria Rosaria Masullo and Stefania Petracca), held in Benevento (Italy) from 18 to 22 September, 2017, this third workshop of the series was organised jointly between CERN and EPFL and it took place in Zermatt (Switzerland) from 23 to 27 September, 2019. This ICFA Mini-Workshop on “Mitigation of Coherent Beam Instabilities in Particle Accelerators" (MCBI2019) focused on all the mitigation methods for all the coherent beam instabilities, reviewing in detail the theories (and underlying assumptions), simulations and measurements on one hand, but on the other hand trying to compare the different mitigation methods (e.g. with respect to other effects such as beam lifetime) to provide the simplest and more robust solutions for the day-to-day operation of the machines.
A random collection of photographs from the Workshop