Transverse Coupled-bunch Instabilities Research Articles

Source of instability in the rapid cycling synchrotron of the China spallation neutron source

The rapid cycling synchrotron (RCS) of the China spallation neutron source accumulates 1.56 ×1013 protons and accelerates them from 80 MeV to 1.6 GeV at a repetition rate of 25 Hz, delivering a 100 kW proton beam to the target. Despite predictions that no instabilities would occur at high beam intensity, an unexpected coherent oscillation of the beam was observed during the beam commissioning. To confirm and address the instability, a series of systematic measurements and studies were conducted, revealing that the issue is a transverse coupled bunch instability and identifying a narrow-band impedance with a low frequency in the RCS. Further bench measurements confirmed that ceramic chambers with RF shields are the source of this impedance, which is consistent with the analysis of the experimental data. Based on these findings, a tune curve during the ramping process and chromaticity optimization have been implemented to completely mitigate the instability in the RCS at 100 kW.

Broad band waveguide to coaxial transition for HOM suppression in RF cavities for future synchrotron light sources

In the modern storage ring light sources, exploiting multi-bunch beams, the longitudinal and transverse coupled bunch instabilities are predominantly driven by higher order modes (HOM) of the accelerator RF cavities. In order to suppress the HOM to a harmless level, we propose using a modified broadband waveguide to coaxial line transitions placed on the cavity body, similar to those used for the DAΦNE collider RF cavities. Such a solution has a simple design that avoids the application of the ferrite materials under the ultra-high vacuum and dissipates the HOM power on the external loadings. Different from DAΦNE with a single cavity per ring, where the damping waveguides are placed laterally on the cavity body, we consider the possibility of allocating the waveguides vertically. Since the modern synchrotron light sources require using more RF cavities to compensate for the synchrotron radiation losses, such a solution helps to save the occupied space when placing the cavities in a row next to each other. This paper describes the design optimization process and discusses the obtained results concerning the effectiveness of the HOM suppression and minimization of the impact of the transitions on the fundamental mode parameters.

Coupled-bunch instability for arbitrary multibunch configurations

The coupled-bunch instability for arbitrary multibunch configurations is investigated in its generality. The theoretical framework adopted is based on the general eigenvalue analysis based on the known formulas of the complex frequency shifts for the uniform multibunch configuration case. Closed formulas are derived for special cases. For the configuration consisting of a uniform filling pattern with a gap of missing bunches, the theoretical results are found to be in good agreement with measurements of the transverse coupled-bunch instability driven by the resistive wall impedance performed at the NSLS-II storage ring.

Modeling and control of transverse coupled bunch mode levels in Indus-2 using artificial neural network.

Transverse coupled bunch instability (TCBI) is a major concern at high beam current operations at all synchrotron light sources. Techniques for the mitigation of TCBI include higher order mode tuning of RF cavities, optimization of vacuum chamber designs, increasing the damping rate of beam oscillations, optimization of betatron tune values, and multi-bunch feedback systems. Due to uncertainties, time-variation, and disturbances, the dynamic behavior of accelerators requires further tuning of beam parameters beyond theory-based set points for minimizing the transverse coupled bunch mode (TCBM) instability. In this work, an artificial neural network (ANN) based system is developed to minimize average TCBM levels in the Indus-2 synchrotron light source at the Raja Ramanna Centre for Advanced Technology in Indore, India. The ANN is trained based on various TCBM measurements collected at the Indus-2 for various values of betatron tune and chromaticity in order to learn how to map beam measurements directly to parameters such as optimal betatron tunes and chromaticity values that are sent to a beam feedback control system. The ANN takes as input real-time beam data and is coupled to a feedback controller, thereby creating an adaptive feedback that is able to adjust in real time to variation of the accelerator and beam. We provide a detailed overview of our approach as well as experimental results in which the ANN-guided feedback approach increases the operational beam current of Indus-2 from a limit of ∼170 mA up to ∼230 mA within ∼21 min. We believe that this general method can be useful for a wide range of synchrotron sources operating at high bunch currents.

Stabilizing effects of chromaticity and synchrotron emission on coupled-bunch transverse dynamics in storage rings

We present a theory that can compute the transverse coupled-bunch instability growth rates at any chromaticity and for any longitudinal potential provided only that the long-range wakefield varies slowly over the bunch. The theory is expressed in terms of the usual coupled-bunch eigenvalues at zero chromaticity, and when the longitudinal motion is simple harmonic our solution only requires numerical root-finding that is easy to implement and fast to solve; the more general case requires some additional calculations, but is still relatively fast. The theory predicts that the coupled-bunch growth rates can be significantly reduced when the chromatic betatron tune spread is larger than the coupled-bunch growth rate at zero chromaticity. Our theoretical results are compared favorably with tracking simulations for the long-range resistive wall instability, and we also indicate how damping and diffusion from sychrotron emission can further reduce or even stabilize the dynamics.

Measurement and parametric analysis of transverse coupled bunch instabilities for electron synchrotron radiation source Indus-2

The performance of synchrotron radiation sources at high beam current gets often degraded due to the excitation of longitudinal and transverse coupled bunch instabilities (CBI). Hence, measurement of the coupled bunch instabilities may give insight into the performance of the machine, which in turn, may help supress these instabilities. Transverse coupled bunch instability is sensitive to the operating parameters of the accelerator such as betatron tune and sextupole magnet strength. In this paper, we report the measurement on transverse coupled bunch modes (CBM). The effect of betatron tune values and sextupole magnet strengths on transverse coupled bunch instability is discussed. For this study, betatron tune values and sextupole strengths are chosen in the vicinity of the routine operating points. With the help of this parametric study, an optimum operating point is identified in the beam operation with a minimum level of transverse coupled bunch instability. Further, an artificial neural network (ANN) is used to deduce a functional model between average transverse CBM levels and sextupole strengths.

Suppression of transverse beam instabilities by stripline kickers at TPS

Collective beam instabilities could limit the accelerator performance if proper countermeasures are not in place. Active beam feedback systems are commonly used to suppress beam instabilities. The resistive wall impedance including phase-II insertion devices at TPS are calculated with analytic formulas. The growth rate of transverse coupled bunch instabilities due to wall impedance is estimated by theory. The RF properties of existing stripline kickers in TPS are analysed with a 3-D electromagnetic simulation code GdfidL. Based on the above analysis, the requirements for a beam feedback system are calculated and the results are reported.

Impact of the resistive wall impedance on beam dynamics in the Future Circulare+e−Collider

The Future Circular Collider study, which aims at designing post-LHC particle accelerator options, is entering in the final stage, which foresees a conceptual design report containing the basic requirements for a hadron and a lepton collider, as well as options for an electron-proton machine. Due to the high beam intensities of these accelerators, collective effects have to be carefully analyzed. Among them, the finite conductivity of the beam vacuum chamber represents a major source of impedance for the electron-positron collider. By using numerical and analytical tools, a parametric study of longitudinal and transverse instabilities caused by the resistive wall is performed in this paper for the case of the Future Circular Collider lepton machine, by taking into account also the effects of coating, used to fight the electron cloud build up. It will be proved that under certain assumptions the coupling impedance of a two layer system does not depend on the conductivity of the coating and this property represents an important characteristic for the choice of the material itself. The results and findings of this study have an impact on the machine design in several aspects. In particular the quite low threshold of single bunch instabilities with respect to the nominal beam current and the not negligible power losses due to the resistive wall are shown, together with the necessity of a new feedback system to counteract the fast transverse coupled bunch instability. The importance of a round vacuum chamber to avoid the quadrupolar tune shift is also discussed. Finally the crucial importance of the beam pipe material coating and thickness choice for the above results is underlined.

Resistive-wall impedance effects for the new KEK Light Source

Effects of resistive-wall (RW) impedance on a 3-GeV storage ring of the KEK Light Source (KEK-LS) are presented. Cu sheets used for in-vacuum undulators (IVUs) are regarded as the main source of the RW impedance. Although the calculated heating power per unit length due to the longitudinal impedance is more than 20 W, it is not serious for the water-cooled IVUs. The maximum growth rate of the coupled-bunch instability caused by the transverse impedance is calculated and as a result, a transverse feedback system with the damping rate of more than 104 s-1 is required for the instability suppression. NEG coating of about 1 μm can be used for the KEK-LS vacuum pipe because increase of the heating power due to the NEG coating impedance is small and the effect on the transverse coupled-bunch instability is negligible.

Transverse coupled-bunch instability thresholds in the presence of a harmonic-cavity-flattened rf potential

A small vacuum chamber aperture is a present trend in the design of future synchrotron light sources. This leads to a large resistive-wall impedance that can drive coupled-bunch instabilities. Another trend is the use of passively driven cavities at a harmonic of the main radio frequency to lengthen the electron bunches in order to increase the Touschek lifetime and reduce emittance blowup due to intrabeam scattering. In some cases, the harmonic cavities may be tuned to fulfill the flat potential condition. With this condition met, it has been predicted in simulation that the threshold current for coupled-bunch resistive-wall instabilities is much higher than with no bunch lengthening at all. In this paper, the features of a bunch in the flat potential that would contribute toward this stabilization are identified and discussed. The threshold currents for these instabilities are estimated for the MAX IV 3 GeV storage ring at different values of chromaticity using macroparticle simulations in the time domain and, within the limits of the existing theory, frequency domain calculations. By comparing the results from these two methods and analyzing the spectra of the dominant head-tail modes, the impact of each of the distinguishing features of a bunch in the flat potential can be explained and quantified in terms of the change in threshold current. It is found that, above a certain chromaticity, the threshold current is determined by the radial structure of the zeroth-order head-tail mode. This happens at a lower chromaticity if the bunch length is longer.

Self-consistent simulations and analysis of the coupled-bunch instability for arbitrary multibunch configurations

A parallel tracking code with a Fokker-Planck solver and perturbation theory are used to study transverse coupled bunch instabilities with nonuniform filling pattern.

Analysis of coupled-bunch instabilities for the NSLS-II storage ring with a 500 MHz 7-cell PETRA-III cavity

The NSLS-II storage ring is designed to operate with superconducting RF-cavities with the aim to store an average current of 500mA distributed in 1080 bunches, with a gap in the uniform filling for ion clearing. At the early stage of the commissioning (phase 1), characterized by a bare lattice without damping wigglers and without Landau cavities, a normal conducting 7-cell PETRA-III RF-cavity structure has been installed with the goal to store an average current of 25mA. In this paper we discuss our analysis of coupled-bunch instabilities driven by the Higher Order Modes (HOMs) of the 7-cell PETRA-III RF-cavity. As a cure of the instabilities, we apply a well-known scheme based on a proper detuning of the HOMs frequencies based upon cavity temperature change, and the use of the beneficial effect of the slow head–tail damping at positive chromaticity to increase the transverse coupled-bunch instability thresholds. In addition, we discuss measurements of coupled-bunch instabilities observed during the phase 1 commissioning of the NSLS-II storage ring. In our analysis we rely, in the longitudinal case, on the theory of coupled-bunch instability for uniform fillings, while in the transverse case we complement our studies with numerical simulations with OASIS, a novel parallel particle tracking code for self-consistent simulations of collective effects driven by short and long-range wakefields.

Collective beam instability study using a correlation-moment analysis

A general formalism for treating simultaneously the transverse coupled-bunch and transverse coupled-mode instabilities is presented. In this approach, the equations of motion of a coupled multibunch beam are expanded to yield a system of equations involving correlation moments of the transverse and longitudinal motions. After a proper truncation, the system of equations is closed and can be solved. This approach allows us to formulate within one framework several known instability mechanisms including the single-bunch mode-coupling instability, the coupled-bunch instability, the mode-coupling instability, and the coupled-mode coupled-bunch instability as particular cases.

Transverse coupled bunch instabilities in low-energy injection storage rings

The normal-conducting accelerating ring (NAR) is a synchrotron radiation source that uses a low-energy (15 MeV) injection scheme. This paper shows that a transverse coupled bunch instability occurs in NAR just after injection and that this instability limits the amount of current that can be stored. At such a low energy, the bunch length remains long because of the long radiation damping time. Sacheler's theory shows that the bunch length is so long that small changes in chromaticity produce a large effect on the form factor and thus on the growth rate of the instability. This chromaticity dependence of transverse coupled bunch instability has been observed experimentally in NAR.

Construction of a high frequency quadrupole magnet used to cure transverse coupled-bunch instabilities

A high frequency quadrupole magnet (HFQM), which can split betatron tunes from bunch to bunch, was developed at the Photon Factory storage ring at KEK. The effect of introducing a bunch-to-bunch tune spread on transverse coupled-bunch instabilities was investigated in detail. A remarkable rise in the threshold currents of transverse coupled-bunch instabilities was observed using the HFQM.

Transverse coupled-bunch instabilities in damping rings of high-energy linear colliders.

In this paper we present methods for studying and controlling transverse coupled-bunch instabilities. Our primary motivation is the study of damping rings for next-generation linear colliders in which many bunches are damped in the same ring simultaneously; however, the methods presented are also applicable to other situations. The theory developed here treats the motion of the bunch centroids, since the coherent dipole modes of coupled-bunch oscillation are expected to be strongly dominant. A formalism to obtain the $n$ normal modes of oscillation of $n$ bunches is developed. The imaginary part of the frequency of each normal mode determines its stability. However, not only the long-term stability of each oscillation mode, but also the transient behavior of the bunches just after injection, must be considered in damping rings. Two methods of studying the transient behavior are presented: (1) A Laplace-transform method, using the eigenmodes and corresponding eigen-frequencies found by the normal-modes formalism, and (2) computer tracking, using a localized-kick approximation. Examples are given for damping-ring designs appropriate to a linear collider of about 0.5-1.0 TeV center-of-mass energy.

Critical Test of Coupled-Bunch Instability Theory

Longitudinal and transverse coupled-bunch instabilities were observed in the Photon Factory storage ring. They were all caused by the high shunt impedances of the RF accelerating cavities and their properties were studied in detail. The frequency dependences of threshold currents of these instabilities were measured, and well described in terms of the frequency dependent structures of the cavity impedances. Absolute values of the thresholds are discussed in a comparison with perturbation theory.

Collective Beam Instabilities Caused by RF Cavities in Tristan

Summarized are the works done at KEK to study the collective beam instabilities caused by the RF cavities in TRISTAN. The works include the higher-order mode loss, the longitudinal and transverse coupled-bunch instabilities and the single bunch fast instabilities for longitudinal and transverse motions. A design aim of 4 mA/bunch and two bunches per beam can be achieved when feedback systems for longitudinal and transverse dipole oscillations are used. The other cures such as the higher-harmonic cavities, the wigglers, the couplers and the change of radiation damping partititon numbers are also desirable.

A Single Beam Multibunch Instability at CESR

A transverse coupled bunch instability has been observed in the Cornell Electron Storage Ring CESR for both positrons and electrons. This instability shows strong horizontal or vertical coherent signals but very weak longitudinal signals. Positron injection, which requires sixty-one uniformly spaced bunches in CESR, was originally restricted by the enlarged effective horizontal beam size resulting from this instability. Although several cures have been discovered, only external octupoles provide a sufficient increase in the threshold and are compatible with injection. The theory for coupled bunch motion correctly predicts the instability threshold assuming that the driving mechanism is a 1140 MHz parasitic resonance in the RF cavity. Changes in the threshold with tune and octupole field strength are also correctly predicted.