Longitudinal Coupled-bunch Instabilities Research Articles

Suppression of longitudinal coupled-bunch instabilities with RF feedback systems in CEPC main ring

Suppression of longitudinal coupled-bunch instabilities with RF feedback systems in CEPC main ring

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.

Beam-based characterization of higher-order-mode driven coupled-bunch instabilities in a fourth-generation storage ring

Longitudinal coupled-bunch instabilities are driven by monopole higher-order modes (HOMs) in the active and passive radio-frequency (rf) cavities at the MAX IV 3 GeV electron storage ring. By combining different beam and rf-based techniques, we have performed a systematic survey of the properties of these resonant modes as a function of cavity temperatures and fundamental mode frequency. This information was then used to setup a HOM model that allowed us to infer optimized temperature ranges for the cavities. An important feature of the optimization method is that it takes into account not only the need to minimize the growth rates (given by the resistive component of the sum of HOM impedances) from each individual cavity but also aims to minimize the total reactive component of the impedance of HOMs that are present in more than one cavity. The resulting small real coherent tune shifts allow the coupled-bunch modes driven by these HOMs to be effectively Landau damped. Further optimization of the cavity temperatures was performed by minimizing the measured electron beam energy spread within the temperature ranges defined by the HOM model. The optimum temperature search was performed at 300 mA stored beam current and in multi-bunch mode using the RCDS (Robust Conjugate Direction Search) algorithm and succeeded in bringing the electron energy spread to within 10% of the zero current value determined solely by quantum excitation and radiation damping.

Research and development of the longitudinal feedback system digital signal processing electronics in BEPCII

The current strategy to achieve high luminosity for high energy physics experiments is to store huge currents distributed in many bunches in circular machines such as BEPCII, so the longitudinal coupled bunch instabilities of the beam are inevitable. Therefore, a longitudinal feedback system is needed to suppress longitudinal oscillation. Otherwise, the beam energy spread will increase; the luminosity and the beam lifetime will decrease under a certain beam current. For filter design of the feedback system, the time domain least square fitting (TDLSF) method is compared to the selective wave filter method; digital signal processing electronics based on commercial board have been developed and tested on BEPCII. The final result shows that the self-developed longitudinal feedback system can suppress the longitudinal beam oscillation at 750 mA beam current and meet the requirements of BEPCII; the restrain depth to the sidebands reaches to 40.8 dB.

Beam gap transient analysis and mitigations in high-current storage rings for an electron-ion collider

The U.S. electron ion collider will utilize high current electron and ion storage rings with many bunches and large rf systems. Because of the dissimilarity of the two rings, the rf transients created by gaps or variations in the current distributions will be very different in the two rings. These transients cause a shift in the synchronous phase of the beams as a function of rf bucket position, can impact the luminosity through shifts in longitudinal position of the IP, will affect the performance of the rf and LLRF control loops, and may require significant rf power overhead to control. A machine design that uses superconducting crab cavities will also have sensitivity to gap transients and synchronous phase variations along the bunch train with variations in crab cavity voltage seen by each bunch, since the high $Q$ of the crab cavities precludes modulating them to compensate for the time of arrival shifts caused by the gap transients in the main rf systems. All these effects make the problem of managing gap transients crucial to the operation of the EIC. This work presents methods to study the dynamics of the rf and LLRF systems for these heavily beam loaded facilities. An illustrative machine design example is presented and used to investigate the expected magnitudes of the rf gap transients, and exploration of various possible remedies to match the gap transients in the two dissimilar EIC rings. In addition to the study of the power required and gap transients, this work also estimates longitudinal coupled-bunch instabilities due to the baseline cavity fundamental impedance. The work is motivated to emphasize the importance of tools and methods to estimate these effects as part of the early design phase of the Electron-Ion Collider or any high current storage ring design.

Harmonic-cavity stabilization of longitudinal coupled-bunch instabilities with a nonuniform fill

In synchrotrons, nonuniform fill patterns, which give rise to beam phase transients and a spread in synchrotron tune between bunches, have been observed to damp longitudinal coupled-bunch instabilities driven by higher-order modes in rf cavities. The transients are especially large in the presence of Landau cavities, which are used commonly in storage-ring light sources and particularly in the new generation of diffraction-limited storage rings. A method has recently been devised to predict the beam transient including complex form factors for the different bunches. This has now been extended to accurately predict the growth-rates and oscillation frequencies of coupled-bunch modes for arbitrary fill patterns, taking the individual complex form factors and equilibrium phases of the different bunches into account. In this paper, the extended method is presented and the theory is outlined. For a case with significant transient beam loading, predictions of the resulting beam transient and bunch profiles are compared to measurements. Predictions of coupled-bunch mode behavior are then benchmarked against results from the macroparticle tracking code mbtrack with good agreement. Finally, the method is used to predict the behavior of coupled-bunch modes as a function of the fields in passive Landau cavities.

Advanced damper system with a flexible and fine-tunable filter for longitudinal coupled-bunch instabilities caused by the accelerating mode in SuperKEKB

SuperKEKB is an electron–positron circular collider aiming to achieve unprecedented luminosity by using a large beam current and a new collision method. The longitudinal coupled-bunch instabilities caused by the accelerating mode of cavities will be a serious impediment in reaching the design current; estimates suggest that the so-called μ=−1, −2, and −3 modes of the instabilities will be excited. We developed a new damper system for suppressing these modes using recent digital technologies. In our system, the feedback parameters for each mode, for example, the phase, the loop gain, and the frequency offset, can be easily fine-tuned independently. We verified the performance of the new damper during Phase-2 commissioning of SuperKEKB. In the demonstration, instabilities ( μ=−1 and −2 modes) were excited by intentionally detuning a superconducting cavity, and the feedback control with the new damper was applied to the low-level RF control system. The new damper successfully suppressed the longitudinal coupled-bunch instabilities in SuperKEKB. Consequently, it is expected that this damper will make a substantial contribution to achieving the design luminosity by suppressing the coupled-bunch instabilities due to the accelerating cavities.

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.

Cavity fundamental mode and beam interaction in CEPC main ring

CEPC is a 100-kilometer-long electron-position collider, aiming to produce Higgs, W and Z-pole. Double ring (DR) is the baseline design of its main ring, and advanced partial double ring (APDR) is the alternative one. The purpose of this paper is to study the beam loading effects and the corresponding longitudinal beam dynamics of CEPC DR and APDR. The phase shift of the bunches modulated by the bunch gap is calculated with the approximation formulas and simulated with the program. All these methods are compared, and the application conditions of them are also elaborated. In addition, the longitudinal coupled-bunch instability in CEPC main ring is calculated by analytical formulas. In CEPC DR high-lumi Z, the phase shift can be reduced to 0.51 deg( $$^\circ $$ ). Besides, the total number of unstable longitudinal modes is 15 in CEPC DR high-lumi Z when no feedback system is added. The phase shift of the bunches in CEPC can be reduced to an acceptable value if the optimal filling pattern is chosen. For CEPC APDR, the RF parameters are calculated and the beam loading effects are tolerable.

Fundamental cavity impedance and longitudinal coupled-bunch instabilities at the High Luminosity Large Hadron Collider

The interaction between beam dynamics and the radio frequency (rf) station in circular colliders is complex and can lead to longitudinal coupled-bunch instabilities at high beam currents. The excitation of the cavity higher order modes is traditionally damped using passive devices. But the wakefield developed at the cavity fundamental frequency falls in the frequency range of the rf power system and can, in theory, be compensated by modulating the generator drive. Such a regulation is the responsibility of the low-level rf (llrf) system that measures the cavity field (or beam current) and generates the rf power drive. The Large Hadron Collider (LHC) rf was designed for the nominal LHC parameter of 0.55 A DC beam current. At 7 TeV the synchrotron radiation damping time is 13 hours. Damping of the instability growth rates due to the cavity fundamental (400.789 MHz) can only come from the synchrotron tune spread (Landau damping) and will be very small (time constant in the order of 0.1 s). In this work, the ability of the present llrf compensation to prevent coupled-bunch instabilities with the planned high luminosity LHC (HiLumi LHC) doubling of the beam current to 1.1 A DC is investigated. The paper conclusions are based on the measured performances of the present llrf system. Models of the rf and llrf systems were developed at the LHC start-up. Following comparisons with measurements, the system was parametrized using these models. The parametric model then provides a more realistic estimation of the instability growth rates than an ideal model of the rf blocks. With this modeling approach, the key rf settings can be varied around their set value allowing for a sensitivity analysis (growth rate sensitivity to rf and llrf parameters). Finally, preliminary measurements from the LHC at 0.44 A DC are presented to support the conclusions of this work.

Investigations of Bunch Filling Patterns to Suppress the Longitudinal Coupled-Bunch Instability at the Pohang Light Source

A longitudinal coupled-bunch instability may be generated at the 2.5 GeV Pohang Light Source (PLS), depending on the parameters of the rf system and the machine parameters of the storage ring. In the near future, one more rf cavity will be inserted into the storage ring to raise stored beam current. Then, the performance of the storage ring may be limited by the longitudinal coupled-bunch instability due to the higher-order modes in the rf cavities as the beam current increases. Accordingly, in order to suppress the longitudinal coupled-bunch instability, the dependence of the longitudinal coupled-bunch instability in the higher beam current on the bunch filling patterns in the ring were intensively investigated by using a simulation method. Our simulation shows that the beam energy spread due to the longitudinal coupled-bunch instability in the ring can be suppressed by choosing optimal bunch filling patterns with empty buckets between bunches and gap buckets.

Longitudinal dynamics with rf phase modulation in the Brazilian electron storage ring

In the Brazilian synchrotron light source (LNLS---Laborat\'orio Nacional de Luz S\'{\i}ncrotron), we observed that modulating the phase of the accelerating fields at approximately twice the synchrotron frequency suppressed remarkably well a longitudinal coupled-bunch mode of the beam driven by a higher order mode in one of the radiofrequency (rf) cavities. In this work, we present the results of a set of systematic measurements, in single and multibunch mode, aimed at characterizing the effects of rf phase modulation on the beam. We compare those experiments with the results of tracking simulations and of a theoretical model in which Landau damping is the stabilizing mechanism that explains the suppression of the longitudinal coupled-bunch instability. We also measure the frequency of the stable islands created in longitudinal phase space by phase modulation and the longitudinal beam transfer function as a function of the modulation frequency and amplitude. The experimental results are in good agreement with theoretical expectations.

Rf amplitude modulation to suppress longitudinal coupled bunch instabilities in the CERN Super Proton Synchrotron

Without specific counter measures, the LHC type beam in the SPS suffers from longitudinal coupled bunch instabilities. To prevent them, the SPS impedance has been decreased over the last few years and the operation of a high frequency Landau damping system has been established. In the absence of this Landau damping system one may alternatively introduce an rf amplitude modulation to stabilize the beam. We present results obtained by this method in the SPS and considerations for a potential increase of the longitudinal beam stability in the LHC.

Suppression of longitudinal coupled bunch instabilities by LFS in PLS storage ring

Abstract The Pohang Light Source (PLS) storage ring uses a longitudinal feedback system (LFS) that is a bunch-by-bunch feedback system employing the digital electronics and the DSP filter algorithm to cure the longitudinal coupled bunch instabilities due to higher order modes of RF cavities. The LFS is able to suppress all longitudinal instabilities in stored beam below 320 mA at 2 GeV. Above 320 mA, however, transverse instabilities appeared and the LFS ceased to control longitudinal instabilities. The performance of the LFS is very reliable and repeatable. This paper describes on the PLS LFS test results of suppressing the longitudinal instabilities.

Light source performance achievements

More and more third generation light sources (3GLS) have come into operation. All of them were successful in reaching their performances. Some of them, like the ESRF, achieved brilliances up to two orders of magnitude higher than their initial target. Experience with the operation of existing machines indicates some imperfections and possibilities for new projects to integrate possible corrections in their design. These include: operation at the diffraction limit with even higher brilliances, higher position stability, enhanced Touschek lifetimes with larger momentum acceptances combined with low chromaticity and feedback of coupled bunch transverse resistive wall instability, efficient control of the longitudinal coupled bunch instability, higher currents in single bunch, better signal to noise ratio by localising losses at selected places in the ring and avoiding the emission of high energy bremsstrahlung photons in the direction of beamlines, possibilities of permanent injection, production of focused photon beams, high quality insertion devices, etc. Over the last 5 years, intensive R&D was dedicated to linac driven SASE FELs. They are considered as genuine 4th generation light sources. Results are encouraging, but there is still a certain way to go before planning an X-ray FEL facility. Therefore, rings are likely to remain for a long time the sources of excellence for users.

Improvement in the beam lifetime by means of an rf phase modulation at the KEK Photon Factory storage ring

In the 2.5-GeV Photon Factory storage ring at KEK, we have found that the beam lifetime can be improved by modulating the phase of an rf accelerating voltage at a frequency of 2 times the synchrotron oscillation frequency. By applying this phase modulation with a peak-to-peak amplitude of 3.2\ifmmode^\circ\else\textdegree\fi{}, the beam lifetime could be improved, typically, from 22 to 36 h under a beam current of about 360 mA. At the same time, the longitudinal coupled-bunch instability could be considerably suppressed. The improvement in the beam lifetime can be explained as an improved Touschek lifetime, which was caused by a quadrupole-mode longitudinal oscillation of the stored bunches.

High beam current storage at low energy for compact synchrotron radiation rings (invited)

A study of high beam current storage at a low energy is being conducted on the compact electron storage ring NIJI-1. In general, it is said that the stored beam lifetime is rapidly shortened as the beam energy decreases, and the high beam current storage is difficult to obtain. However, a stored beam current above a 350 mA was obtained at an injection energy of 100 MeV, and the lifetime of the stored beam is considerably long. For example, e-folding lifetime is about 2 h at 100 MeV. In this paper, we estimate the beam current decay rate due to the residual gas scattering, the ion trapping effect, and the Touschek effect, and make clear these contributions to the beam lifetime. It was clear that the Touschek lifetime is lengthened according to the bunch size growth, which is roughly explained by the longitudinal coupled bunch instability.

Measurement of bunch lengthening in TERAS

The bunch length was measured by using a highly sensitive streak camera with a time resolution of 2 ps. It was found that fine structures appeared in the electron bunch shape and that the shapes of electron bunches were described by a Gaussian distribution on the average. The dependence of bunch length on beam current was measured for an electron beam of 607 MeV. The bunch length was well represented by a power function of beam current with an exponent of 0.197 at currents lower than 35 mA or 0.30 at high currents. The experimental results suggest that the longitudinal coupled-bunch beam instability takes place at low beam currents and the turbulent instability dominates at high currents. It was also found from the three-dimensional bunch shape measurements that the bunch shape tended to blow up at high currents.

Suppression of Longitudinal Coupled-Bunch Instability by Decoupling Method

The decoupling method to suppress the longitudinal coupled-bunch instability in the UVSOR electron storage ring was tried. Synchrotron frequencies of individual bunches were spread by means of the modulation of the effective acceleration voltage in order to decouple these synchrotron oscillations. The instability is successfully damped by this method when the beam current is not high and the growth rate is moderate. The limitation of this method is not in the principle but in the maximum modulation index available in this experiment.

Equilibrium phase instability in the double RF system for Landau damping

A longitudinal coupled bunch instability in an electron storage ring was suppressed by the Landau damping in a double rf system composed of a second harmonic rf cavity. The damping became ineffective, however, above a beam current of 30 mA; the beam bunch slipped out of the optimum phase of the total rf voltage for the damping, which accompanied a simultaneous deformation of the total voltage. The unexpected phenomenon of the phase slip is explained by the concept of equilibrium phase instability of the beam bunch based on a rigid bunch model. The phase slip of the bunch was suppressed by introducing a phase feedback loop, resulting in an improvement of the maximum beam current for the damping. Discussions are made on various conditions of the equilibrium phase instability, including another possibility for avoiding the phase slip.