Transverse Mode Coupling Instability Research Articles

Wakefields excited in the FCC-ee collimation system

The purpose of this paper is to calculate the longitudinal and transverse wakefields of the FCC collimators using the electromagnetic codes ECHO3D and IW2D. We cross-checked our results using CST particle studio for long bunches, and found them to be in good agreement. The obtained results show that the collimators give one of the highest contributions to the overall FCC-ee wake potentials. In particular, using the code PyHEADTAIL, we have found that the geometric contribution of the collimators' wakefield reduces significantly the transverse mode coupling instability threshold. Therefore, it is imperative to explore and implement solutions that effectively mitigate this wakefield source.

Simulations and measurements of the transverse mode coupling instability in the LHC

Simulations and measurements of the transverse mode coupling instability in the LHC

The report of machine studies related to the vertical beam size blow-up in SuperKEKB LER

In the low energy ring (LER) for positrons in the SuperKEKB, a vertical beam size blow-up was observed when the bunch current was approximately 1 mA. If a beam size blow-up occurs, the design luminosity cannot be achieved. Therefore, beam size blow-ups must be pre-vented. According to calculations, the bunch current threshold of the transverse mode coupling instability (TMCI) is 2 mA or more, and the observed value is 50% or smaller. Ordinary TMCI cannot explain this vertical beam size blow-up. This paper shows that the cause of the vertical beam size blow-up can be determined by analyzing factors such as beam oscillation. The study results showed that the vertical beam size blow-up in the LER was caused by a -1 mode instability.

Description of beam instabilities in synchrotrons with wakefields and space charge forces using the circulant matrix model

A new model for the description of beam instabilities in synchrotrons featuring wakefields and space charge forces is proposed, using the circulant matrix approach. The predictions of this model are discussed in light of past ones, with a particular emphasis on the possible mitigation of the transverse mode coupling instability by space charge forces. The existence of transient amplification in spite of the absence of unstable eigenvalues in configuration featuring strong space charge forces is also addressed. It is shown that this behavior can be recovered when considering an airbag distribution. Yet when considering a more realistic Gaussian distribution, the radial modes lead to other types of mode coupling instabilities. The predictions of the new model are then compared to results of an experiment conducted at the CERN Super Proton Synchrotron, showing a reasonable agreement.

Imaginary tune split and repulsion single-bunch instability mechanism in the presence of a resistive transverse damper and its mitigation

A resistive transverse damper is often needed in particle accelerators operating with many bunches and it is usually very efficient as it can considerably reduce the necessary amount of nonlinearities needed to reach beam stability through Landau damping. In the CERN LHC for instance, the required current in the Landau octupoles is predicted to be reduced by an order of magnitude for zero chromaticity (for the beam and machine parameters used during the last year of Run 2, in 2018, this corresponded to $\ensuremath{\sim}2000\text{ }\text{ }\mathrm{A}$ without damper and $\ensuremath{\sim}200\text{ }\text{ }\mathrm{A}$ with damper, knowing that the maximum current available in the Landau octupoles is $\ensuremath{\sim}550\text{ }\text{ }\mathrm{A}$). However, a resistive transverse damper also destabilizes the single-bunch motion below the transverse mode coupling instability intensity threshold (for zero chromaticity), introducing a new kind of instability, which has been called ITSR instability (for imaginary tune split and repulsion). Until now, only one type of impedance-driven transverse coherent instability has been explained for a single bunch in a circular particle accelerator, at zero chromaticity and without a multiturn wake: the transverse mode coupling instability. A transverse mode coupling instability can also be observed in the presence of Landau damping, beam-beam, electron cloud or space charge. However, the ITSR instability exhibits a different mechanism, which is not due to mode coupling. The purpose of this article is to explain in detail both this new instability mechanism and its mitigation using a simplified analytical model, which has been carefully benchmarked, using the pyheadtail macroparticle tracking code, by Oeftiger (one of the code's developers).

Intrabunch motion

Impedance-driven (but not only) coherent beam instabilities are usually studied analytically with the linearized Vlasov equation, ending up with an eigenvalue system to solve. The eigenvalues describe the beam oscillation mode-frequency shifts, leading in particular to intensity thresholds defined by the longitudinal mode coupling instability in the longitudinal plane and by the transverse mode coupling instability in the transverse plane in the absence of chromaticity. This can be directly compared to measurements in particular for the lowest modes and in the absence of tune spread. In the presence of nonlinearities or when higher-order modes are involved, this becomes quite difficult, if not impossible, and the coupling between the modes cannot be directly measured (or simulated) anymore. Another important observable is the intrabunch motion, which can be also accessed analytically thanks to the eigenvectors. To the author's knowledge, until now, the intrabunch signal has only been explained theoretically for independent longitudinal or transverse beam oscillation modes, i.e., when the bunch intensity is sufficiently low compared to the mode coupling threshold. It was never explained theoretically in detail when two (or more) modes are involved. For instance, no answers were already given to these questions: is (are) there some fixed point(s) when the transverse mode coupling instability starts? If yes, where is it (are they)? And what happens in the presence of mode decoupling? Any number of modes can be treated with the general approach discussed in this paper, which is based on the galactic Vlasov solver (which was previously successfully benchmarked against the pyheadtail macroparticle tracking code as concerns the beam oscillation mode-frequency shifts). However, to be able to clearly see what happens when the bunch intensity is increased, the simple case of two modes is discussed in detail. The purpose of this paper is to describe the different regimes, below, at, above the transverse mode coupling instability and also after the mode decoupling (as it happens sometimes), using a simple analytical model (where two modes are considered together), which helps to really understand what happens at each step. Better characterizing an instability is the first step before trying to find appropriate mitigation measures and push the performance of a particle accelerator. The evolution of the intrabunch motion with intensity is a fundamental observable with high-intensity high-brightness beams.

Longitudinal and transverse mode coupling instability: Vlasov solvers and tracking codes

The study of collective effects in circular accelerators can be tackled by solving numerically the Vlasov equation or by using tracking codes. The two methods are obtained with different approaches: Vlasov solvers consider a continuous distribution function and describe the beam with coherent oscillation modes in frequency domain (ending up usually with an eigenvalue system to solve), while tracking codes use macroparticles and wakefields in time domain. In this paper we present two Vlasov solvers for the study of collective effects (from impedances/wakefields only) which evaluate the frequency shift of coherent oscillation modes and possible mode coupling instability in the single-bunch case for both longitudinal and transverse planes. In the longitudinal plane the Vlasov solver also takes into account the potential well distortion due to the wakefields under some conditions. In parallel to this theoretical approach, tracking codes, which include collective effects, have been used as benchmark. In particular, starting from their results, we also propose a new method to study the frequency shift of coherent modes and compare it with the output of the Vlasov solvers.

Examining RF jitter and transverse mode-coupling instability in triple-frequency RF systems

Examining RF jitter and transverse mode-coupling instability in triple-frequency RF systems

Comment on “Instability studies at the CERN Proton Synchrotron during transition crossing”

In the article of Migliorati, Aumon, Koukovini-Platia, Huschauer, Metral, Sterbini and Wang [Phys. Rev. Accel. Beams 21, 120101 (2018)], hereafter the Article and the Authors, the long-standing qualification of the PS instability as the transverse mode-coupling instability, or TMCI, is not mentioned, while a model of the beam breakup (BBU) is discussed. Do the observations and modeling of the Article refute the long-standing idea that the PS instability is the TMCI?

Effect of bunch shape on its transverse mode coupling instability spectrum and threshold with high space charge

Transverse mode coupling instability of bunched beam is investigated in the paper at different form of the bunches with space charge included. Equation of transverse motion of the bunch in parabolic potential well of synchrotron oscillations is derived and analysed. The bunch of constant density (flat bunch) is examined in detail to make comparison with the square well model. It is shown that both models result in very close instability thresholds of the flat bunch. Then different form bunches are investigated in the parabolic potential well. It is shown that decrease of the bunch r.m.s length leads to the growth of its threshold, that is the flat bunch model gives only a minimal estimation of the threshold. The results are treated in terms of Landau damping due to spread of the space charge tune shift.

Transverse mode-coupling instability and space charge

Transverse mode-coupling instability (TMCI) is known to limit bunch intensity. Since space charge (SC) changes coherent spectra, it affects the TMCI threshold. Generally, there are only two types of TMCI with respect to SC: the vanishing type and the strong space charge (SSC) type. For the former, the threshold value of the wake tune shift is asymptotically proportional to the SC tune shift, as it was first observed twenty years ago by M. Blaskiewicz for exponential wakes. For the latter, the threshold value of the wake tune shift is asymptotically inversely proportional to the SC, as it was shown by one of the authors. In the presented studies of various wakes, potential wells, and bunch distributions, the second type of instability was always observed for cosine wakes; it was also seen for the sine wakes in the case of a bunch within a square potential well. The vanishing TMCI was observed for all other wakes and distributions we discuss in this paper: always for the negative wakes, and always, except the cosine wake, for parabolic potential wells. At the end of this paper, we consider high-frequency broadband wake, suggested as a model impedance for CERN SPS ring. As expected, TMCI is of the vanishing type in this case. Thus, SPS Q26 instability, observed at strong SC almost with the same bunch parameters as it would be observed without SC, cannot be TMCI.

Broadband Impedance of Pumping Holes and Interconnects in the FCC-hh Beamscreen

In the proposed Future Circular Collider (FCC-hh) pumping holes and interconnects between sections of the beamscreen can be sources of unwanted broadband impedance, potentially leading to the transverse mode coupling instability (TMCI). The pumping holes pose a greater challenge to the impedance calculation due to their small contribution per hole. Unlike for the Large Hadron Collider (LHC), analytical methods cannot be applied due to the complex beamscreen geometry and the greater size of the holes. Instead, two computational methods are used and compared to each other. For the interconnects, the impedance due to a sophisticated system of tapers is also estimated using computational methods.

Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall

Author(s): Venturini, M | Abstract: The effect of rf harmonic cavities on the transverse mode-coupling instability (TMCI) is still not very well understood. We offer a fresh perspective on the problem by proposing a new numerical method for mode analysis and investigating a regime of potential interest to the new generation of light sources where resistive wall is the dominant source of transverse impedance. When the harmonic cavities are tuned for maximum flattening of the bunch profile we demonstrate that at vanishing chromaticities the transverse single-bunch motion is unstable at any current, with growth rate that in the relevant range scales as the 6th power of the current. With these assumptions and radiation damping included, we find that for machine parameters typical of 4th-generation light sources the presence of harmonic cavities could reduce the instability current threshold by more than a factor two.

Threshold of transverse mode coupling instability with arbitrary space charge

Transverse mode coupling instability of a bunch with space charge and wake field is considered in frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as the basis for solution of the equations with the wake field included. Dispersion equation for the bunch eigentunes is obtained in the form of an infinite continued fraction. It is shown that influence of space charge on the instability essentially depends on the wake sign. In particular, threshold of the negative wake increases in absolute value until the space charge tune shift is rather small, and goes to zero at higher space charge. The explanation of this behavior is developed by analysis of the bunch spectrum. A comparison of the results with published articles is represented.

Transverse mode coupling instability threshold with space charge and different wakefields

Threshold of the transverse mode coupling instability is calculated in frameworks of the square well model at arbitrary value of space charge tune shift. A new method of calculation is developed beyond the traditional expansion technique. The square, resistive, and exponential wakes are investigated. It is shown that the instability threshold goes up without limit when the tune shift increases. A resemblance of the results to conventional case of the parabolic potential well is demonstrated and explained.

Collective effects in a diffraction-limited storage ring.

This paper gives an overview of collective effects that are likely to appear and possibly limit the performance in a diffraction-limited storage ring (DLSR) that stores a high-intensity ultra-low-emittance beam. Beam instabilities and other intensity-dependent effects that may significantly impact the machine performance are covered. The latter include beam-induced machine heating, Touschek scattering, intra-beam scattering, as well as incoherent tune shifts. The general trend that the efforts to achieve ultra-low emittance result in increasing the machine coupling impedance and the beam sensitivity to instability is reviewed. The nature of coupling impedance in a DLSR is described, followed by a series of potentially dangerous beam instabilities driven by the former, such as resistive-wall, TMCI (transverse mode coupling instability), head-tail and microwave instabilities. In addition, beam-ion and CSR (coherent synchrotron radiation) instabilities are also treated. Means to fight against collective effects such as lengthening of the bunch with passive harmonic cavities and bunch-by-bunch transverse feedback are introduced. Numerical codes developed and used to evaluate the machine coupling impedance, as well as to simulate beam instability using the former as inputs are described.

Transverse mode coupling instability of colliding beams

In high brightness circular colliders, coherent and incoherent beam dynamics are dominated by beam-beam interactions. It is generally assumed that the incoherent tune spread introduced by the beam-beam interactions is sufficiently large to cure any instabilities originating from impedance. However, as the two counterrotating beams interact they can give rise to coherent dipole modes and therefore modify the coherent beam dynamics and stability conditions. In this case, coherent beam-beam effects and impedance cannot be treated independently and their interplay should be taken into account in any realistic attempt to study the beam stability of colliding beams. Due to the complexity of these physics processes, numerical simulations become an important tool for the analysis of this system. Two approaches are proposed in this paper: a fully self-consistent multiparticle tracking including particle-in-cell Poisson solver for the beam-beam interactions and a linearized model taking into account finite bunch length effects. To ensure the validity of the results a detailed benchmarking of these models was performed. It will be shown that under certain conditions coherent beam-beam dipole modes can couple with higher order headtail modes and lead to strong instabilities with characteristics similar to the classical transverse mode coupling instability originating from impedance alone. Possible cures for this instability are explored both for single bunch and multibunch interactions. Simulation results and experimental evidences of the existence of this instability at the LHC will be presented for the specific case of offset collisions.

Review of collective beam instabilities in electron-positron storage rings

The review of studies of collective beam instabilities in electron-positron storage rings is presented. The processes of excitation and suppression of the longitudinal microwave instability, transverse mode coupling instability, longitudinal and transverse multi-bunch instabilities, and instabilities induced by an interaction of a beam with ions or electron clouds are discussed. Important equations for estimation of the threshold beam currents and the rise time of instabilities, as well as the references to the major original works are given. The methods for diagnostics and suppression of instabilities are considered using specific examples.

Transverse instability of a bunched beam with space charge and wakefield

Transverse instability of a bunch in a ring accelerator is considered with space charge and wakefield taken into account. It is assumed that space charge tune shift significantly exceeds the synchrotron tune. Bunch spectrum, instability growth rate, and effects of chromaticity are studied with different bunch and wake forms. Fast instability caused by coupling of transverse modes is studied in detail. It is shown that, for monotonic wakes, the transverse mode coupling instability is possible only with a certain sign of the wake. Its threshold and growth rate are calculated precisely over a wide range of parameters.

Head-tail modes for strong space charge

The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The Landau damping rates are also found. The suppression of the transverse mode coupling instability by the space charge is explained.