Mode Coupling Instability Research Articles

Asymmetric influence of the amplitude-dependent tune shift on the transverse mode-coupling instability

At the 3 GeV ring of the MAX IV Laboratory, a fourth-generation ring-based synchrotron light source, an asymmetric influence of the sign of the amplitude-dependent tune shift (ADTS) on the transverse mode-coupling instability has been observed. Measurements of the instability, in dedicated single-bunch experiments at low chromaticity, revealed a significant dependence of the dynamics of the instability above threshold on the sign of the ADTS. While for a negative sign of the ADTS, the crossing of the instability does not lead to a loss of beam current, a positive sign results in the loss of 40% or more of the beam current at the threshold. In order to investigate the observed asymmetry, the systematic measurement of beam dynamics above the threshold has been conducted in combination with particle tracking simulations with 2 and theoretical calculations of the Landau damping due to the ADTS. The findings point toward an influence of the Landau damping in combination with the low synchrotron frequency, which indicates that this effect could become relevant in the future low-emittance electron storage rings. Published by the American Physical Society 2024

Effects of space charge force on the beam-beam mode coupling instability

Recent e+e− colliders operate with very low emittance and high current. The space-charge tune shift is not negligible in tau-charm and B factories. The vertical space-charge tune shift is on the order of 0.02–0.1 and is comparable to the synchrotron tune and the beam-beam tune shift. The beam-beam mode coupling instability has been studied with and without vacuum environment impedance. The mode coupling is influenced by the space-charge force, which exhibits similar characteristics to the beam-beam force. The combined effect of beam-beam, space charge, and vacuum environment impedance is discussed within the framework of the mode coupling theory. Strong-strong beam-beam simulation, considering the space-charge force and the impedance, are conducted to validate the theory and to study general cases such as asymmetric colliders. Published by the American Physical Society 2024

Analysis of a brake squeal functional model using a linear parameter varying perspective

Brake squeal is a limit cycle vibration induced by mode coupling instability that depends on operating conditions such as applied pressure, temperature, and disc velocity. This work proposes a simplified functional model of brake squeal that reproduces the main characteristics observed in a full-scale industrial test campaign: vibration growth, limit cycle saturation, vibration decay and parametric dependence. The proposed functional model differs from the well-known Hoffmann model by the introduction of a nonlinear contact law and a quasi-static pressure loading. First, using a harmonic balance perspective, non-linear forces are shown to lead to a pressure and amplitude dependent contact stiffness. This Linear Parameter Varying perspective allows complex mode computations in the pressure/amplitude domain which are then correlated with a series of transient responses of the nonlinear modes for three different pressure profiles. The chosen profiles represent usual experiments: drag where a constant pressure is applied, pressure ramps and pressure oscillations mimicking the effect of wheel spin on the contact surfaces.

Experimental investigation on brake squeal unpredictability: Role of the friction noise

Dynamic contact instabilities represent a common issue in brake industry, causing noise and passenger dissatisfaction. Past works identified mode coupling as the cause of brake squeal, but the conditions for its occurrence are still not fully understood, making this phenomenon hardly predictable. This work investigates the relationship between the friction noise, intended as the dynamic excitation generated by the local interface interactions (ruptures, impacts …), and the unstable response of the system. An experimental measurement campaign, conducted on a dedicated tribometer, highlighted that, even in presence of the same macroscopic friction coefficient, mode coupling instability occurred only when in presence of high values of friction noise. Therefore, the friction noise is proposed as a trigger factor for brake squeal occurrence.

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

Dynamic Instability of Rigid Shoe Modes in a Drum Brake System

This study examined the dynamic instability of a drum brake induced by the rigid modes of the brake shoe. The brake shoe was modeled as a rigid curved plate subject to frictional contact with a rotating drum. In the presence of a negatively sloped friction curve, dynamic instability was numerically analyzed with respect to variation in the system parameters. The results showed that mode-coupling instability did not occur, but dynamic instability was induced by negative damping in a specific rigid mode, and its propensity varied with the operating conditions and geometric changes.

Analytical expressions of friction-induced self-excited vibration amplitudes of the marine rubber bearing-shaft system

By the analytical method, this paper investigates the mode-coupling friction-induced instability and the resulting stick-slip self-excited vibration of the marine stern water-lubricated rubber bearing-shaft system. The 2-DOF simplified theoretical model is reasonably developed to characterize stern water-lubricated rubber bearing-shaft system. The complex eigenvalue analysis is conducted to analyze the instability behaviors of the model. Results show the normal force and nonlinear stiffness often deteriorate the stability of the model. Subsequently, two types of analytical expressions for stick-slip vibration amplitude of the model are by the Krylov-Bogoliubbov-Mitropolsky method, which match well with the results from numerical integration. Then, parameter discussion about the influences of friction coefficient, damping, normal force and nonlinear contact stiffness on self-excited vibration amplitudes are performed. The results indicate that the bearing-shaft system can keep the steady-state static equilibrium or the oscillations with small amplitude if the proper parameter values of the variables are chosen, which will benefits controlling the friction-induced vibration of the water-lubricated rubber bearing-shaft system. The novelty of this work is to give analytical expressions for stick-slip self-excited vibration amplitude of the simplified model.

Efficacy of velocity feedback control for suppression of the friction-induced oscillation due to mode-coupling instability in a two degrees-of-freedom mechanical system

The present article focuses on suppressing mode-coupling instability in frictional systems, which can cause unwanted vibrations such as squeal in braking systems. Mode-coupling instability occurs when two or more modes of a system approach each other. This article proposes the use of resonant velocity feedback control to eliminate friction-induced oscillations generated by mode-coupling instability. A two degree-of-freedom linear model is used to capture the instability due to friction-induced mode coupling. The efficacy of the control is demonstrated through linear stability analysis, and by optimizing control parameters using pole crossover method to minimize the transient time of the response. The robustness analysis demonstrates the ability of the control to effectively mitigate the instability even under parametric perturbations. The controlled system is simulated in MATLAB Simulink to validate analytical results. The effects of time delay, which is commonly present in feedback systems, are also investigated. Finally, the effectiveness of the control is studied in the presence of nonlinearity in the system. The nonlinear dynamics are analyzed by creating bifurcation diagrams with different bifurcation parameters.

Dependence of ion wake characteristics on experimental conditions

Two-dimensional microparticle crystals can be formed in the sheath of a gas discharge plasma. Ions from the bulk plasma are accelerated in the sheath electric field, flowing past the grains to create a positive ion wake downstream from the grains. Interaction between the ion wake and neighboring grains creates additional coupling between oscillation modes and can trigger mode-coupling instability (MCI). In order to better understand MCIs, the interaction between dust grains and ion wakes must be understood; however, the relationship between the discharge parameters and ion wake characteristics is unknown. A molecular dynamics simulation of ion dynamics and dust charging is used to self-consistently determine the dust charge and ion wake characteristics for different synthetic experimental conditions. It is found that the ion wake is strongly dependent on the background gas pressure but not affected much by the discharge power.

Modelling and stability analysis of a high-speed train braking system

The stability of a braking system is crucial for the steady and safe operation of trains. To investigate the dynamic behaviors and stability of a train braking system as influenced by key parameters, a numerical model integrating mode-coupling, negative friction–velocity slope (NFVS), and stick–slip theories was established. Additionally, the wheelset connected with the braking system was contained in the model considering that mode-coupling and stick–slip characteristics were affected by system structures. Based on this model, the influence and mechanism of stiffness, damping, and NFVS characteristics on mode-coupling of the braking system were revealed. The results showed that when the tangential and normal contact stiffness values of the pad were close, the system experienced mode-coupling instability and vibrations in these two directions were coupled. When the tangential and normal damping values of the pad were unequal, the energy dissipation in the two directions became different and the system instability was enhanced. Additionally, the system complex eigenvalues always had positive real parts and the dynamic behaviors were more complicated by considering NFVS at relatively low speeds. This is because NFVS characteristics can be equivalent to negative damping values, which cause the difference in tangential and normal damping values and continuously input energy into the braking system, then weakening the system stability.

Longitudinal mode-coupling instabilities of proton bunches in the CERN Super Proton Synchrotron

In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation modes, which belong to either the same or adjacent azimuthal modes, respectively. We show that both instability mechanisms exist in the SPS by applying the Oide-Yokoya approach to compute van Kampen modes for the realistic longitudinal impedance model of the SPS. The results agree with macroparticle simulations and are consistent with beam measurements. In particular, we see that the uncontrolled longitudinal emittance blowup of single bunches observed before the recent impedance reduction campaign (2018--2021) is due to the radial mode-coupling instability. Unexpectedly, this instability is as strong as the azimuthal mode-coupling instability, which is possible in the SPS for other combinations of bunch length and intensity. We also demonstrate the significant role of rf nonlinearity and potential-well distortion in determining these instability thresholds. Finally, we discuss the effect of the recent impedance reduction campaign on beam stability in single- and double-rf configurations.

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.

Erratum: Reply to “Comment on ‘Fast-slow mode coupling instability for coasting beams in the presence of detuning impedance’” [Phys. Rev. Accel. Beams 24 , 078002 (2021)

Received 7 November 2022DOI:https://doi.org/10.1103/PhysRevAccelBeams.25.129901Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBeam impedanceBeam instabilitiesAccelerators & Beams

Controlling mode-coupling instability in friction-induced vibration by acceleration feedback

Self-excited friction-induced oscillation, such as brake squeal, railway wheel squeal, chattering in machine tools, etc., is harmful in many mechanical systems. In the present study, the efficacy of acceleration feedback control with a second order filter is theoretically studied to mitigate friction-induced mode-coupling instability. Two different control strategies based on acceleration feedback are employed to control friction-induced mode-coupling instability of a two degrees-of-freedom linear system. Linear stability analysis near the equilibrium point of the system shows the efficacy of control laws to stabilize the system. The optimum filter parameters are determined by the pole crossover optimization method to attenuate the transient response as well as to achieve greater relative stability of the system. The Robustness study confirms the ability of the controller to stabilize the system in the presence of uncertainties in system parameters. Analytical results match closely with simulation results. Finally, nonlinearity in the form of stiffness is incorporated into the system for which the dynamics of the system show the presence of subcritical, supercritical Hopf bifurcation, and cyclic fold bifurcation. In the presence of nonlinearity, the feedback control is also able to reduce the range of instability of static equilibrium as well as the amplitude of the self-excited oscillation. The method of averaging is used to determine the stability and amplitude of the limit cycle. For the nonlinear system, the bifurcation diagram is constructed in AUTO and validated with results obtained from MATLAB SIMULINK and the method of averaging.

Deep Gaussian Process for the Approximation of a Quadratic Eigenvalue Problem: Application to Friction-Induced Vibration

Despite numerous works over the past two decades, friction-induced vibrations, especially braking noises, are a major issue for transportation manufacturers as well as for the scientific community. To study these fugitive phenomena, the engineers need numerical methods to efficiently predict the mode coupling instabilities in a multiparametric context. The objective of this paper is to approximate the unstable frequencies and the associated damping rates extracted from a complex eigenvalue analysis under variability. To achieve this, a deep Gaussian process is considered to fit the non-linear and non-stationary evolutions of the real and imaginary parts of complex eigenvalues. The current challenge is to build an efficient surrogate modelling, considering a small training set. A discussion about the sample distribution density effect, the training set size and the kernel function choice is proposed. The results are compared to those of a Gaussian process and a deep neural network. A focus is made on several deceptive predictions of surrogate models, although the better settings were well chosen in theory. Finally, the deep Gaussian process is investigated in a multiparametric analysis to identify the best number of hidden layers and neurons, allowing a precise approximation of the behaviours of complex eigensolutions.

Investigation on mode-coupling parametric vibrations and instability of spillway radial gates under hydrodynamic excitation

Flow-induced parametric oscillation of the spillway radial gates occurs under hydrodynamic excitation due to flow fluctuation, threatening the hydropower systems’ safety. However, the underlying instability mechanisms of the spillway radial gates are still not clear. In this work, we explore the dynamic instability of spillway radial gates with multiple modes considered during the gate-lifting dynamic process. A numerical method for transferring dynamic instability problem of the gate to the generalized eigenvalue problem is developed by using Galerkin method, Floquet theorem and harmonic balance methods. The results reveal that, the critical gate opening exists during the gate lifting process, and the number and distribution of critical gate openings in dynamic instability regions are the key factors inducing the gate's instability. The presented instability intensity can be used to diagnose the vibration state of the gate. The mode-coupling effect renders the radial gate more dynamically instability, increasing the damping ratio is an effective measure on dynamic instability mitigation. The proposed insights in this work can provide guidelines for evaluating the gate's safety and bring rational decision-making in design and operation stages.

Stability of two-dimensional complex plasma monolayers in asymmetric capacitively coupled radio-frequency discharges.

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure p_{cryst}, the monolayer always crystallizes; (ii) below a specific pressure p_{MCI}, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between p_{MCI} and p_{cryst}, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below p_{MCI}, the monolayer remains in the fluid phase until it reaches p_{cryst} at which it recrystallizes; when decreasing the pressure from above p_{cryst}, the monolayer remains in the crystalline phase until it reaches p_{MCI} at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of p_{MCI} as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.

Robust optimization of nonlinear energy sinks used for mitigation of friction-induced limit cycle oscillations

This paper aims at proposing robust methods to optimize nonlinear energy sinks (NES) used for the mitigation of friction-induced vibrations due to mode coupling instabilities. The study is based on a mechanical system composed of two NES coupled to the well-known two-degrees-of-freedom Hultèn’s model. In such an unstable system coupled with NES, it is usual to observe a discontinuity in the steady-state amplitude profile which separates the parameter space into two parts corresponding respectively to the mitigated and unmitigated regimes. The discontinuity is predicted by a methodology previously developed by the authors and based on Multi-Element generalized Polynomial Chaos. The method allows to determine the Propensity of the system to undergo a Harmless Steady-State Regime (PHSSR). The objective of the present work is therefore to maximize the value of the PHSSR to obtain a robust optimal design of the NES. To this end, several stochastic optimization problems are presented that take into account the dispersion of the uncertain parameters using two approaches; in the first one, the parameters of the NES are considered as deterministic, and in the second one they are also supposed uncertain but with a known probability law.

Prediction and suppression of chaotic instability in brake squeal

Chaotic instability in a vibration phenomenon, known as brake squeal, is investigated including the combined effects of falling friction, sprag-slip and mode coupling. Brake squeal is a high-pitched noise that occurs sometimes when a vehicle is decelerated using disc brakes. The equations of motion for the two dominant coupled modes of the brake system reduce to two autonomous coupled nonlinear second-order systems. The mode coupling instability via friction causes limit cycle behaviour via a supercritical Hopf bifurcation. This limit cycle is shown to break up into chaotic motion characterised by a Poincare map with a less than one-dimensional attractor, similar to that found in a forced dry friction oscillator. For the first time, conservative analytical conditions for brake squeal chaos are developed and verified numerically over a range of sprag angles and brake pressures for fundamental and real brake systems. The predictive model is then used to identify and quantify means to suppress brake squeal chaos to unlikely, excessive friction levels. The results provide predictive insight into conditions under which brake squeal chaos occurs and its suppression.