Mode Coupling Instability Research Articles

Experimental studies of two-dimensional complex plasma crystals: waves and instabilities

A review of experimental studies on waves, phonon dispersion relations, and mode-coupling instability in two-dimensional complex plasma crystals is presented. An improved imaging method allowing simultaneous measurements of the three wave modes (compression in-plane, shear in-plane, and out-of-plane) is given. This method is used to evidence the formation of hybrid modes and the triggering of the mode-coupling instability due to wake-mediated interactions. The main stages of the mode-coupling instability are analyzed. In the early stages, synchronization of microparticle motion at the hybrid mode frequency is reported. The spatial orientation of the observed synchronization pattern correlates well with the directions of the maximal increment of the shear-free hybrid mode. When the instability is fully developed, a melting front is formed. The propagation of the melting front has similarities with flame propagation in ordinary reactive matter. Finally, it is experimentally demonstrated that an external mechanical excitation of a stable 2D complex plasma crystal can trigger the mode-coupling instability and lead to the full melting of a two-dimensional complex plasma crystal.

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?

Investigation of friction-induced vibration in a disk brake model, including mode-coupling and gyroscopic mechanisms

The brake squeal reduction has been extensively investigated in many academic and industrial researchers. Friction-induced vibrations can be considered as a dynamic instability problem. Generally, automotive engineers and researchers working in the domain of disk brake noise treat instabilities due to the force of friction as a friction-induced vibration. In the case of squeal noise, mode coupling may cause instability of the system. The aim of this article is to propose a minimal two degree of freedom disk brake model in order to investigate the effects of different parameters on mode-coupling instability. This model takes into account self-excited vibration, gyroscopic effect, friction-induced damping, and brake pad geometry. Thus, a stability analysis of equilibrium by calculating complex eigenvalues is presented to investigate the influence of the main parameters on the stability zone such as the opening angle of the brake pad and preload. For the validation of the stability analysis, squeal index and time domain response are used. The results obtained show the importance of optimizing the physical and geometrical parameters of the brake and that some of these parameters have greater effects compared to the others to reduce noise.

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.

On the Passive Control of Friction-Induced Instability Due to Mode Coupling

This study investigates a passive controller for a coupled two degrees-of-freedom (DOFs) oscillator to suppress friction-induced mode-coupling instability. The primary system is acted upon by a friction force of a moving belt and static coupling of the oscillator provided with an oblique spring. The combined system, original system plus absorber, response is governed by two sets of differential equations to include contact and loss of contact between the mass and the belt. Therefore, the model accounts for two sources of nonlinearity in the system: (1) discontinuity in the friction force and (2) intermittent loss of contact. Friction coefficient and absorber orientation are used to define planar parameter space for stability analysis. For various mass ratios, the parameter space is divided into stable and unstable zones by defining stability boundaries. In general, an absorber expands the stability region and provides a significant reduction in transient response overshoot and settling time. Incorporation of the absorber also prevents mass-belt separation, thereby suppressing the belt-speed-overtake by the primary mass.

Convective instabilities of bunched beams with space charge

For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI. For sufficiently strong space charge (SC), the instability threshold of the wake-driven coherent tune shift normally increases linearly with the SC tune shift, as independently concluded by several authors using different methods. This stability condition has, however, a very strange feature: at strong SC, it is totally insensitive to the number of particles. Thus, were it correct, such a beam with sufficiently strong SC, being stable at some intensity, would remain stable at higher intensity, regardless of how much higher! This paper suggests a resolution of this conundrum: while SC suppresses TMCI, it introduces head-to-tail convective amplifications, which could make the beam even less stable than without SC, even if all the coherent tunes are real, i.e. all the modes are stable in the conventional {\it absolute} meaning of the word. This is done using an effective new method of analysis of the beam's transverse spectrum for arbitrary space charge and wake fields. Two new types of beam instabilities are introduced: the {\it saturating convective instability}, SCI, and the {\it absolute-convective instability}, ACI.

Tracking and Linking of Microparticle Trajectories During Mode-Coupling Induced Melting in a Two-Dimensional Complex Plasma Crystal.

In this article, a strategy to track microparticles and link their trajectories adapted to the study of the melting of a quasi two-dimensional complex plasma crystal induced by the mode-coupling instability is presented. Because of the three-dimensional nature of the microparticle motions and the inhomogeneities of the illuminating laser light sheet, the scattered light intensity can change significantly between two frames, making the detection of the microparticles and the linking of their trajectories quite challenging. Thanks to a two-pass noise removal process based on Gaussian blurring of the original frames using two different kernel widths, the signal-to-noise ratio was increased to a level that allowed a better intensity thresholding of different regions of the images and, therefore, the tracking of the poorly illuminated microparticles. Then, by predicting the positions of the microparticles based on their previous positions, long particle trajectories could be reconstructed, allowing accurate measurement of the evolution of the microparticle energies and the evolution of the monolayer properties.

Nonlinear control of friction-induced limit cycle oscillations via feedback linearization

Abstract This paper deals with the active control of friction-induced limit cycle oscillations that are generated from the mode-coupling mechanism, and that are often undesirable in numerous applications of nonlinear dynamical friction systems. The objective is to suppress the oscillations while taking into account the nonlinearities inherent to the friction systems and that result for example from the nonlinear laws of contact and friction. For this purpose, nonlinear control schemes based on the feedback linearizing approach are proposed and investigated in this study by considering a friction system with mode-coupling instabilities. Based on numerical simulations, an interesting potential is shown for the proposed control schemes and, more generally, insights about the opportunity to exploit them for an efficient mitigating of mode coupling instabilities, are stated.

Full finite element models and reduction strategies for the simulation of friction-induced vibrations of rolling contact systems

The aim of this paper is to develop a full Finite Element (FE) computational method for the dynamics of unstable frictional rolling contact systems in order to calculate reference solutions in many applications, especially curve squeal for railway transportation but also roller bearing or metal cutting. The proposed method is characterized by the use of a fine FE discretization of the contact surface in a Eulerian frame, nonlinear frictional contact laws and model reduction techniques. An application to the frictional rolling contact between two annular cylinders is presented in both quasi-static and dynamic cases with mode coupling instabilities. The validation of the approach in quasi-static conditions is carried out by comparison with CONTACT software. Stability and transient results show that the technique is able to simulate friction-induced vibrations at high frequencies. Reduced models are tested and show a good agreement with the full model.

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.

Mode-coupling instability in a single-layer complex plasma crystal: Strong damping regime

Mode-coupling instability (MCI) in a single-layer complex plasma crystal was studied experimentally in the regime of strong neutral gas damping. To trigger MCI, the discharge power was reduced at constant gas pressure. Surprisingly, at the onset of MCI the mean interparticle spacing became larger and the normalized neutral gas damping rate marginally increased. A steady-state regime where MCI occurred but was suppressed by the neutral gas friction was observed. Suppressed MCI caused heating up of the plasma crystal but did not lead to its melting. A theoretical model is proposed which describes well our experimental observations.

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.

Model reduction for friction-induced vibration of multi-degree-of-freedom systems and experimental validation

Most frictional systems are composed of components that are in sliding contact. Thus they have natural contact interfaces on which normal contact forces and tangential friction forces are acting. These real systems are complicated and friction brings further complexity, which presents a challenge to their dynamic analysis and control. In this paper, a model reduction strategy for complicated frictional systems is put forward based on the idea of mode synthesis, and its applications and experimental validation are presented. Firstly, the accuracy of the reduction method and the feasibility of the reduced model in stability analysis are verified on a theoretical multi-degree-of-freedom frictional system. Then, a tribometer in the form of a pad-on-disc test rig is designed and built and its corresponding detailed finite element (FE) model is constructed. A specific reduction strategy for this real friction system which involves direct contact at the pad-disc interface, is proposed. It is found that the reduced model with 80 modes of each of the two substructures of the system can already correctly predict the mode-coupling instability of the full FE model (which has over 900,000 degrees of freedom) of the real system, and unstable frequencies that are fairly close to the unstable frequencies of the FE full model computed by Abaqus CEA and the vibration frequencies measured in the test on the tribometer, which demonstrates the efficiency and accuracy of the model reduction strategy for dynamic analysis of real friction systems. Its computational efficiency would be even much greater when applied to nonlinear dynamic analysis of real friction systems. Model reduction for friction-induced vibration validated by experiments has not been reported in the literature.

Full melting of a two-dimensional complex plasma crystal triggered by localized pulsed laser heating.

The full melting of a two-dimensional plasma crystal was induced in a principally stable monolayer by localized laser stimulation. Two distinct behaviors of the crystal after laser stimulation were observed depending on the amount of injected energy: (i) below a well-defined threshold, the laser melted area recrystallized; (ii) above the threshold, it expanded outwards in a similar fashion to mode-coupling instability-induced melting, rapidly destroying the crystalline order of the whole complex plasma monolayer. The reported experimental observations are due to the fluid mode-coupling instability, which can pump energy into the particle monolayer at a rate surpassing the heat transport and damping rates in the energetic localized melted spot, resulting in its further growth. This behavior exhibits remarkable similarities with impulsive spot heating in ordinary reactive matter.

Interaction between contact behaviour and vibrational response for dry contact system

Abstract This work wants to provide insights on the coupling between contact behaviour (local scale) and vibrational response (global scale) which brings to different contact scenarios arising in dry frictional systems. A newer setup, named TriboWave, has been developed in order to reproduce and investigate the system response to frictional contact, under well-controlled boundary conditions. The experimental results highlighted how a simple frictional system can switch from stable friction-induced vibrations to unstable vibrations, i.e. either macroscopic stick–slip instabilities or mode coupling instabilities. The effect of the contact surface roughness on the reproduced frictional scenario has been investigated too.

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.

On the nonlinear dynamics of shift gearbox models

When the so-called eek effect emerges while shifting a vehicle shift gearbox, car drivers perceive audible noise and vibrations of drivetrain components. Some physical approaches have been provided in order to explain the effect as well as to search for countermeasures. In Jehle and Fidlin (ZAMM J Appl Math Mech 94(11):911–916 (2014), the interaction of sliding clutch disk and gears is addressed in a rigid body model. The clutch disk’s non-conservative follower forces in combination with geometric coupling in gears imply the action of non-symmetric restoring- and velocity-proportional forces. The desired motion of gearbox components can therefore undergo a mode-coupling flutter instability, out of which vibrations emerge with exponentially growing amplitudes. As the contacts in clutch and gears hold non-smooth transitions such as the possibility of sticking and opening, dynamic solutions are both limited and complex. In this contribution, first of all model details concerning the gear formulation are revised: rigid and viscoelastic normal contact are compared, which imply differences in the nature of the solution and method of stability analysis. Nevertheless the two approaches are shown to converge. Finally, the dynamics behind the loss of stability of the desired motion is investigated.

Influence of Heterogeneous Contact Stiffness and Heterogeneous Friction Coefficient on Frictional Squeal

Contact stiffness and friction coefficient are excitation sources and key influencing factors to frictional squeal with obvious inhomogeneous characteristic that is always neglected. In this paper, a multipoint contact flexible pin‐on‐disc system is established considering tangential stiffness. Then influence of contact stiffness and friction coefficient with heterogeneous distribution on frictional squeal is studied using the complex modal analysis. The research shows that contact stiffness and friction coefficient heterogeneities influence the likelihood of occurrence of the squeal, the frequency of the squeal, and the real part of the complex eigenvalue of the system. And when the contact stiffness and friction coefficient are close to the boundary of the region of mode‐coupling instability, flexible pin‐on‐disc system with homogeneous contact stiffness and friction coefficient cannot predict whether frictional squeal occurs or not. Besides, uncertain distribution of contact stiffness and friction coefficient can induce the uncertainty of brake squeal.

FE Squeal and Vibration Analysis with Pattern of Brake Disc Surface

In this paper, the relationship between the frequency split and the mode-coupling in the disc doublet mode, which is expressed according to the pattern of the surface of the disc, is utilized by using of 3 types(Chaos, Vent-hole, Normal). As the frequency split between the doublet mode disc that is expressed in the model through the interpretation is larger, and analogy through interpretation mode-coupling instability also lower. Vent-hole, which has a relatively large frequency split of disc doublet mode in 3 types(Chaos, Vent-hole, Normal) model, showed a large value of critical coefficient of friction in which mode-coupling instability is expressed. In addition, it was confirmed by analysis that the Vent-hole had a relatively large frequency split than the other models by analyzing the change in contact stiffness. It can be concluded that the larger the frequency split of the disc doublet mode, the lower the instability due to the mode-coupling.

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.