Transverse mode-coupling instability with longitudinal impedance

Transverse mode-coupling instability(TMCI)is a dangerous transverse single-bunch instability that can lead to severe par-ticle loss.The mechanism of TMCI can be explained by the coupling of transverse coherent oscillation modes owing to the transverse short-range wakefield(i.e.,the transverse broadband impedance).Recent studies on future circular colliders,e.g.,FCC-ee,showed that the threshold of TMCI decreased significantly when both longitudinal and transverse impedances were included.We performed computations for the circular electron-positron collider(CEPC)and observed a similar phenom-enon.Systematic studies on the influence of longitudinal impedance on the TMCI threshold were conducted.We concluded that the imaginary part of the longitudinal impedance,which caused a reduction in the incoherent synchrotron tune,was the primary reason for the reduction in the TMCI threshold.Additionally,the real part of the longitudinal impedance assists in increasing the TMCI threshold.

Novel mode-coupling vibrations of AlN thin film bulk acoustic resonator operating with thickness-extensional mode

The dispersion curves of bulk waves propagating in both AlN and ZnO film bulk acoustic resonators(FBARs)are presented to illustrate the mode flip of the thickness-extensional(TE)and 2nd thickness-shear(TSh2)modes.The frequency spectrum quantitative prediction(FSQP)method is used to solve the frequency spectra for predicting the coupling strength among the eigen-modes in AlN and ZnO FBARs.The results elaborate that the flip of the TE and TSh2 branches results in novel self-coupling vibration between the small-wavenumber TE and large-wavenumber TE modes,which has never been observed in the ZnO FBAR.Besides,the mode flip leads to the change in the relative positions of the frequency spectral curves about the TE cut-off frequency.The obtained frequency spectra can be used to predict the mode-coupling behaviors of the vibration modes in the AlN FBAR.The conclusions drawn from the results can help to distinguish the desirable operation modes of the AlN FBAR with very weak coupling strength from all vibration modes.

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa- tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site model with Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode- coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.

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

A longitudinal accumulation scheme based on a triple-frequency RF system,in which the static radio frequency(RF)bucket is lengthened to be compatible with the realizable raise time of a fast pulse kicker,is proposed in this paper.With this technique,the bunch from a booster can be captured by the longitudinal acceptance without any disturbance to the stored bunch,which remains at the center.This composite RF system consists of three different frequencies,which can be regarded as the conventional bunch lengthening RF system(usually containing fundamental and third harmonic cavities)extended by an additional second harmonic RF cavity.In this paper,we discuss the RF jitter and the transverse mode-coupling instability(TMCI)when using this special RF system.Considering several different bunch profiles,we discuss the beam stability with regard to the RF jitter.However,for the TMCI we assume an ideal bunch profile,where the bunch is exactly lengthened to the maximum extent.While macroparticle simulation is the main method used to study the impact of the RF jitter,numerical analysis and simulations for the TMCI while using a triple-frequency RF system are also presented in this paper.An approximation formula,based on the existing model,is also derived to estimate the impact of the TMCI on the single bunch current threshold when using harmonic cavities.

Mode-Coupling Theory for Glass Transition of Active-Passive Binary Mixture

Collective behaviours of active particle systems have gained great research attentions in re- cent years. Here we present a mode-coupling theory （MCT） framework to study the glass transition of a mixture system of active and passive Brownian particles. The starting point is an eff）ctive Smoluchowski equation, which governs the dynamics of the probability dis- tribution function in the position phase space. With the assumption of the existence of a nonequilibrium steady state, we are able to obtain dynamic equations for the intermediate scattering functions （ISFs）, wherein an irreducible memory function is introduced which in turn can be written as functions of the ISFs based on standard mode-coupling approximations. The effect of particle activity is included through an effective difIusion coefficient which can be obtained via short time simulations. By calculating the long-time limit of the ISF, the Debye-Waller （DW） factor, one can determine the critical packing fraction ηc of glass transition. We find that for active-passive （AP） mixtures with the same particle sizes, ηc increases as the partial fraction of active particle xA increases, which is in agreement with previous simulation works. For system with different active/passive particle sizes, we find an interesting reentrance behaviour of glass transition, i.e., ηc shows a non-monotonic dependence on xa. In addition, such a reentrance behaviour would disappear if the particle activity is large enough. Our results thus provide a useful theoretical scheme to study glass transition behaviour of active-passive mixture systems in a promising way.

Mode-Coupling Analysis of Parametric Decay Instability in Magnetized Plasmas

In this paper, derived from Maxwell and fluid equations of plasmas, unified nonlinear wave equations are used to describe the parametric decay instability （PDI） in magnetized plasmas, and in view of mode-coupling, we can obtain all the possible PDI channels. By solving the nonlinear equations with a mode-coupling method, we obtain the growth rate of the PDI, of which all of the three waves are ordinary mode （O-mode） or extraordinary mode （X-mode） wave. Under the dipole approximation, an explicit formula of the growth rate of the X-mode and the condition of the equilibrium density scale are obtained. According to the existence conditions of three X-mode waves, this kind of instability might exist in ECRH with the second harmonic X-mode wave.

Mode dynamics of Bose–Einstein condensates in a single-well potential

We investigate dynamics of Bose–Einstein condensates(BECs) in a single-well potential using the mode-coupling method. Symmetry is shown to play a key role in the coupling between modes. A proper mode-coupling theory of the dynamics of BECs in a single-well potential should include at least four modes. In this context, the ideal BEC system can be decomposed into two independent subsystems when the coupling is caused by external potential perturbation and is linear. The mode dynamics of non-ideal BECs with interaction shows rich behavior. The combination of nonlinear coupling and initial condition leads to the different regimes of mode dynamics, from regularity to non-regularity, which also indicates a change of the dependence of coupling on the symmetry of modes.

Influences of harmonic cavities on single-bunch instabilities in electron storage rings

Harmonic cavities(HCs)are widely used in electron storage rings,mainly to increase the Touschek lifetime by lengthening bunches.HCs have become critical components of almost all fourth-generation synchrotron light sources.In addition to the benefits of increasing the Touschek lifetime,they also affect the collective beam instabilities in electron storage rings.However,the influ-ence of HC settings on collective beam instabilities is still not well understood.HCs are typically designed to operate under so-called ideal lengthening conditions,which do not necessarily optimize the suppression of collective beam instabilities.We therefore extended earlier studies of col-lective beam instabilities to consider more general HC settings.We present preliminary studies and analyses of the influences of different HC settings on microwave and transverse mode-coupling instabilities.

Effect of a Submerged Porous Plate on the Hydroelastic Response of a Very Large Floating Structure

Scattering of oblique flexural-gravity waves by a submerged porous plate in a finite water depth is investigated under the assumptions of linearized surface waves and small-amplitude structural response. The study is carried out using eigenfunction expansions and the corresponding orthogonal mode-coupling relations associated with flexural-gravity waves in uniform water depth. The characteristics of the roots of the complex dispersion relation are examined using the principle of counting argument and contour plot. Characteristics of the flexural-gravity waves are studied by assuming both the floating elastic plate and the submerged porous plate are infinitely extended in horizontal directions. The effectiveness of the submerged porous structure on the reflection, transmission, and dissipation coefficients is analyzed for various wave and structural parameters.

Chatter stability and precision during high-speed ultrasonic vibration cutting of a thin-walled titanium cylinder

Titanium alloys are widely used in the aviation and aerospace industries due to their unique mechanical and physical properties.Specifically,thin-walled titanium(Ti)cylinders have received increasing attention for their applications as rocket engine casings,aircraft landing gear,and aero-engine hollow shaft due to their observed improvement in the thrust-to-weight ratio.However,the conventional cutting(CC)process is not appropriate for thin-walled Ti cylinders due to its low thermal conductivity,high strength,and low stiffness.Instead,high-speed ultrasonic vibration cutting(HUVC)assisted processing has recently proved highly effective for Ti-alloy machining.In this study,HUVC technology is employed to perform external turning of a thinwalled Ti cylinder,which represents a new application of HUVC.First,the kinematics,tool path,and dynamic cutting thickness of HUVC are evaluated.Second,the phenomenon of mode-coupling chatter is analyzed to determine the effects and mechanism of HUVC by establishing a critical cutting thickness model.HUVC can increase the critical cutting thickness and effectively reduce the average cutting force,thus reducing the energy intake of the system.Finally,comparison experiments are conducted between HUVC and CC processes.The results indicate that the diameter error rate is 10%or less for HUVC and 51%for the CC method due to a 40%reduction in the cutting force.In addition,higher machining precision and better surface roughness are achieved during thin-walled Ti cylinder manufacturing using HUVC.