Theoretical Dispersion Relation Research Articles

Negative damping of terahertz plasmons in counter-streaming double-layer two-dimensional electron gases

Abstract The plasmon excitation in two-dimensional electron gases (2DEGs) is a significant way of achieving micro-nanoscale terahertz (THz) devices. Here, we establish a kinetic simulation model to study the THz plasmons amplification in a semiconductor double-quantum-well system with counter-streaming electron drift velocities. By comparing the simulation results with theoretical dispersion relations, we confirm two competing mechanisms of negative damping suitable for THz amplification: Cherenkov-type two-stream instability and a new non-Cherenkov mechanism called kinetic relaxation instability. The former is caused by the interlayer coupling of two slow plasmon modes and only exists when the drift velocities are much greater than the fermi velocities. The latter is a statistical effect caused by the momentum relaxation of electron-impurity scattering and predominates at lower drift velocities. We show that an approximate kinetic dispersion relation can accurately predict the wave growth rates of the two mechanisms. The results also indicate that the saturated plasmonic waves undergo strong nonlinearities such as wave distortion, frequency downshift, wave-packet formation, and spectrum broadening. The nonlinear evolution can be interpreted as the merging of bubble structures in the electron phase-space distribution. The present results not only reveal the potential mechanisms of the plasmonic instabilities in double-layer 2DEGs, but also provide a new guideline for the design of on-chip THz amplifiers.

Bandgap characteristics of a hybrid multi-resonator elastic metamaterial with negative stiffness mechanism and its application to mitigate seismic response of building structures

Seismic metamaterials have attracted extensive attention due to their unique ability to attenuate the transmission of elastic waves in their frequency bandgaps. However, generating a metamaterial with a low-frequency and wide bandgap remains challenging. Previous studies have shown that negative stiffness mechanisms can lower the frequency range of bandgaps while employing a multi-resonator technique can broaden the width of bandgaps. In this study, by combining these two techniques, a negative stiffness enhanced multi-resonator elastic metamaterial (NMEM) is first proposed. The feasibility of NMEM is validated by comparing the theoretical dispersion relation and the transmission spectra of a finite cell model. The results demonstrate that low-frequency and wide bandgaps can be realized by NMEM. To further widen the bandgap, a hybrid NMEM is proposed by connecting multiple types of cells in series. The proposed hybrid NMEM consists of two types of cells, one with a single resonator and another with two resonators, which merge individual bandgaps into a continuous and wider bandgap. The proposed hybrid NMEM is then adopted as a meta-basement for a case building to demonstrate its effectiveness in mitigating seismic responses. The results show that the seismic responses of the building with the hybrid meta-basement are considerably reduced than those of the building with the conventional basement. However, the hybrid meta-basement may lead to larger structural displacement response when the dominant frequency of ground motion is outside the designed bandgap.

Oblique streaming waves observed in multipactor-induced plasma discharge above a dielectric surface

In a recent discovery (Wen et al 2022 Phys. Rev. Lett. 129 045001), streaming waves were found in multipactor-induced plasma discharges. However, due to the limitations of a 1D simulation setup, these waves displayed only transverse dynamics. In this letter, an extended 2D particle-in-cell/Monte Carlo model is used to simulate multipactor-induced plasma discharge above a dielectric surface. The results reveal that the streaming waves are not solely transverse but oblique, featuring both transverse and longitudinal components of the wave vector. Furthermore, it is identified that the sheath-accelerated field-emission electrons, rather than the previously reported secondary emission electrons, predominantly cause the excitation of streaming waves. The simulated wave spectrum achieves an excellent agreement with the theoretical dispersion relation. The identification of oblique streaming waves provides new insights into multipactor physics and is anticipated to inspire novel mitigation strategies for multipactor-induced breakdown processes.

2D FDM Simulation of Seismic Waves and Tsunamis Based on Improved Coupling Equations Under Gravity

To understand the characteristics of seismic waves and tsunamis recorded simultaneously by the ocean-bottom observation networks, the coupling between the solid Earth and the ocean has to be modeled in the presence of gravity. However, previous coupled simulations adopted approximate equations that did not fully incorporate the effects of gravity. In this study, we derived correctly linearized governing equations under gravity and compared them with those of previous studies. Numerical experiments were performed for a two-dimensional P-SV wavefield, using the finite difference method (FDM). To validate the accuracy of the calculated tsunamis, we computed the theoretical tsunami dispersion relation using a propagator matrix and compared it with our results and those of previous studies. We found that our proposed method provided more accurate results than those of previous studies, particularly in the short-period band. We also investigated the applicability of the proposed method to distant tsunamis by examining the difference between calculated and theoretical tsunami phase velocities in the long-period band. The proposed formulation provides accurate results that properly incorporate gravity into the simultaneous simulation of seismic waves and tsunamis.

Easy method to establish the dispersion relation of capillary waves on water jets

A simple, intuitive, and low-cost setup for generating and measuring capillary waves is presented enabling a precise determination of the dispersion relation for a cylindrical water jet. By setting the phase velocity and measuring the wavelength of capillary waves directly, this method provides an intuitive way for students to understand the dispersion relation of a cylindrical water jet. The setup produced measurements of wavelength versus phase velocity over a broader range of values than earlier work. The resulting data are generally consistent with earlier results but show an error of up to 15% at both the higher and lower end of the measured range of wavelengths compared to the theoretical dispersion relation of cylindrical water jets. For the shorter wavelengths, the deviation is in the opposite direction from that of earlier work.

Dispersion analysis of numerical schemes using 2D compressible linearized Navier–Stokes equation for direct numerical simulation

The dispersion analysis of numerical schemes for finite difference computations based on 2D compressible linearized Navier–Stokes equation (LNSE) is presented here. The analysis presents a more holistic view of the applicability of the schemes while solving compressible NSE, rather than analyzing model 1D or 2D convection or convection–diffusion equations. A theoretical dispersion analysis of model 2D−LNSE is performed first which categorizes it into vortical, entropic and two acoustic modes. The variation of the theoretical dispersion relation for each of the modes with wavenumber, Mach number and Reynolds number is analyzed. It is noted that the entropic mode is the most diffusive among all the modes. Two acoustic modes are less diffusive than the vortical mode up to a certain absolute wavenumber Kb depending upon the Mach number and Reynolds number. It is also shown that while vortical and entropic modes are non-dispersive in nature, the two acoustic modes are dispersive only up to K=Kb. Next, numerical dispersion and diffusion corresponding to each of the modes are analyzed for second order central difference (CD2) and sixth order central compact difference scheme proposed in Lele (J. Comput. Phys., Vol-103(1), 1992) for discretization of convective and diffusive derivatives using fourth-order Runge–Kutta (RK4) time integration method. Results show the existence of numerical unstable zone and regions where spurious upstream propagating waves are noted for each of the modes in the spectral plane. From these and the relative size of the dispersion relation preserving zones for the modes, applicability of the numerical schemes can be assessed. Analysis of the variation of the numerical unstable zone with Mach number, orientation of the mean flow and the unit CFL number Nc=Δt/Δx for each of the modes are presented. It is noted that entropic mode displays the lowest critical CFL number of all the four modes. Lastly, linearized and nonlinear numerical simulations for the convection of acoustic and vortical pulse with varying spectral content are presented. The linearized simulations are also compared with corresponding exact solutions. Obtained results indicate a direct correspondence of the stability analysis performed based on 2D−LNSE even for nonlinear simulations which result in additional intra modal energy transfer and interactions.

Numerical investigation of cavitating tip vortex dynamics and how they influence the acoustic characteristics

The surface waves traveling on tip vortex cavities are one of the main contributors to underwater radiated noise (URN). However, these waves cannot be easily predicted, especially the mode associated with the cavity volume variations, which hinders research into the hydroacoustic mechanism. This paper presents a method for extracting the surface waves from numerical predictions, which successfully captured all the theoretical dispersion relations of these surface waves. This method was then used to analyze the tip vortex cavitation (TVC) dynamics and how they influence the URN with an acoustic analogy. Low- and medium-frequency URN are shown to be mainly emitted by the surface waves related to the cavity volume variations. The significant tones at the dominant frequency and the broadband hump center frequency are further studied with the main noise sources found to be the cavity radial fluctuations and the TVC resonance.

Multispacecraft Analysis of the Properties of Magnetohydrodynamic Fluctuations in Sub-Alfvénic Solar Wind Turbulence at 1 au

We present observations of three-dimensional magnetic power spectra in wavevector space to investigate the anisotropy and scalings of sub-Alfvénic solar wind turbulence at magnetohydrodynamic (MHD) scale using the Magnetospheric Multiscale spacecraft. The magnetic power distributions are organized in a new coordinate determined by wavevectors () and background magnetic field () in Fourier space. This study utilizes two approaches to determine wavevectors: the singular value decomposition method and multispacecraft timing analysis. The combination of the two methods allows an examination of the properties of magnetic field fluctuations in terms of mode compositions without any spatiotemporal hypothesis. Observations show that fluctuations (δ B ⊥1) in the direction perpendicular to and prominently cascade perpendicular to , and such anisotropy increases with wavenumbers. The reduced power spectra of δ B ⊥1 follow Goldreich–Sridhar scalings: and . In contrast, fluctuations within the plane show isotropic behaviors: perpendicular power distributions are approximately the same as parallel distributions. The reduced power spectra of fluctuations within the plane follow the scalings and . Comparing frequency–wavevector spectra with theoretical dispersion relations of MHD modes, we find that δ B ⊥1 are probably associated with Alfvén modes. On the other hand, magnetic field fluctuations within the plane more likely originate from fast modes based on their isotropic behaviors. The observations of anisotropy and scalings of different magnetic field components are consistent with the predictions of current compressible MHD theory. Moreover, for the Alfvénic component, the ratio of cascading time to the wave period is found to be a factor of a few, consistent with critical balance in the strong turbulence regime. These results are valuable for further studies of energy compositions of plasma turbulence and their effects on energetic particle transport.

Using Noncontact Measurement of Water Surface Dynamics to Estimate River Discharge

AbstractEstimating river discharge requires simultaneous measurement of velocity and flow depth. While surface velocities are relatively easy to measure using noncontact techniques, depth measurement usually requires physically intrusive instrumentation. This limits our capability to remotely monitor discharge in natural rivers subject to bed level variations. This work tests the potential to estimate the surface velocity, the water depth, the depth average velocity, and then discharge of a river using only a sequence of images of the dynamic water surface. The method is based on a comparison between the spatiotemporal Fourier spectra of the pixel intensities of these images and the theoretical dispersion relations of turbulence‐generated surface fluctuations and gravity‐capillary waves. The method is validated through the analysis of water surface videos obtained with fixed cameras from two river sections equipped with conventional discharge gauging. The applicability of the approach is demonstrated and the measurement uncertainties are quantified. The method is affected by two main sources of uncertainty: one derives from the estimation of the velocity index and the other from the obtainable resolution of the Fourier analysis. This resolution strongly controls the observation of depth and/or velocity variations in space and in time. The technique has advantages over current approaches: it has clear physical foundations; the equipment is low cost and is highly mobile; it does not need artificial tracers or physical equipment to measure depth; and it can directly provide estimates of the key flow parameters just from time series of images of the water surface.

Observational Evidence of Generation and Propagation of Barotropic Rossby Waves Induced by Tropical Instability Waves in the Northeastern Pacific

AbstractTropical instability waves (TIWs) in the equatorial eastern Pacific exhibit 25–40‐day westward‐propagating fluctuations with seasonal and interannual variations, which are stronger during July–December and La Niña periods. There is evidence that the instability of the equatorial currents that generates TIWs also induce radiation of barotropic Rossby waves (BTRWTIW). Long‐term near‐bottom current measurements at 10.5°N and 131.3°W during 2004–2013 revealed a spectral peak at 25–40 days, where significant coherences were found with satellite‐measured sea surface height with maxima approximately 5°N. Simulated deep currents from a data‐assimilated ocean model concur with the observed near‐bottom currents, and both currents vary seasonally and interannually, consistent with the typical characteristics of TIW. Further analyses using 25–40‐day bandpass‐filtered barotropic velocity data from the model revealed that they reasonably satisfied the theoretical dispersion relation of BTRWTIW. The in situ and model analysis support the conclusion that BTRWTIW propagate north of 10°N in the northeastern Pacific.

An E and B gyrokinetic simulation model for kinetic Alfvén waves in tokamak plasmas

The gyrokinetic particle simulation is a powerful tool for studies of transport, nonlinear phenomenon, and energetic particle physics in tokamak plasmas. While most gyrokinetic simulations make use of the scalar and vector potentials, a new model (GK-E&B) has been developed by using the E and B field in a general form and has been implemented in simulating kinetic Alfvén waves in uniform plasma [Chen et al., Sci. China: Phys., Mech. Astron. 64, 245211 (2021)]. In our work, the Chen et al. GK-E&B model has been expressed, in general, tokamak geometry using the local orthogonal coordinates and general tokamak coordinates. Its reduction for uniform plasma is verified, and the numerical results show good agreement with the original work. The theoretical dispersion relation and numerical results in the local model in screw pinch geometry are also in excellent agreement. Numerical results show excellent performance in a realistic parameter regime of burning plasmas with high values of β/(Mek⊥2ρi2), which is a challenge for traditional methods due to the “cancellation” problem. As one application, the GK-E&B model is implemented with kinetic electrons in the local single flux surface limit. With the matched International Tokamak Physics Activity-Toroidicity-induced Alfvén Eigenmodes parameters adopted, numerical results show the capability of the GK-E&B in treating the parallel electron Landau damping for realistic tokamak plasma parameters. As another application, the global GK-E&B model has been implemented with the dominant electron contribution in the cold electron limit. Its capability in simulating the finite E|| due to the finite electron mass is demonstrated.

Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling

Context. Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. Aims. Rossby waves create small-amplitude, very-low frequency motions, on the order of the rotation rate and lower, which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well. Methods. We analyze 4 and 8 years of Helioseismic and Magnetic Imager (HMI) data and consider coupling between different-degree acoustic modes (of separations 1 and 3 in the harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes. Results. We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes, where the azimuthal order is the same as the harmonic degree, s = |t|. Our results are consistent with prior measurements of Rossby modes with azimuthal orders over the range t = 4 to 16 with maximum power occurring at mode t = 8. The amplitudes of these modes vary from 1 to 2 m s−1. We place an upper bound of 0.2 m s−1 on the sectoral t = 2 mode, which we do not detect in our measurements. Conclusions. This effort adds credence to the mode-coupling methodology in helioseismology.

Direct evidence of gradient drift instability being the origin of a rotating spoke in a crossed field plasma

A plasma rotating spoke in a crossed field discharge is studied using 2D radial-azimuthal fully kinetic particle-in-cell Monte Carlo collision simulations. The kinetic model reveals the whole perturbation spectrum of the gradient drift instability in the linear stage: Simon–Hoh, lower hybrid, and ion sound modes, providing direct evidence of the spoke of gradient drift instability nature. The two-fluid dispersion relation of gradient drift instability was utilized to analyze the linear development of instabilities in the simulations. The charge separation effect was incorporated in the fluid linear theory and a super-resolution signal processing method (multiple signal classification) was applied to obtain the numerical frequency spectrum. The simulated spectrum and growth rate show excellent agreement with the theoretical dispersion relation (real frequency and imaginary frequency) in the investigated cases. The most linearly unstable mode was found to be the lower hybrid instability and the mode transition into the m = 1 macroscopic rotating structure after saturation of the linear phase is accompanied by an inverse energy cascade. In the nonlinear stage, pronounced spoke phenomena can occur when the heating of E θ × B electron flow channeled in the spoke front passage suffices to provide enhanced ionization.

Characteristics of parametric spin waves in rectangular magnonic blocks

The characteristics of parametric spin-wave pumping are investigated in three rectangular permalloy blocks with in-plane aspect ratios of 12, 6, and 4. Micro-Brillouin light scattering (BLS) spectroscopy is utilized to detect the intrinsic properties of excited spin waves under various excitation conditions of an external magnetic field and microwave power. Based on the theoretical dispersion relation and BLS intensity and its spatial profile, the parametric spin wave with a frequency of is found to be excited in fundamental mode in a block of largest aspect ratio while the other block have higher-order or edge-localized modes along the width direction. The data shows that the nature of spin waves is quite sensitive on the conditions of sample geometry, applied field and microwave power. Thus, with the appropriate combination of the three parameters, it would be possible to control the nature of spin wave in each block simultaneously, which increase the blocks’ potential in magnonic applications, such as spin-logic and interferometer.

Seismic inversion of shale reservoir properties using microseismic-induced guided waves recorded by distributed acoustic sensing

Shale formation properties are crucial for the hydrocarbon production performance of unconventional reservoirs. Microseismic-induced guided waves, which propagate within the low-velocity shale formation, are an ideal candidate for accurate estimation of shale thickness, velocity, and anisotropy. A distributed acoustic sensing fiber deployed along the horizontal section of a monitor well can provide a high-resolution recording of guided waves excited by microseismic events during hydraulic fracturing operations. These guided waves manifest a highly dispersive behavior that allows for seismic inversion of the shale formation properties. An adaptation of the propagator matrix method is presented to estimate guided-wave dispersion curves, and its accuracy is validated by comparison to 3D elastic wavefield simulations. The propagator matrix formulation holds for cases of vertical transverse isotropy (VTI) as well. A sensitivity analysis of the theoretical dispersion relations of the guided waves indicates that they are mostly influenced by the thickness and S-wave velocity of the low-velocity shale reservoir. The VTI parameters of the formation are also shown to have an impact on the dispersion relations. These physical insights provide the foundation for a dispersion-based model inversion for a 1D depth-dependent structure of the reservoir and its surroundings. The inversion procedure is validated in a synthetic case and applied to the field records collected in an Eagle Ford hydraulic fracturing project. The inverted structure agrees well with a sonic log acquired several hundred meters away from the monitor well. Therefore, seismic inversion using guided-wave dispersion indicates promise to become a novel and cost-effective strategy for in situ estimation of reservoir structure and properties, which complements microseismic-based interpretation and production-related information.

An enhanced dual-resonator metamaterial beam for low-frequency vibration suppression

Structural vibrations seriously affect the working performance of and even cause fatal hazards in host structures. The use of a metamaterial is a novel way to suppress structural vibrations across a wide frequency band. This paper presents an enhanced dual-resonator metamaterial beam (DRMB), where the free end of a traditional series dual-resonator is periodically connected to the rigid body with a spring. The mass and frequency response of the enhanced dual-resonator is derived. The theoretical dispersion relation and band structure are obtained using a transfer matrix method. The effects of the number of cells, mass ratio, and spring stiffness ratio on the bandgap and transmissibility performance of the proposed DRMB are analyzed and discussed. An experiment is carried out to verify the theoretical model. The results show that with increasing number of cells, mass ratio, and spring stiffness ratio of the DRMB, the bandgap changes significantly, thereby enhancing the vibration suppression performance in a low-frequency range. The dual-resonator with three springs suppresses beam vibration.

Intraseasonal Abyssal Current Variability of Bottom-Trapped Topographic Rossby Waves in the Southwestern East Sea (Japan Sea)

Examining the deep-water exchange through the Ulleung Interplain Gap (UIG) between the Ulleung Basin (UB) and the Japan Basin in the East Sea (Sea of Japan) is critical for understanding the vigorous circulation and material cycles of the sea. The exchange features an asymmetric flow structure across the UIG: a broad and weak inflow (into the UB) in the western UIG, and a narrow and strong outflow (out of the UB) in the eastern UIG, with the latter closely associated with the Dokdo Abyssal Current (DAC), a long-term mean, strong abyssal current near Dokdo. In this study, the linear theory of bottom-trapped topographic Rossby waves (TRWs) is applied to explain the previously unexplored longer intraseasonal band (30–50 days) DAC variability by analyzing multi-year moored current-meter observations and HYCOM reanalysis data, as they are significantly correlated in the period band (though not at the shorter intraseasonal band of 5–25 day explored previously). Bottom-intensified DAC variability is characterized by TRW parameters with a vertical trapping scale of 1100–2100 m, a horizontal wavelength of 49–111 km, a propagating speed of 1.3–3.0 km day-1, and a propagating direction aligned with isobaths within a 2°–23° range (shallower water on the right). The departure angle between the energy-propagating direction of the waves and the isobath direction is estimated from the spectra of the along- and cross-slope abyssal currents and from the TRW theoretical dispersion relation for a given buoyancy frequency and bottom slope. These values are then compared to examine the significance of the bottom-trapped TRW dynamics, yielding a small (< 16°) difference. The results support the significance of bottom-trapped TRWs on the longer intraseasonal variability of abyssal currents near the steeply sloped eastern side of the UIG, and an asymmetric abyssal flow structure across the UIG in the southwestern East Sea.

Strongly coupled Yukawa trilayer liquid: Structure and dynamics.

The equilibrium structure and the dispersion relations of collective excitations in trilayer Yukawa systems in the strongly coupled liquid regime are examined. The equilibrium correlations reveal a variety of structures in the liquid phase, reminiscent of the corresponding structures in the solid phase. At small layer separation substitutional disorder becomes the governing feature. Theoretical dispersion relations are obtained by applying the quasilocalized charge approximation (QLCA) formalism, while numerical data are generated by microcanonical molecular dynamics simulations. The dispersions and polarizations of the collective excitations obtained through both of these methods are compared and discussed in detail. We find that the QLCA method is, in general, very satisfactory, but that there are phenomena not covered by the QLCA. In particular, by analyzing the dynamical longitudinal and transverse current fluctuation spectra we discover the existence of a structure not related to the collective mode spectra. This also provides insight into the long-standing problem of the gap frequency discrepancy, observed in strongly coupled layered systems in earlier studies.

Deep Eddy Kinetic Energy in the Tropical Pacific From Lagrangian Floats

AbstractAt the ocean surface, satellite observations have shown evidence of a large spectrum of waves at low latitudes. However, very little is known about the existence and properties of the deep variability. Most of the subsurface observations rely on localized measurements, which do not allow for a global estimation of this variability. In this study, we use velocity estimates, provided by Argo float drifts at 1,000 m, to analyze the spatial and temporal distribution of the deep eddy kinetic energy (EKE) and its spectral signature with an unprecedented time and space coverage. In the tropical Pacific, high EKE is found along the equator, at the western boundary and poleward of 7°N. EKE meridional distribution is also found to vary at the scale of the meridionally alternating mean zonal jets: it is higher inside eastward currents. We develop an original statistical scale analysis to determine the temporal and spatial scale dependence of this deep EKE footprint. We show the presence of periodic features whose characteristics are compatible with theoretical equatorial waves dispersion relations. Annual and semiannual Rossby waves are observed at the equator, as well as ∼30‐day Yanai waves, consistent with surface tropical instability waves. The location and intensification of these waves match the downward energy propagation predicted by ray tracing linear theory. Short‐scale variability (with ∼70‐day periods and 500‐km wavelength) has also been detected poleward of 7°N. The generation mechanisms of this variability are discussed, as well as its potential importance for the mean circulation.

A semi-active metamaterial beam with electromagnetic quasi-zero-stiffness resonators for ultralow-frequency band gap tuning

Introducing a negative-stiffness mechanism (NSM) into a traditional linear resonator to form a high-static-low-dynamic-stiffness (HSLDS) resonator is an ideal way to create a low-frequency band gap. However, with the decrease in frequencies of the band gap, the band width narrows, which could hinder the application of the metamaterials for attenuating ultralow-frequency elastic waves. In this paper, a regulatory mechanism (RM) constituted by an electrically charged coil and a magnet ring is introduced into an HSLDS resonator to devise a semi-active quasi-zero-stiffness (QZS) resonator. With these semi-active resonators attached onto a beam periodically, a semi-active metamaterial beam (meta-beam) is realized. The expressions of both the restoring force and the stiffness of the semi-active resonator are derived firstly, and then the theoretical dispersion relation and the band structure are obtained by the transfer matrix method. Finally, by establishing and then numerically solving the equation of motion of the semi-active meta-beam, the wave transmissibility is acquired and utilized to validate the theoretically predicted band structure. The analytical and numerical results show that the band gap can be effectively tuned by the RM, which enables excellent wave manipulation in an ultralow and wide frequency range.