Dispersion of Dust Acoustic Modes and Perturbations of Plasma Flux Balance

Previous considerations of dust acoustic waves is demonstrated to be inconsistent ‐ the required equilibrium state for perturbations was not defined since balance of plasma fluxes was neglecting. The self‐consistent treatment shows that plasma flux perturbations are accompanying any collective waves propagating in dusty plasmas and can play an important role in wave dispersion, wave damping and can create instabilities. This is illustrated by the derivation of dispersion relation for dust acoustic modes taking into account the plasma flux balances and plasma flux perturbations by waves. The result of this approach shows that the dust acoustic waves with linear dependence of wave frequency on the wave number exist only in restricted range of the wave numbers. Only for wave numbers larger than some critical wave number for low frequency modes the frequency can be have approximately a linear dependence on wave number and can be called as dust acoustic wave but the phase velocity of these waves is different from that which can be obtained neglecting the flux balance and depends on grain charge variations which are determined by the balance of fluxes. The presence of plasma fluxes previously neglected is the main typical feature of dusty plasmas. The dispersion relation in the range of small wave numbers is found to be mainly determined by the change of the plasma fluxes and is quite different from that of dust acoustic type, namely it is found to have the same form as the well known dispersion relation for the gravitational instability. This result proves in general way the existence of the collective grain attractions of negatively charged grains for for large distances between them and for any source of ionization. The attraction of grains found from dispersion relation of the dust acoustic branch coincides with that found previously for pair grain interactions using some models for the ionization source. For the existing experiments the effective Jeans length for such attraction is estimated to be about 8 – 10 times larger than the ion Debye length and the effective gravitational constant for the grain attraction is estimated to be several orders of magnitude larger than the usual gravitational constant. The grain attraction at large inter‐grain distances described by the gravitationlike grain instability is considered as the simplest explanation for observed dust cloud clustering, formation of dust structures including the plasma crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrostatic instability in magnetically confined inhomogeneous plasma driven by nonlinear force

A theoretical investigation on amplification of electrostatic ion acoustic wave in magnetically confined plasma has been presented in this paper. This investigation considers nonlinear wave–particle interaction process, called plasma maser effect, in presence of drift wave turbulence supported by magnetically confined inhomogeneous plasma. The role of associated nonlinear dissipative force in this effect in a confined plasma has been analyzed. The nonlinear force, which arises as a result of resonant interaction between electrons and modulated fields, is shown to drive the instability. Using the ion fluid equation and the ion equation of continuity, the nonlinear dispersion relation of a test ion acoustic wave has been derived, and the growth rate of ion acoustic wave in presence of low frequency drift wave turbulence has been estimated using Helimak data.     

受激布里渊散射的非线性增强和饱和

针对典型激光聚变等离子体参数条件,利用弗拉索夫程序研究非均匀流等离子体中受激布里渊散射的非线性行为。在动理学效应占主导的参数区域,观察到受激布里渊散射激发的离子声波由于非线性动理学频移和非均匀流空间失谐相互补偿引起的离子声波自共振增长,这会导致受激布里渊水平量级的增强;提出用光束时间去相干抑制这种绝对增长。在流体非线性占主导的参数区域,观察到由于离子声波谐波导致的孤立波产生、离子加热以及受激布里渊散射饱和现象。     

考虑频散效应的一维非线性地震波数值模拟

非线性理论是解决地学问题的重要手段, 充分认识非线性波动特征有助于解释实际观测资料中的一些特殊地震现象. 本文基于Hokstad改造的非线性本构方程, 利用交错网格有限差分法实现了固体介质中一维非线性地震波数值模拟; 采用通量校正传输方法消除非线性数值模拟中波形振荡, 提高模拟精度. 通过与解析解的对比验证了模拟结果的正确性. 研究结果显示了非线性系数对地震波的传播有重要影响, 并且当取适当的非线性和频散系数时, 地震波表现出孤立波的传播特性. 最后分析了不同的非线性地震波在固体介质中的传播演化特征.     

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研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

声单向操控研究进展

电子二极管的发明标志着现代电子学的诞生, 在整个人类社会中引起了科技的深刻变革. 声波是一种具有非常悠久的研究历史的经典波, 却始终被认为仅具有对称的传播形式. 若能制造出可像电子二极管控制电流般实现声波单向导通的声学器件, 显然将对整个声学研究领域产生重大影响, 具有重要的科学意义及应用价值. 第一个基于非线性媒质与声子晶体的声二极管利用非线性突破声学互易原理的局限, 首次实现了将声能流限制在单一方向上的声整流效应. 针对非线性系统转换效率低下的固有缺陷, 在线性体系内围绕声单向传播这个重要科学问题开展了一系列理论和实验研究, 设计与制备了多种具有特殊结构和性能的线性声学单向结构, 在器件的效率、带宽及尺寸方面产生了突破. 在声二极管研究的基础上, 第一个可以像电子三极管操控电流般对声流进行操控与放大的声三极管理论模型也被提出. 本文介绍了声单向传播这一新兴且富有蓬勃生机的研究领域中的主要进展.     

强耦合尘埃等离子体中正电扰动下的尘埃声激波

研究了强耦合尘埃等离子体的尘埃声波的线性色散关系和尘埃声孤波的非线性传播。考虑一个包含电子、离子、正电扰动尘埃颗粒的完全电离的三成分模型等离子体。假定其电子、离子数密度服从玻尔兹曼分布,而大质量的尘埃成分用一组经典流体方程描述,对系统方程进行线性化,得到了尘埃声波的线性色散关系,发现离子的集中参数对色散关系的影响很大。用约化摄动法对系统方程进行展开,得到了描述小振幅孤波的伯格斯方程。基于伯格斯方程研究了尘埃声孤波的基本特性,发现尘埃颗粒的强耦合效应对尘埃声孤波有很大的修正作用。该研究结果有助于理解尘埃空间等离子体中局域波的一些特性。     

Frequency band structure and absorption predictions for multi-periodic acoustic composites

This article introduces a computational framework for studying frequency band structure and absorption behavior in multi-periodic acoustic composite structures. Herein, multi-periodic acoustic composite structures are defined as periodically-layered acoustic media wherein each layer is composed of periodically-repeated fluid unit cells, especially those arising from the study of porous materials. Hence, at least two periodic scales (microscopic and mesoscopic, respectively) comprise the macroscopic acoustic composite media. Exploitation of the multi-periodicity allows for efficient generation of dispersion and absorption curves via the conventional multi-scale asymptotic method (for homogenizing the mesoscale) coupled to the acoustic transfer matrix methods (for the macroscale). The combined computational framework results in a single analysis procedure for evaluating complex dispersion relationships and acoustic absorption. The dispersion curves can be used to reveal frequency stop bands wherein the wave vector is highly imaginary—i.e., plane waves experience rapid attenuation. They can also be used to reinterpret classical absorption curves. The framework is applied to four multi-periodic acoustic composite structures in order to demonstrate the framework's utility and to reveal novel properties, particularly those which can be influenced by design of the mesoscopic unit cell.     

一种减小尺寸的声彩虹捕获效应结构*

该文提出了一种减小尺寸的彩虹捕获效应结构,在铁板上刻上深度相同的空气凹槽阵列并加入周期性缝板单元,通过调节缝宽得到不同的等效折射率。该文对1000 Hz～2000 Hz的声波进行仿真实验,仿真结果表明不同频率的声波被局域在不同的位置,即实现了彩虹捕获效应。由于局域处声波群速度很小,局域处声场能量得到很大的提升。相对于传统的深度渐变的空气凹槽结构,我们的结构尺寸更小,可调性更强,更容易实现对低频声波的捕获效应。该结构具有能量加强和声波空间分离的效应,相信在声吸收、声波识别等领域有着潜在的应用前景。     

Dust acoustic waves in collisional uniform dense magnetoplasma

In order to study the characteristics of dust acoustic waves in a uniform dense dusty magnetoplasma system, a nonlinear dynamical equation is deduced using the quantum hydrodynamic model to account for dust–neutral collisions. The linear dispersion relation indicates that the scale lengths of the system are revised by the quantum parameter, and that the wave motion decays gradually leading the system to a stable state eventually. The variations of the dispersion frequency with the dust concentration, collision frequency, and magnetic field strength are discussed. For the coherent nonlinear dust acoustic waves, new analytic solutions are obtained, and it is found that big shock waves and wide explosive waves may be easily produced in the background of high dusty density, strong magnetic field, and weak collision. The relevance of the obtained results is referred to dense dusty astrophysical circumstances.     

Determination of boundaries of unsteady oscillatory zone in asymptotic solutions of non-integrable dispersive wave equations

We propose a simple general method for analytic determination of the boundaries of the expanding nonlinear oscillation zone occurring in the decay of a step problem for non-integrable dispersive wave equations. A remarkable feature of the method is that it essentially uses only the dispersionless limit and the linear dispersion relation of the original nonlinear dispersive wave system. A concrete example pertaining to collisionless plasma dynamics is considered and complete agreement with the results of earlier numerical simulations is demonstrated.     

The use of a hybrid model to compute the nonlinear acoustic performance of silencers for the finite amplitude acoustic wave

In the present study, a hybrid method is proposed for predicting the acoustic performance of a silencer for a nonlinear wave. This method is developed by combining two models: (i) a frequency-domain model for the computation of sound attenuation due to a silencer in a linear regime and (ii) a wavenumber space model for the prediction of the nonlinear time-evolution of finite amplitudes of the acoustic wave in a uniform duct of the same length as the silencer. The present method is proposed under the observation that the physical process of the nonlinear sound attenuation phenomenon of a silencer may be decoupled into two distinct mechanisms: (a) a linear acoustic energy loss that owes to the mismatch in the acoustic impedance between reactive elements and/or the sound absorption of acoustic liners in a silencer; (b) a nonlinear acoustic energy loss that is due to the energy-cascade phenomenon that arises from the nonlinear interaction between components of different frequencies. To establish the validity of the present model for predicting the acoustic performance of silencers, two model problems are considered. First, the performance of simple expansion mufflers with nonlinear incident waves has been predicted. Second, proposed method is applied for computing nonlinear acoustic wave propagation in the NASA Langley impedance duct configuration with ceramic tubular liner (CT57). Both results obtained from the hybrid models are compared with those from computational aero-acoustic techniques in a time-space domain that utilize a high-order finite-difference method. Through these comparisons, it is shown that there are good agreements between the two predictions. The main advantage of the present method is that it can effectively compute the nonlinear acoustic performance of silencers in nonlinear regimes without time-space domain calculations that generally entail a greater computational burden.     

Linear and Nonlinear Coupling of Electrostatic Drift and Acoustic Perturbations in a Nonuniform Bi-Ion Plasma with Non-Maxwellian Electrons

Linear and nonlinear coupling of drift and ion acoustic waves are studied in a nonuniform magnetized plasma comprising of Oxygen and Hydrogen ions with nonthermal distribution of electrons. It has been observed that different ratios of ion number densities and kappa and Cairns distributed electrons significantly modify the linear dispersion characteristics of coupled drift-ion acoustic waves. In the nonlinear regime, KdV (for pure drift waves) and KP (for coupled drift-ion acoustic waves) like equations have been derived to study the nonlinear evolution of drift solitary waves in one and two dimensions. The dependence of drift solitary structures on different ratios of ion number densities and nonthermal distribution of electrons has also been explored in detail. It has been found that the ratio of the diamagnetic drift velocity to the velocity of the nonlinear structure determines the existence regimes for the drift solitary waves. The present investigation may be beneficial to understand the formation of solitons in the ionospheric F-region.     

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

We investigate the acoustic wave propagation in bubbly liquid inside a pilot sonochemical reactor which aims to produce antibacterial medical textile fabrics by coating the textile with ZnO or CuO nanoparticles. Computational models on acoustic propagation are developed in order to aid the design procedures. The acoustic pressure wave propagation in the sonoreactor is simulated by solving the Helmholtz equation using a meshless numerical method. The paper implements both the state-of-the-art linear model and a nonlinear wave propagation model recently introduced by Louisnard (2012), and presents a novel iterative solution procedure for the nonlinear propagation model which can be implemented using any numerical method and/or programming tool. Comparative results regarding both the linear and the nonlinear wave propagation are shown. Effects of bubble size distribution and bubble volume fraction on the acoustic wave propagation are discussed in detail. The simulations demonstrate that the nonlinear model successfully captures the realistic spatial distribution of the cavitation zones and the associated acoustic pressure amplitudes.     

局域共振型声学超材料机理探讨

本文以二维固体薄板中的弹性波传播为例, 对基于共振子结构的声学超材料带隙机理进行了探讨, 证明在声学超材料中带隙形成既与共振子对波的散射相位有关, 也与波在共振体之间的几何传播相位有关. 通过调节散射相位和几何传播相位均能实现对色散关系的调控. 基于这一理解, 探究了弹性波超材料中的次波长缺陷态和负折射现象的实现条件.     

Linear and nonlinear excitations in warm dense matter

Small and large amplitude linear and nonlinear ion acoustic and Langmuir waves are investigated for plasma with the generalized equation of state (EoS). This EoS covers a wide range of energy-density conditions from dilute classical regime up to the relativistically degenerate matter. Investigation shows that the linear dispersion and localized excitations of ion acoustic waves are significantly affected by the plasma parameters. It is also found that the criterion for ordinary soliton existence is significantly different for fully degenerate and nondegenerate plasma regimes with given electron temperature. In the nondegenerate regime, bright solitons form only for Mach numbers above a critical value which is only a function of the fluid temperature.     

Soliton generation via continuous stokes acoustic self-scattering of hypersonic waves in a paramagnetic crystal

A new mechanism is proposed for continuous frequency down-conversion of acoustic waves propagating in a paramagnetic crystal at a low temperature in an applied magnetic field. A transverse hypersonic pulse generating a carrier-free longitudinal strain pulse via nonlinear effects is scattered by the generated pulse. This leads to a Stokes shift in the transverse hypersonic wave proportional to its intensity, and both pulses continue to propagate in the form of a mode-locked soliton. As the transverse-pulse frequency is Stokes shifted, its spectrum becomes narrower. This process can be effectively implemented only if the linear group velocity of the transverse hypersonic pulse equals the phase velocity of the longitudinal strain wave. These velocities are renormalized by spin-phonon coupling and can be made equal by adjusting the magnitude of the applied magnetic field. The transverse structure of the soliton depends on the sign of the group velocity dispersion of the transverse component. When the dispersion is positive, planar solitons can develop whose transverse component has a topological defect of dark vortex type and longitudinal component has a hole. In the opposite case, the formation of two-component acoustic “bullets” or vortices localized in all directions is possible.     

Quantum ion acoustic solitary waves in electron-ion plasmas: A Sagdeev potential approach

Linear and nonlinear ion acoustic waves are studied in unmagnetized electron-ion quantum plasmas. Sagdeev potential approach is employed to describe the nonlinear quantum ion acoustic waves. It is found that density dips structures are formed in the subsonic region in a electron-ion quantum plasma case. The amplitude of the nonlinear structures remains constant and the width is broadened with the increase in the quantization of the system. However, the nonlinear wave amplitude is reduced with the increase in the wave Mach number. The numerical results are also presented.     

Nonlinear propagation of fast and slow magnetosonic waves in collisional plasmas

Low-frequency fast and slow magnetosonic waves propagating in electron ion plasmas with damping effects through ions and neutral atoms collisions are investigated. Linear wave analysis is performed to obtain dispersion relation. The reductive perturbation method is applied and it is shown that fast and slow modes of nonlinear magnetosonic wave are governed by damped Korteweg-de Vries (DKdV) equation in the presence of ion neutral collisions in plasmas. The analytical solution of DKdV soliton is presented under the assumption of weak collisional effects and numerical solutions of DKdV equation are also obtained using two-level finite difference scheme with the help of Runge–Kutta method at different plasma parameters. The damping of nonlinear fast and slow magnetosonic wave structures at different times are discussed in the context of space plasma situations where ions and neutral atoms collisions exist.     

K-P-Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

The stationary solution is obtained for the K–P–Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev–Petviashvili(K–P) equation, threedimensional(3D) Burgers equation, and K–P–Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave(DIASW). The K–P equation predictes the existences of stationary small amplitude solitary wave,whereas the K–P–Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.