Self-organization of a plasma due to 3D evolution of the Weibel instability

The nonlinear evolution of the thermal Weibel instability is studied by using three-dimensional particle-in-cell simulations. After a fast saturation due to a reduction in the temperature anisotropy, the instability evolves to a quasistationary state which includes a single mode long wavelength helical magnetic field and a finite degree of temperature anisotropy. The nonlinear stability of this state is explained by periodic variations of the temperature anisotropy axis. At long time scales the magnetic field, wave number, and temperature anisotropy slowly evolve to the decreasing magnitudes.     

相邻双侧边盖驱动方腔流动的三维线性整体稳定性

文章考察了相邻双侧边盖驱动方腔流动（即上壁面向右运动和左侧壁面向下运动）的三维线性整体稳定性.首先,采用Taylor-Hood有限元方法并经由Newton迭代过程计算得到双侧边盖驱动方腔流动的二维稳态基本流.其次,Taylor-Hood有限元在Chebyshev Gauss配置点上进行离散,同时Gauss配置点也可以用于线性稳定性方程的高阶有限差分格式离散.然后,离散得到的矩阵形式的广义特征值问题可以结合shift-and-invert算法采用隐式重启Arnoldi方法计算.最后,通过对线性稳定性方程特征值的计算,发现了一个最不稳定的驻定模态和两对对称行波模态.最不稳定的三维驻定模态的临界Reynolds数为Re_c=261.5,远远小于二维不稳定的临界Reynolds数Re_c2d=1 061.7.通过画出这3类三维不稳定模态的流向扰动速度和扰动涡量的空间等值面图像,可以发现不稳定扰动位于稳态基本流的两个主涡区域,因此可以认为主涡区域是三维扰动失稳的主要能量来源地.      

Convective and absolute Eckhaus instability leading to modulated waves in a finite box

We report an experimental study of the secondary modulational instability of a one-dimensional nonlinear traveling wave in a long bounded channel. Two qualitatively different instability regimes involving fronts of spatiotemporal defects are linked to the convective and absolute nature of the instability. Both transitions appear to be subcritical. The spatiotemporal defects control the global mode structure.     

Secondary instabilities of hexagonal patterns in a Bénard-Marangoni convection experiment

We have identified experimentally secondary instability mechanisms that restrict the stable band of wave numbers for ideal hexagons in Bénard-Marangoni convection. We use "thermal laser writing" to impose long wave perturbations of ideal hexagonal patterns as initial conditions and measure the growth rates of the perturbations. For epsilon=0.46 our results suggest a longitudinal phase instability limits stable hexagons at a high wave number while a transverse phase instability limits low wave number hexagons.     

On the stability of periodic solutions of the generalized Benjamin-Bona-Mahony equation

We study the stability of a four-parameter family of spatially periodic traveling wave solutions of the generalized Benjamin-Bona-Mahony equation under two classes of perturbations: periodic perturbations with the same periodic structure as the underlying wave, and long wavelength localized perturbations. In particular, we derive necessary conditions for spectral instability under perturbation for both classes of perturbations by deriving appropriate asymptotic expansions of the periodic Evans function, and we outline a theory of nonlinear stability under periodic perturbations based on variational methods which effectively extends our periodic spectral stability results.     

A Two-Layer Model for Superposed Electrified Maxwell Fluids in Presence of Heat Transfer

Based on a modified-Darcy-Maxwell model, two-dimensional, incompressible and heat transfer flow of two bounded layers, through electrified Maxwell fluids in porous media is performed. The driving force for the instability under an electric field, is an electrostatic force exerted on the free charges accumulated at the dividing interface. Normal mode analysis is considered to study the linear stability of the disturbances layers. The solutions of thelinearized equations of motion with the boundary conditions lead to an implicit dispersion relation between the growth rate and wave number. These equations are parameterized by Weber number, Reynolds number, Marangoni number, dimensionless conductivities, and dimensionless electric potentials. The case of long waves interfacial stability has been studied. The stability criteria are performed theoretically in which stability diagrams are obtained. Inthe limiting cases, some previously published results can be considered as particular cases of our results. It is found that the Reynolds number plays a destabilizing role in the stability criteria, while the damping influence is observed for the increasing of Marangoni number and Maxwell relaxation time.     

Feedback Stabilization of a Corkscrew Istabilty

An application is made of lumped feedback to achieve stability of a distributed electromechanical system. A conducting elastic wire, placed in an axial magnetic field and carrying a current, exhibits instability at a certain threshold of magnetic pressure. The two dimensional transverse displacement of the wire is sampled and these signals are used to produce proportional feedback forces which allow stable equilibrium to be restored. A stability diagram is determined indicating the minimum feedback force to prevent static instability. For one station feedback, there is a maximum allowable feedback to prevent overstabil1 ity. In addition, the maximum value of destabilizing force which can be stabilized is somewhat less than that required for the second mode to become unstable. The wave dynamics of this corkscrew instability are related to several types of electromechanical interaction. The pinch confinement of a plasma, proposed as a scheme for containing a controlled thermonuclear reaction, suffers from a similar corkscrew instability.     

Dissipation effect on local and global stability of fluid-conveying pipes

In this article, the effect of dissipation on local and global stability of fluid conveying pipes is analyzed. The local approach refers to an infinite medium and uses wave propagation analyses without taking boundary conditions into account. The global approach refers to the same medium, but with finite length and associated with a given set of boundary conditions. The finite length system is generally studied by calculating its eigenmodes and eigenfrequencies. Criteria for local instability are derived in the first part of this paper, and dissipation is found to significantly affect local stability. Moreover, dissipation is found to have a stabilizing or destabilizing effect, depending on the other parameters. Next, numerical computations are presented for finite-length systems and results are analyzed and compared with local stability properties of the corresponding media. When the system is sufficiently long, it is found that critical velocity for global instability tends to a local criterion which can be that of local stability of the damped medium or a local transition criterion of the undamped medium, which is not necessarily the local instability criterion. Finally, a reasoning based on lengthscale ratios is developed. It allows to know which criterion is able to predict the global stability for long systems.     

Rapid beat generation of large-scale zonal flows by drift waves: a nonlinear generic paradigm

The generalized Charney-Hasegawa-Mima equation is unstable to a four wave modulational instability whereby a coherent, monochromatic drift wave can drive a band of modes and associated zonal flows unstable. Although initially the fastest growing modes dominate, a secondary nonlinear instability later drives the longest wavelength zonal flow and its associated sidebands at twice the growth rate of the fastest growing modulationally unstable modes. This results in a direct transfer from strongly unstable short wavelength modes to the weakly unstable long wavelength modes, which drains the short wavelength pump energy. A related but less efficient direct enstrophy cascade generates very short wavelength modes lying outside the band of modulationally unstable modes.     

A study of the transition to instability in a Rijke tube with axial temperature gradient

A horizontal Rijke tube with an electric heat source is a system convenient for studying the fundamental principles of thermoacoustic instabilities both experimentally and theoretically. Given the long history of the device, there is a surprising lack of accurate data defining its behavior. In this work, the main system parameters are varied in a quasi-steady fashion in order to find stability boundaries accurately. The chief purposes of this study are to obtain precise values of the system parameters at the transition to instability with specified uncertainties and to determine how well the experimental results can be explained with existing theory. Measurement errors are reported, and the influence of experimental procedures on the results is discussed. A form of hysteresis effect at stability boundaries has been observed. Mathematical modelling is based on a thermal analysis determining the temperature of the heater and the temperature field in the air inside the tube, which, consequently, affects acoustical mode shapes. Solutions of the linearized wave equation for a non-uniform medium, including losses and a heat source term, determine the stability properties of the eigen modes. Calculated results are compared with experimental data and with results of the modelling based on the common assumption of a constant temperature in the tube. The mathematical model developed here can be applied to designing thermal devices with low Mach number flows, where thermoacoustic issue is a concern.     

Modulation instability of magnetostatic waves in a magnetically coupled two-layer structure

Modulation instability of direct bulk magnetostatic waves in structures consisting of two magnetically coupled planar films separated by a nonmagnetic layer is studied. It is found that, depending on the type of excitation of the waveguide modes, mode coupling can either change the characteristics of the modulation wave instability or ensure their stability with respect to the corresponding perturbations by affecting the dispersion properties of the structure.     

Characterization of acoustic disturbances in linearly sheared flows

The equation describing the plane wave propagation, the stability, or the rectangular duct mode characteristics in a compressible inviscid linearly sheared parallel, but otherwise homogeneous, flow, is shown to be reducible to Whittaker's equation. The resulting solutions, which are real, viewed as functions of two variables, depend on a parameter and an argument the values of which have precise physical meanings depending on the problem. The exact solutions in terms of Whittaker functions are used to obtain a number of known results of plane wave propagation and stability in linearly sheared flows as limiting cases in which the speed of sound goes to infinity (incompressible limit) or the shear layer thickness, or wave number, goes to zero (vortex sheet limit). The usefulness of the exact solutions is then discussed in connection with the problems of plane wave propagation and stability of a finite thickness shear layer with a linear velocity profile. With respect to the plane wave propagation it is shown that, unlike the compressible vortex sheet, the shear layer possesses no resonances and no Brewster angles, whereas with respect to the stability problem it is shown that, again unlike the compressible vortex sheet, the thin layer is unstable to long wavelength disturbances for all Mach numbers. These results imply that the reflection and stability characteristics of a non-zero thickness but thin shear layer (i.e., the long wavelength characteristics) do not go over smoothly into the results of the compressible vortex sheet as the wave number approaches zero, except for a limited range of generally subsonic relative flow of the two parallel streams bounding the shear layer.     

Intramolecular vibrations and noise effects on pattern formation in a molecular helix

Modulational instability in a biexciton molecular chain is addressed. We show that the model can be reduced to a set of three coupled equations: two nonlinear Schr?dinger equations and a Boussinesq equation. The linear stability analysis of continuous wave solutions of the coupled systems is performed and the growth rate of instability is found numerically. Simulations of the full discrete systems reveal some behaviors of modulational instability, since wave patterns are observed for the excitons and the phonon spectrum. We also take the effect of thermal fluctuations into account and we numerically study both the stability and the instability of the plane waves under 300 K. The plane wave is found to be stable under modulation, but displays a gradual increase of the wave amplitudes. Under modulation, the same behaviors are observed and wave patterns are found to resist thermal fluctuations, which is in agreement with earlier research on localized structure stability under thermal noise.     

超高速激光纹影技术测量脉冲功率驱动的磁重联现象

用超高速激光纹影技术测量了Z箍缩等离子体磁重联现象。实验采用超高速光电分幅相机,配合激光纹影技术,测量了XP-1装置上两根金属丝产生的等离子体分布,论证了超高速激光纹影技术研究Z箍缩磁重联现象的可行性。双钨丝实验结果表明,电流加载约10ns后金属丝已有明显膨胀,线性拟合得到平均膨胀速度约8km/s,金属丝内外两侧出现了规则的极有可能是垂直磁场的电热不稳定性扰动,并沿角向高度关联。铝丝负载的实验结果表明,早期的不稳定性波长为0.4mm,电流峰值之后金属丝初始位置仍有大量等离子体,后期的不稳定性波长约1.5mm。这些现象揭示了不稳定性发展的一个主要特征:短波模式受抑制,长波模式将占主导。     

超高速激光纹影技术测量脉冲功率驱动的磁重联现象

用超高速激光纹影技术测量了Z箍缩等离子体磁重联现象。实验采用超高速光电分幅相机,配合激光纹影技术,测量了XP-1装置上两根金属丝产生的等离子体分布,论证了超高速激光纹影技术研究Z箍缩磁重联现象的可行性。双钨丝实验结果表明,电流加载约10 ns后金属丝已有明显膨胀,线性拟合得到平均膨胀速度约8 km/s,金属丝内外两侧出现了规则的极有可能是垂直磁场的电热不稳定性扰动,并沿角向高度关联。铝丝负载的实验结果表明,早期的不稳定性波长为0.4 mm,电流峰值之后金属丝初始位置仍有大量等离子体,后期的不稳定性波长约1.5 mm。这些现象揭示了不稳定性发展的一个主要特征：短波模式受抑制,长波模式将占主导。     

Propagation dynamics of relativistic electromagnetic solitary wave as well as modulational instability in plasmas

By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10²³ m^-3 and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.     

Gas dynamics and thermal-ionization instability of the cathode region of a glow discharge. Part II

The influence of the gas flow structure in the cathode sheath of a glow discharge on the discharge stability is studied numerically. The electric parameters are calculated in a diffusion-drift model that consistently takes into account associative dissociation as an additional electron source. The model also includes equations describing both the thermal mode of the cathode and the nonequilibrium physicochemical gas dynamics of a moderately rarefied gas. It is shown that, in a pulsed discharge, the increasing branch of the current-voltage characteristic, which is associated with the gas rarefaction behind the cathode shock wave, can change to a descending branch associated with the intensification of associative ionization. This gives rise to cathode sheath instability. The results of calculations agree well with experiments.     

Self-oscillations in a jet flow and gaseous flame with strong swirl

Investigation results on unsteady flow dynamics in a gaseous jet flame with strong swirl, vortex breakdown, and precession of a vortex core obtained by panoramic optical methods are presented, as well as the results of theoretical analysis of the fastest growing modes of hydrodynamic instability. Characteristics of the most unstable self-oscillating mode in the initial region of the turbulent strongly swirling propane-air jet burning in the atmospheric air in the form of a lifted flame are determined. Analysis of data by principal component analysis and linear stability analysis revealed that evolution of the dominant self-oscillating mode corresponds to quasi-solid rotation with constant angular velocity of the spatial coherent structure consisting of a jet spiral vortex core and two spiral secondary vortices.     

高速压气机不稳定流动声测量技术研究

本文叙述了用声测量技术研究高速压气机的旋转不稳定特性、失速先兆及失速过程,建立了一套测量方法、测量系统,测量了高速压气机管道内声场的时域波形、频谱和管道声模态,结果分析表明:在没有激波的条件下高速压气机的管道声场中也存在低速压气机中可能存在的不稳定分量,但在有激波存在时无法分辨激波分量和不稳定分量,也未发现激波噪声分量的模态特征。所建立的测量系统具有高速、大容量、连续采集多通道信号的能力,并有快速计算频谱和模态的功能,使这种测量技术可成为一种常规研究压气机不稳定特性、失速机理和失速过程的有效方法。     

Steady-state and stability analysis for a laser with a saturable absorber with a Gaussian transverse profile

We describe the dynamics of a laser with saturable absorber by a two-level model, which assumes a Gaussian radial profile for the electric field. Both the amplifier and the absorber are exactly resonant with the cavity mode frequency. We calculate all the stationary solutions of the system, including those detuned from the resonance frequency. We perform the linear stability analysis of the normal lasing state in the rate equation approximation. The instability range turns out to be somehow smaller in the Gaussian than in the plane wave case.