Finite Larmor radius and Hall effects on thermal instability of a compressible plasma

The effects of compressibility, finite Larmor radius (FLR) and Hall currents are considered on the thermal instability of a plasma in the presence of a uniform horizontal magnetic field. For stationary convection, the compressibility has a stabilizing effect whereas FLR and Hall currents have stabilizing as well as destabilizing effects. For (C _pβ/g)<1, the system is stable. The magnetic field, FLR and Hall currents introduce oscillatory modes in the system for (C _pβ/g)>1.     

Resistive drift instability and Rayleigh-Taylor instability in a dusty plasma

The resistive drift instability and the Rayleigh-Taylor instability are studied self-consistently in a magnetized inhomogeneous dusty plasma. The effect of grain charge fluctuations is taken into consideration. It is found that the presence of the dust grains in the plasma can significantly affect the resistive drift instability but less significantly the Rayleigh-Taylor instability. Further, the grain charge fluctuation has a tendency to stabilize both instabilities.     

可压流体Rayleigh-Taylor不稳定性的离散Boltzmann模拟

使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题:Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性,所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究,得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用,一开始扰动界面被"抹平",演化较慢;随着模式互相耦合而减少,演化开始加速,并经历非线性小扰动阶段和不规则非线性阶段,而后发展成典型的"蘑菇状",后期进入湍流混合阶段.由于扰动模式的耦合与发展,轻重流体的重力势能、压缩能与动能相互转化,系统先是趋于热动平衡态,而后偏离热动平衡态以线性形式增长,接着再次趋于热动平衡态,最后慢慢远离热动平衡态.     

Hall effects on thermosolutal instability of a rotating plasma

Summary The thermosolutal instability of a rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of Hall current. When the instability sets in as stationary convection for the case of no rotation, the Hall effects are found to be destabilizing. The stable solute gradient and rotation are found to have stabilizing effects. In the presence of rotation the Hall currents are found to be stabilizing forT ₁>M(1+x)². the case of overstability is also considered and it is shown that such solutions exist. The variation of the frequency with respect to the wave number at the neutral state is graphically shown. The authors of this paper have agreed to not receive the proofs for correction.     

Ablation effects on weakly nonlinear Rayleigh-Taylor instability with a finite bandwidth

A weakly nonlinear but numerically tractable model (to third order in amplitude and including bandwidth effects) has been developed for the ablative Rayleigh-Taylor (RT) instability. Model results clearly show growth reduction from linear ablative RT values and even amplitude saturation in some realistic cases. For excitation of a band of wave numbers near the cutoff for growth, the behavior is dominated by the mode with the largest linear growth rate, and not by the mode with the largest initial amplitude. This type of model is likely to be important for the future assessment of the RT effects on specific target designs of the inertial confinement fusion.     

Quantum effects on the Rayleigh-Taylor instability of stratified fluid/plasma through porous media

Quantum effect on Rayleigh-Taylor instability of stratified plasma layer through a porous medium are investigated. The linear growth rate is obtained analytically and is analyzed. In the presence of quantum effect, both the porosity of porous medium and the medium permeability has different influence on the coup point () for stability, but they do not have influence on the critical point () for stability. The quantum effect plays the principal role of the complete stability case for the system considered.     

双模瑞利-泰勒不稳定性的预热烧蚀效应研究

针对双模扰动下的烧蚀瑞利-泰勒不稳定性增长问题,采用高精度的数值计算方法,研究了不同预热程度下模耦合产生的多个高次谐波幅值的发展和演化问题。研究表明,三种预热烧蚀条件下,当扰动基模满足长波与短波耦合方式时,谐波中的长波模态占主导,而短波模发展明显受到抑制;当满足短波与短波耦合时,耦合结果带来了许多新的增长较快的长波模态,此时短波模增长呈现小幅震荡形式。比较两种耦合方式可以发现,长波结构在烧蚀瑞利-泰勒不稳定性弱非线性阶段都占主导地位,尤其是短波与短波耦合中气泡与尖钉表现出不同于两个基模的长波模结构。进一步分析预热效应对模耦合增长的影响,发现预热程度越强就越能削弱耦合谐波的增长,这说明预热对烧蚀瑞利-泰勒不稳定性具有致稳作用,这对惯性约束聚变工程中控制烧蚀瑞利-泰勒不稳定性发展具有重要意义。     

Finite Larmor radius effect on thermal instability of a compressible plasma

The thermal instability of a compressible plasma in the presence of a uniform vertical magnetic field is studied to include the effects of finiteness of the ion Larmor radius. When the instability sets in as stationary convection, both the compressibility and the finite Larmor radius are found to have stabilizing effect. The sufficient conditions for the nonexistence of overstability are investigated.     

Magnetically driven Rayleigh-Taylor instability with acceleration gradient

We investigate the stability properties of a slab of accelerating, current-carrying, cold, fluid when the accelerating J_ /spl times/ B_ force is nonuniform throughout the slab and leads to a gradient in the slab acceleration. A nonuniform force that squeezes (stretches) the slab while accelerating it increases (decreases) the Magnetic-Rayleigh-Taylor instability growth rate. This effect can explain recent experiments on thin, magnetically driven, imploding liner shells.     

Three-dimensional array structures associated with Richtmyer-Meshkov and Rayleigh-Taylor instability

A boundary separating adjacent gas or liquid media is frequently unstable. Richtmyer-Meshkov and Rayleigh-Taylor instability cause the growth of intricate structures on such boundaries. All the lattice symmetries [rectangular (pmm2), square (p4mm), hexagonal (p6mm), and triangular (p3m1) lattices] which are of interest in connection with the instability of the surface of a fluid are studied for the first time. They are obtained from initial disturbances consisting of one (planar case, two-dimensional flow), two (rectangular cells), or three (hexagons and triangles) harmonic waves. It is shown that the dynamic system undergoes a transition during development from an initial, weakly disturbed state to a limiting or asymptotic stationary state (stationary point). The stability of these points (stationary states) is investigated. It is shown that the stationary states are stable toward large-scale disturbances both in the case of Richtmyer-Meshkov instability and in the case of Rayleigh-Taylor instability. It is discovered that the symmetry increases as the system evolves in certain cases. In one example the initial Richtmyer-Meshkov or Rayleigh-Taylor disturbance is a sum of two waves perpendicular to one another with equal wave numbers, but unequal amplitudes: a ₁(t=0)≠a ₂(t=0). Then, during evolution, the flow has p2 symmetry (rotation relative to the vertical axis by 180°), which goes over to p4 symmetry (rotation by 90°) at t→∞, since the amplitudes equalize in the stationary state: a ₁(t=∞)=a ₂(t=∞). It is shown that the hexagonal and triangular arrays are complementary. Upon time inversion (t→−t), “rephasing” occurs, and the bubbles of a hexagonal array transform into jets of a triangular array and vice versa. Zh. éksp. Teor. Fiz. 116, 908–939 (September 1999)     

可压缩与不可压缩流体中Rayleigh Taylor不稳定性的比较

 对比研究了可压缩与不可压缩流体的Rayleigh Taylor不稳定性小扰动阶段的增长速率，其中，压力是密度的任意单值函数，这个函数也即是可压缩流体的状态方程。研究表明：在相同密度分布条件下，可压缩流体的界面扰动增长速率总是比相应的不可压缩流体的界面增长率大，其相对增长率随扰动波长的增加而增大，随两种介质的声速减小而增大，在长波和易压缩流体中，相对增长率可达0.8以上。因此，在某些条件下，流体可压缩性对Rayleigh Taylor不稳定性的影响是不能忽略的。     

Rayleigh-Taylor instability of a composite medium with variable viscosity in hydromagnetics

The frictional effect of collisions of ionized with neutral atoms on the Rayleigh-Taylor instability of a composite medium with variable viscosity is considered in the presence of a horizontal magnetic field. It is found that the simultaneous presence of viscosity, magnetic field and collisions has a stabilizing effect and completely stabilizes the wave-number bandk _* wherek _*=(k _x ² V²L/g). The collisions have no effect as such on the stratification, i.e., stable configuration remains stable and unstable configuration remains unstable. However the growth rate, under either of conditions (25), decreases with the increase of collisions.     

Asymptotic behavior of the Rayleigh-Taylor instability

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin and Williams for which we give a simplified demonstration. In particular, we observe that the spike's curvature evolves as t(3), while the overshoot in acceleration shows good agreement with the suggested 1/t(5) law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.     

Granular Rayleigh-Taylor instability: experiments and simulations

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.     

Suppression of Rayleigh-Taylor instability by gyroviscosity and sheared axial flow in imploding plasma pinches

The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations.The gyroviscosity(or finite Larmor radius) effects are introduced in the momentum equation through an anisotropic ion stress tensor.Dispersion relation with the effect of a density discontinuity is derived.The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the gyroviscosity effects.The long wavelength modes are stabilized by the sufficient sheared axial flow.However,the synergistic effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability.This synergistic effect can compress the Rayleigh-Taylor instability to a narrow wave number region.Even with a sufficient gyroviscosity and large enough flow velocity,the synergistic effect can completely suppressed the Rayleigh-Taylor instability in whole wave number region.     

Nonlinear theory of the ablative Rayleigh-Taylor instability

A fully nonlinear sharp-boundary model of the ablative Rayleigh-Taylor instability is derived and closed in a similar way to the self-consistent closure of the linear theory. It contains the stabilizing effect of ablation and accurately reproduces the results of 2D DRACO simulations. The single-mode saturation amplitude, bubble and spike evolutions in the nonlinear regimes, and the seeding of long-wavelength modes via mode coupling are determined and compared with the classical theory without ablation. Nonlinear stability above the linear cutoff is also predicted.     

界面张力对Rayleigh-Taylor不稳定性的影响

将具有简单速度势的Layzer模型和Zufiria模型推广至非理想流体情况, 并分别利用这两种模型研究了界面张力对Rayleigh-Taylor不稳定性的影响. 首先得到了两种模型下气泡的渐近速度和渐近曲率的解析表达式; 其次系统研究了界面张力对气泡的渐近速度和渐近曲率的影响; 最后将两种模型进行了比较, 并将气泡的渐近速度和数值模拟进行了比较. 研究表明: 界面张力压低了气泡的速度, 但对曲率没有影响; 利用简单速度势的Layzer模型所得的气泡的渐近速度比复杂速度势的Layzer模型的值小, 但是比Zufiria模型的值大; 当阿特伍德数等于1时, 简单速度势的Layzer模型和复杂速度势的Layzer模型给出的结果一致. 关键词： Rayleigh-Taylor不稳定性 界面张力 Layzer模型 Zufiria模型     

轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制

利用理想磁流体力学模型对有轴向剪切流的Z箍缩等离子体不稳定性进行了分析。给出了可压缩模型的色散关系,分别对可压缩及不可压缩模型中轴向剪切流对Z箍缩等离子体瑞利-泰勒不稳定性的抑制作用进行了比较,讨论了可压缩性对含有轴向剪切流系统不稳定性的影响。结果表明,可压缩性能够减缓瑞利-泰勒P凯尔文-亥姆霍兹(RTPKH)模扰动的增长,因而使得轴向剪切流对系统不稳定性的抑制作用表现得更为突出。计算结果还说明,在RT不稳定性线性增长阶段,等离子体温度较低,使用可压缩模型能够更真实地描述系统的状态。