Quantum Effects on Rayleigh–Taylor Instability of Incompressible Plasma in a Vertical Magnetic Field

Quantum effects on Rayleigh-Taylor instability of a stratified incompressible plasmas layer under the influence of vertical magnetic field are investigated. The solutions of the linearized equations of motion together with the boundary conditions lead to deriving the relation between square normalized growth rate and square normalized wave number in two algebraic equations and are numerically analyzed. In the case of the real solution of these two equations, they can be combined to generate a single equation. The results show that the presence of vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration.     

Weakly Nonlinear Rayleigh–Taylor Instability in Cylindrically Convergent Geometry

The Rayleigh–Taylor instability(RTI) in cylindrical geometry is investigated analytically through a second-order weakly nonlinear(WN) theory considering the Bell–Plesset(BP) effect. The governing equations for the combined perturbation growth are derived. The WN solutions for an exponentially convergent cylinder are obtained. It is found that the BP and RTI growths are strongly coupled, which results in the bubble-spike asymmetric structure in the WN stage. The large Atwood number leads to the large deformation of the convergent interface. The amplitude of the spike grows faster than that of the bubble especially for large mode number m and large Atwood number A. The averaged interface radius is small for large mode number perturbation due to the mode-coupling effect.     

Simulation of the Weakly Nonlinear Rayleigh–Taylor Instability in Spherical Geometry

The Rayleigh-Taylor instability at the weakly nonlinear(WN) stage in spherical geometry is studied by numerical simulation.The mode coupling processes are revealed.The results are consistent with the WN model based on parameter expansion,while higher order effects are found to be non-negligible.For Legendre mode perturbation Pn(cos B),the nonlinear saturation amplitude(NS A) of the fundamental mode decreases with the mode number n.When n is large,the spherical NSA is lower than the corresponding...     

Interface coupling effects of weakly nonlinear Rayleigh–Taylor instability with double interfaces

Taking the Rayleigh–Taylor instability with double interfaces as the research object,the interface coupling effects in the weakly nonlinear regime are studied numerically.The variation of Atwood numbers on the two interfaces and the variation of the thickness between them are taken into consideration.It is shown that,when the Atwood number on the lower interface is small,the amplitude of perturbation growth on the lower interface is positively related with the Atwood number on the upper interface.However,it is negatively related when the Atwood number on the lower interface is large.The above phenomenon is quantitatively studied using an analytical formula and the underlying physical mechanism is presented.     

Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang–Mills Equations

With the help of some reductions of the self-dual Yang Mills （briefly written as sdYM） equations, we introduce a Lax pair whose compatibility condition leads to a set of （2 ＋ 1）-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation, the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new （2 ＋ 1）-dimensional nonlinear integrable systems, in particular, obtains a kind of （2 ＋ 1）-dimensional integrable couplings of a new （2 ＋ 1）- dimensional integrable nonlinear equation.     

Propagation of Lorentz–Gaussian Beams in Strongly Nonlocal Nonlinear Media

In this paper the propagation of Lorentz-Gaussian beams in strongly nonlinear nonlocal media is investi- gated by the ABCD matrix method. For this purpose, an expression for field distribution during propagation is derived and based on it, the propagation of Lorentz-Gaussian beams is simulated in this media. Then, the evolutions of beam width and curvature radius during propagation are discussed.     

Nonlinear modes in rotating double well potential with parity–time symmetry

We investigate the nonlinear modes in a rotating double well potential with 79T symmetry. Focus on the existence and stability of the nonlinear PT modes in this system, we found that five types of PT modes can stably exist by given certain parameter settings. The multistable area between these modes are studied numerically and the bistable and tristable areas are delimited. With different input trial wavefunctions, five types of solitary wave modes are identified. We found that the rotating of the potential can significantly affect the power flow of the fundamental harmonic mode, whose effect is absent for the other modes.     

Comment on ＂Application of the （G＇/G）-Expansion Method for Nonlinear Evolution Equations＂ [Phys. Lett. A 372 （2008）3400]

In this paper, some travelling wave solutions involving parameters of the Modified Zakharov-Kuznetsov equation [Phys. Lett. A 372 （2008） 3400] are investigated. We will show that these solutions are not new travelling wave solutions.     

Numerical Simulation of Anisotropic Preheating Ablative Rayleigh-Taylor Instability

The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability （ARTI） is studied by numerical simulations. The preheating model κ （T）=κSH [1＋f（T）] is applied, where f（T） is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 （2007） 245001].     

用高精度有限差分法模拟烧蚀瑞利-泰勒不稳定性

求解烧蚀面附近流场的定常解,并以此作为基本流实现用高精度的WENO格式对烧蚀瑞利-泰勒不稳定性的数值模拟.线性增长率与Lindl公式以及线性稳定性分析给出的结果相符合,证明该数值模拟方法的准确性与精度,该方法还具有较好的界面变形捕捉能力.     

烧蚀瑞利-泰勒不稳定性线性增长率的预热致稳公式

烧蚀瑞利泰勒(RT)不稳定性增长的准确估计是惯性约束聚变(ICF)的重要研究课题.增大低温电子热传导系数以考虑烧蚀面预热效应时,烧蚀面密度分布得到改善,烧蚀RT不稳定性线性增长率的二维计算值明显降低,与美国利弗莫尔实验室的实验值符合较好.考虑烧蚀面预热效应后,Lindl公式γ=kg/(1+kL)-βkVa与二维计算值有较大偏差.在分析研究发生偏差原因的过程中,发现了预热情况的Atwood数变小致稳现象.在合理近似下,得到了烧蚀RT不稳定性线性增长率的预热致稳公式γ=Akg/(1+AkL)-2kVa.此公式     

Weakly Nonlinear Rayleigh-Taylor Instability in Incompressible Fluids with Surface Tension

A weakly nonlinear model is established for incompressible Rayleigh—Taylor instability with surface tension. The temporal evolution of a perturbed interface is explored analytically via the third-order solution. The dependence of the first three harmonics on the surface tension is discussed. The amplitudes of bubble and spike are greatly affected by surface tension. The saturation amplitude of the fundamental mode versus the Atwood number A is investigated with surface tension into consideration. The saturation amplitude decreases with increasing A. Surface tension exhibits a stabilizing phenomenon. It is shown that the asymmetrical development of the perturbed interface occurs much later for large surface tension effect.     

Rayleigh-Taylor不稳定性弱非线性阶段界面效应对谐波的影响

为了更好地理解不同空间坐标系下流体界面对Rayleigh-Taylor（RT）不稳定性弱非线性阶段谐波的影响,文章采用3阶小扰动展开法,解析研究了球坐标空间经典RT不稳定性弱非线性阶段谐波的演化规律,并和柱坐标空间以及直角坐标空间相应结果进行了对比研究.当球坐标系和直角坐标系中RT不稳定性界面扰动波长相同,球坐标系中初始扰动半径为无穷大时（即球坐标下RT不稳定性初始扰动半径相对于扰动波长为无穷大时）,球坐标下RT不稳定性前4次谐波的结果和直角坐标系下的相应结果相同.研究表明:由初始界面曲率引起的Bell-Plesset（BP）效应和空间效应（直角坐标空间、柱坐标空间和球坐标空间）对谐波发展有较大的影响.即在不同正交曲线坐标系下,不同曲率的流体界面效应对RT不稳定性谐波发展有较大的影响.对于柱坐标空间和球坐标空间,2阶对0次谐波的反馈加强了界面向内收缩.研究还表明:界面效应增加了2次谐波的负反馈,然而,对于基模和3次谐波却有不同的影响.      

Weak Nonlinearity of Ablative Rayleigh--Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh-Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh-Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.     

磁瑞利-泰勒不稳定性非线性演化数值模拟

基于理想磁流体力学模型,采用5阶WENO有限差分格式结合磁场伪散度清除投影算法,发展二维数值模拟程序,利用线性理论对程序进行检验,在此基础上研究磁瑞利-泰勒(MRT)不稳定性非线性演化物理过程和发展规律.结果表明:垂直于加速度方向磁场在线性和非线性阶段对MRT扰动发展都有较强的制稳作用,而平行于加速度方向磁场在线性阶段...     

Nonlinear Evolution of Lower-Hybrid Drift Instability in Harris Current Sheet

We perform 2.5-dimensional particle-in-cell simulations to investigate the nonlinear evolution of the lower hybrid drift instability (LHDI) in Harris current sheet. Due to the drift motion of electrons in the electric field of the excited low hybrid drift (LHD) waves, the electrons accumulate at the outer layer, and therefore there is net positive charge at the inner edge of the current sheet. This redistribution of charge can create an electrostatic field along the z direction, which then modifies the motions of the electrons along the y direction by E×B drift. This effect strongly changes the structure of the current sheet.     

表面张力对Rayleigh-Taylor不稳定性谐波的影响

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability (RTI) for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third harmonics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.     

Effects of Compressibility on the Rayleigh-Taylor Instability in Z-pinch Implosions

In this paper we shall consider the effect of compressibility on the RT instability in Z-pinch implosions, importance is the comparing growth rates of the RT instability for two systems of the compressible and incompressible MHD plasma. For which reason, we shall use as simple model as possible. Obviously, slab geometry is the most simple. For example, in the case of annular plasma implosion, during the linear growth phase of the RT instability there are vacuums at both sides of the annular plasma shell and its thickness is sufficiently smaller than the pinch radius, allowing us to use slab geometry instead of the annular one. For simplicity, we do not consider the effects of the finite Larmor radius and the sheared axial flow which are the important physical mechanisms to compress the RT instabilities.