Nonlinear quantum ion acoustic shock wave dynamics with exchange-correlation effects

The dynamics of linear and nonlinear electrostatic shock excitations is studied in homogeneous, unmagnetized, unbounded and dissipative quantum plasma consisting of electrons and ions. The dissipation in the system is taken into account by incorporating the ion kinematic viscosity. The system is modelled using the quantum hydrodynamic equations in which the electrons are significantly affected by the quantum forces, viz., the quantum statistical pressure, the quantum Bohm potential and electron exchange-correlations due to electron spin. In the weakly nonlinear limit, using reductive perturbation method deformed Korteweg-de Vries Burgers’s (KdVB) equation, which elegantly combines the effects of nonlinearity, dispersion and dissipation is derived. It is found that the present model predicts the existence of both nonlinear oscillatory and monotonic shock structures. The temporal evolution, stability and phase-space dynamics of nonlinear ion acoustic shocks are investigated numerically to elucidate the effects of quantum diffraction, electron exchange correlation and ion kinematic viscosity.     

Bifurcation analysis of ion-acoustic waves for Schrödinger equation in nonextensive Solar wind plasma

Bifurcation analysis of ion-acoustic wave (IAWs) solutions of the nonlinear Schrödinger equation (NLSE) is explored for the first time in an electron-ion (e-i) magnetized solar wind plasma. The existence of ion-acoustic (IA) periodic, superperiodic, kink, antikink, compressive and rarefactive solitary wave solutions are revealed. Special values of Solar wind plasma parameters at a normalized distance from the Sun are considered for numerical simulation. The IA wave solutions are derived analytically. These solutions are analyzed numerically considering the influence of parameters, namely, wave number (k), velocity (V) of traveling wave and nonextensive parameter (q). Computational simulation reveals that only IA periodic wave grows in amplitude as waves moves from the Sun.     

Superthermal electron’s effects on lump solitons structures in magnetized auroral plasma

Based on the considerations of the acknowledgements of the numerous space observations by satellites in the auroral plasma, astrophysics plasmas, spacecraft observations, various plasma models have been framed and revealed different interesting features, like electrostatic structures, solitary waves, double layers, supersolitons, etc. Soliton theory is a very efficient and competent way to describe nonlinear features. Using Viking satellite data in the auroral plasma, we have derived lump soliton solutions of the Kadomstev-Petviashvili (KP) equation by employing Hirota bilinear method. Due to its wide range of applications, the study of lump soliton is very attractive and important too. It has been shown that the lump solitons structures as well as in the one-dimensional form of lump soliton are varied with associated parameters in the auroral magnetized plasma. During the analysis of the features of the lump solitons, it is found that the system parameters play a pivotal role on the lump solitons structures.     

Gas-dynamic approach to the theory of non-linear ion-acoustic waves in plasma with Kaniadakis’ distributed species

The non-linear theory of ion-acoustic waves in two-spesies isotropic collisionless plasma is developed. Both light electron and heavy ion species in the plasma are distributed with Kaniadakis’ statistics. Kaniadakis’ gas law is derived. The exact formula for the Sagdeev pseudopotential in parametric form is derived by the method based on the integration of the inverse function. The pseudopotential is analyzed. It is shown that periodic ion-acoustic waves and solitons are possible in the studied plasma. The differential equation describing the profile of the ion concentration in the wave is derived. The profiles of this concentration in the periodic ion-acoustic wave and soliton are calculated.     

Small amplitude ion acoustic solitons in a weakly magnetized plasma with anisotropic ion pressure and kappa distributed electrons

The Zakharov–Kuznetzov (ZK) equation is derived for nonlinear electrostatic waves in a weakly magnetized plasma in the presence of anisotropic ion pressure and superthermal electrons. The anisotropic ion pressure is defined using Chew–Goldberger–Low (CGL) while a generalized Lorentzian (kappa) distribution is assumed for the non-thermal electrons. The standard reductive perturbation method (RPM) is employed to derive the two dimensional ZK equation for the dynamics of obliquely propagating low frequency ion acoustic wave. The influence of spectral index (kappa) of non-thermal electron on the soliton is discussed in the presence of anisotropic ion pressure in plasmas. It is found that ion pressure anisotropy and superthermality of electrons affect both the width and amplitude of the solitary waves. On the other hand the magnetic field is found to alter the dispersive property of the plasma only, and hence the width of the solitons is affected while the amplitude of the solitary waves is independent of external magnetic field. The numerical results are also presented for illustrations.     

Solitary and periodic waves in magneto–rotating plasmas: Effect of the Kappa–Cairns distributed electrons

The nonlinear propagation of ion–acoustic (IA) waves in a magneto–rotating plasma is studied by considering the Kappa-Cairns electron distribution. Employing the perturbation scheme, Korteweg–de Vries equation is derived. It is seen that both positive and negative potential solitons can be supported in the present plasma model. The numerical results reveal that the Kappa-Cairns distributed electrons modify features of the electrostatic waves significantly. The effects of non–thermal parameters, plasma rotation frequency, ion temperature, and the wave propagation angle on electrostatic solitary wave structures are also discussed here. It is found that the plasma parameters considerably influence the propagation of IA waves in rotating plasmas. Furthermore, using the bifurcation theory of planar dynamical systems to the K-dV equation, we have presented the existence of solitary and periodic traveling waves. Our study may be helpful to understand the behavior of ion–acoustic wave in the rotating plasma.     

空间飞行体与压缩区内等离子体非稳态相互作用的数值模拟

在压缩区内，飞行体天线辐射出的高频调制场影响着等离子体中的电荷分布，而电荷分布的扰动又反过来影响场量，采用FTCS有限差分格式方法，利用二维三分量轴对称，对空间飞行体与压缩区内等离子体非稳态相互作用过程进行数值模拟，得到了电荷密度扰动与电场的变化情况，计算结果表明，这种非线性相互作用可以引起场的塌缩并出现密度空洞，通过对密度空洞变化的探测，可对隐身飞行体进行跟踪。     

离子温度对磁化等离子体中非线性静电波的影响

本文讨论了无碰撞磁化低β等离子体中离子温度对非线性静电波的影响。结果表明,在参量α≡T_i/T_e≠0条件下,存在着三种非线性静电波(T_i和T_e分别为离子和电子的热能):在波速ν_p>(1+α)(1/2)c_s情况下存在着非线性离子回旋周期波;在(1+α)(1/2)c_scosθp<(1+α)(1/2)c_s情况下存在着离子声孤立波;在v_p<(1+α)(1/2)c_scosθ情况下存在着非线性离子声周期波。当参量α增加时,孤立波的波幅(最大电位)减小,而另外两种非线性周期波的电位幅度都几乎保持不变。      

Interaction of magnetoacoustic solitons in electron-positron plasmas

The interaction between two, four and six magnetoacoustic solitons in electron-positron plasmas are investigated. The extended Poincaré–Lighthill–Kuo (PLK) perturbation method is employed to derived two KdV equations for magnetoacoustic solitons moving towards each other and studied the head-on collision between them and their phase shifts. The Hirota bilinear method is used to have multi-soliton solutions of already derived two KdV equations for right and left moving solitons. The four and six magnetoacoustic solitons solutions of the two KdV equations are obtained to discuss their interaction and phase shifts. It is found that only compressive magnetoacoustic solitons structures are formed in electron-positron plasma. The present study may be useful to understand the collective phenomena related to head-on and overtaking magnetoacoustic solitons interaction in electron-positron plasmas that may occur in a pulsar magnetosphere.     

Effect of q-nonextensive hot electrons on bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves

Nonlinear and supernonlinear ion-acoustic periodic waves are investigated in a three-component unmagnetized plasma which consists of mobile fluid cold ions, Maxwellian cold electrons and q-nonextensive hot electrons employing phase plane analysis. Using the traveling wave transformation, the plasma system is reduced to a planar autonomous dynamical system. Utilizing phase plane analysis of planar dynamical systems, all possible phase portraits including nonlinear homoclinic orbit, nonlinear periodic orbit, supernonlinear homoclinic orbit and supernonlinear periodic orbit are presented depending on physical parameters $q,\alpha ,\sigma$ and V. Using numerical simulations, nonlinear and supernonlinear ion-acoustic periodic waves are shown for different conditions. It is found that the nonextensive parameter q plays a crucial role in the bifurcations of nonlinear and supernonlinear ion-acoustic periodic waves. Our study may be applicable to understand the nonlinear and supernonlinear periodic features in auroral plasma.     

非线性油膜力作用下转子弯扭耦合振动特性研究

建立了非线性油膜力作用下转子-轴承系统弯扭耦合振动的数学模型.采用Rugge-Kutta数值积分方法计算模拟了转子升速过程中弯曲振动和扭转振动的不平衡响应,得到了转子弯曲振动的三维谱图和分岔图.分析发现,转子的弯曲振动会发生倍周期和概周期等复杂的非线性动力学行为.通过与不考虑弯扭耦合作用的系统特性进行比较,指出在转子弯曲振动临界转速附近,弯扭耦合作用对转子弯曲振动特性影响最大.数值分析揭示了扭转振动随转速升高,振幅基本保持不变,频率减小,有助于更深入地认识转子-轴承系统的弯扭耦合振动特性.     

无碰撞低β磁流管中的非线性波

对无碰撞低β磁流管中柱对称状态下等离子体非线性静电波的存在进行了研究, 其结果表明: (1)若参数满足0<|(a/M2-1)E₀|<1, 存在着非线性周期波;(2)若|(a/M2-1)E₀|=1, 存在着隆起和下凹的孤立波, 也存在着激波;(3)若|(a/M2-1)E₀|>1, 存在着周期波, 也存在着隆起的孤立波。还对波的某些特性进行了研究。      

有限振幅重力波波包在等温可压大气中的非线性传播

采用交替方向隐格式(ADI)建立了二维可压大气全非线性动力学模型，模拟了不同初始振幅的重力波波包的非线性传播，模拟结果表明非线性效应是与波振幅相关的；强非线性效应将严重阻碍波振幅的增长，使波数谱明显变化，同时减小了波包的能量传输速度，在传播过程中，强非线性效应将显著加速平均流，其结果与非线性饱和理论的预测接近。     

阿尔芬波的调制不稳定性

考虑由有质动力引起的密度变化和流速改变两个非线性效应,运用Karpman方法研究阿尔芬波的调制不稳定性,对左、右圆偏振波两个分支,分别得出了具有波包孤子解和反波包孤子解的条件、密度扰动和阿尔芬波能量密度间的关联等结果.      

声重波激发的赤道Spread—F的拓扑特性研究

本文对声重波激发的Spread-F扰动的非线性制约方程的拓扑特性进行了定性讨论和数值计算．研究了Spread-F的混沌特征及参数范围．结果表明声重波在不同条件时对Spread-F的激发作用有本质的不同．     

利用谱方法数值求解三维球坐标系下的Navier-Stokes方程

从三维球坐标系下的Navier-Stokes方程出发,采用谱配置方法建立了一个三维球坐标系下中层大气波动传播的全非线性动力学数值模式;构造了合理的纬向边界,并利用初始给定的重力波波包对该模式进行了数值检验．计算结果展示了重力波波包在大气中传播的三维图像,波包整体向上传播,波相关扰动速度随高度的增加而增长．     

A numerical model characterizing internal gravity wave propagation into the upper atmosphere

A new two-dimensional, time-dependent and fully nonlinear model is developed to numerically simulate plane wave motions for internal gravity waves in a non-isothermal and windy atmosphere that accounts for the dissipation due to eddy and molecular processes. The atmosphere has been treated as a well mixed total gas with a constant mean molecular weight. The effects of Rayleigh friction and Newtonian cooling are applied near the upper boundary of the model to simulate the radiation conditions as well as to act as a sponge layer; lateral boundaries are periodic over a horizontal wavelength to simulate a horizontally infinite domain. The thermal excitation to initiate upward propagating waves is spatially localized in the troposphere and is a Gaussian function of time. A time-splitting technique is applied to the finite difference equations that are derived from the Navier–Stokes equations. The time integration for these highly coupled equations is performed using an explicit second order Lax–Wendroff scheme and an implicit Newton–Raphson scheme. The wave solutions derived from the model are found to be broadly agreeable with those derived from a Wentzel–Kramers–Brillouin theory.     

太阳大气中有限振幅磁场扰动的动力学过程

本文从完整的磁流体动力学方程组出发,通过太阳大气中磁力线管根部有限振幅磁场的扰动,研究了非线性磁场的动力学演化。假设初始磁场位形足β<<1的势场,根部磁力线管磁场扰动,驱动等离子体运动,一部分磁能转换为等离子体动能。等离子体压缩运动具有快磁声波的特性。计算结果给出非线性磁场演化的定量关系,可以解释太阳大气中日冕活动过程。也可用于模拟实验室里高β实验装置中的等离子体的持性。      

一种基于等效采样的周期信号谐波分析方法

为了突破周期信号谐波分析中采样保持与模数转换时间对分析信号频率范围的限制,将准均匀采样与等效采样相结合,提出了一种新的等效采样周期信号谐波分析方法。首先,给出了在奇数个信号周期内进行2的整数次方次均匀采样的等效采样谐波分析理论;其次,计入定时时钟周期对采样时间的影响,在等效采样中结合准均匀采样以实现同步采样;进一步分析了采样过程中的时间离散与幅值量化所带来的谐波分析误差;最后,给出了新的等效采样谐波分析的具体算法。借助含有小幅谐波分量的实验信号对等效采样谐波分析算法进行了数值仿真。理论分析和数值仿真均表明：新方法有效拓宽了分析信号的频率范围,并且可直接利用FFT进行快速计算。     

Numerical simulations of a continuously injected relativistic electron beam relaxation into a plasma with large-scale density gradients

In this paper the influence of large-scale decreasing and increasing gradients of the density of magnetized plasma on the relaxation process of a continuously injected relativistic electron beam with an energy of 660 keV ($v_b=0.9c$) and a pitch-angle distribution is studied using particle-in-cell numerical simulations. It is found that for the selected parameters in the case of a smoothly decreasing gradient and in a homogeneous plasma the formation of spatially limited plasma oscillations of large amplitude occurs. In such cases, modulation instability develops and a long-wave longitudinal modulation of the ion density is formed. In addition, the large amplitude of plasma waves accelerates plasma electrons to energies on the order of the beam energy. In the case of increasing and sharply decreasing gradients, a significant decrease in the amplitude of plasma oscillations and the formation of a turbulent ion density spectrum are observed. The possibility of acceleration of beam electrons to energies more than 2 times higher than the initial energy of the beam particles is also demonstrated. This process takes place not only during beam propagation in growing plasma density, but also in homogeneous plasma due to interaction of beam particles with plasma oscillations of large amplitude.