高能离子在稠密等离子体中的传输和能量沉积

用相对论福克-普朗克方程对高能离子在稠密氘氚等离子体中的碰撞动力学进行了研究，用球谐函数来展开方程的解：格林函数，然后简明地求出了不同能量质子和α粒子在等离子体中的停止时间、减速距离、纵向弥散距离和横向偏转距离.与以前研究离子在等离子体中运动的方法相比，没有假设高能离子在等离子体中损失能量远远小于入射离子能量，求解了纵向弥散距离；并且可以求解横向偏转距离.这些计算对实验上用高能离子加热冷的稠密等离子体，然后进行科学研究具有指导作用，并且可以用来研究快点火的可能性. 关键词： 高能离子 福克-普朗克方程     

Paul阱中共面两离子系统的能量本征态

通过对Paul阱中共面两离子体系的研究，考虑共面两离子在Paul阱中库仑关联，得到了两离子系统Schrdinger方程的精确解；椐方程的精确解，分析了质心能级简并情况，计算了两离子的平衡距离和低能级的几个态函数，设计程序作出了质心径向概率分布图. 关键词： Paul阱 两离子 共面 量子逻辑操作     

用Hartree-Fock-Slater-Boltzmann-Saha模型研究等离子体细致组态原子结构及其状态方程

等离子体的辐射不透明度和状态方程是工程物理中的重要参数，这些物理参数取决于等离子体内大量离子的统计行为。由于高温稠密等离子体内的离子类型多达百万，一般只能用平均原子模型进行模拟。当计算轻元素稀薄等离子体原子结构时，平均原子结果与实验有一定的偏差，而此时等离子体内离子类型数目有限，正是细致组态模型适用的情况。标准的Saha方程需要孤立离子的能级，计算孤立离子结构的程序很多。当然，这些离子能级还可从实验获得。但是，标准的Saha方程使用的能级不含等离子体背景效应，能级数会发散。为了消除该缺陷，Saha方程中引进了等离子体背景修正。     

前鞘等离子体的LB碰撞输运模型

本文从离子动力学方程出发，利用ＬＢ碰撞模型研究了离子－离子碰撞效应对前鞘等离子体输运的影响。电子分布假定为等温麦克斯韦－玻耳兹曼分布。结果表明，在低碰撞频率和高碰撞频率下，ＬＢ碰撞模型都能较好地描述前鞘等离子体中的离子－离子碰撞行为。离子－离子碰撞对表面等离子体的输运行为有较大影响。     

激光场对快速分子离子与固体相互作用的影响

利用线性化的流体力学方程和泊松方程，描述了在强激光场作用下快速分子离子在固体中产生的电激发过程，并推导出分子离子中两个离子之间的动力学相互作用势和相互作用力的一般表达式.通过数值求解离子的运动方程，研究了激光场的参量对分子离子库仑爆炸过程和能量损失的影响. 关键词： 激光场 分子离子 库仑爆炸 能量损失     

弱相对论等离子体横向扰动下的离子声孤波

在低阶近似下，得到了描述无磁场相对论热离子等离子体的KP(Kadomtsev-Petviashvilli) 方程.研究表明，相对论热离子等离子中的非线性离子声孤波在高阶横向拢动下是稳定的， 且在相对论热离子等离子体中仅存在压缩型孤波. 关键词： 离子等离子体 孤波 声波 约化摄动法     

磁约束等离子体中杂质离子的输运方程

以非平衡态统计理论为基础,从福克尔-普朗克动理学方程出发推导出了各种杂质离子、氘离子和电子的输运动力学方程,即特殊的多组分等离子体输运方程。各级电离过程中形成的带不同电荷杂质离子的输运动力学过程以及不同粒子间碰撞相互作用的贡献在文中进行了系统的分析。此外,在重新推导并优化的基本方程组基础上,得到了各种杂质离子的输运动力学方程。     

磁约束等离子体中杂质离子的输运方程

以非平衡态统计理论为基础,从福克尔-普朗克动理学方程出发推导出了各种杂质离子、氘离子和电子的输运动力学方程,即特殊的多组分等离子体输运方程。各级电离过程中形成的带不同电荷杂质离子的输运动力学过程以及不同粒子间碰撞相互作用的贡献在文中进行了系统的分析。此外,在重新推导并优化的基本方程组基础上,得到了各种杂质离子的输运动力学方程。     

Tb，Tm：YVO4晶体的激光性能分析

Tm：YVO4和Tb，Tm：YVO4晶体中激活离子之间或激活离子与敏化离子间的交叉弛豫、与无辐射跃迁及激光上能级的辐射跃迁的几率是相近的，对这种双掺离子晶体的激光阈值理论估算式中必须同时考虑离子间交叉弛豫。从激活离子能级跃迁速率方程和激光、抽运光传输方程推导出端面抽运的包含交叉弛豫几率等光学参量的激光阈值的理论估算式。用这些方程讨论了Tm：YVO4和Tb，Tm：YVO4的1．5μm和1．9μm波长的激光性能，并论述了Tb3 离子的作用。结果表明。Tb3 离子的的掺入，增加1．5μm波段激光的强度，降低阈值能量，但对1.9μm波长激光有负面作用。     

介质阻挡均匀大气压辉光放电数值模拟研究

通过数值求解一维电子、离子连续性方程和动量方程，以及电流连续性方程，计算了氦气介 质阻挡大气压辉光放电电子、离子密度和电场在放电空间的时空分布，以及放电电流密度和 绝缘介质板充电电荷密度随时间的变化. 分析讨论所加电压频率、幅值及介质板性质等对均 匀大气压辉光放电性质的影响. 当外加电压频率足够高时，大量离子被俘获在放电空间，空 间电荷场又引起足够多的电子滞留在放电空间. 这些种子电子使得在大气压下发生汤森放电 ，放电空间结构类似于低气压辉光放电，即存在明显的阴极位降区、负辉区、法拉第暗区和 等离子体正柱 关键词： 大气压辉光放电 介质阻挡 数值模拟 等离子体     

Nonlinear ion‐acoustic cnoidal wave in electron‐positron‐ion plasma with nonextensive electrons

Effects of plasma nonextensivity on the nonlinear cnoidal ion‐acoustic wave in unmagnetized electron‐positron‐ion plasma have been investigated theoretically. Plasma positrons are taken to be Maxwellian, while the nonextensivity distribution function was used to describe the plasma electrons. The known reductive perturbation method was employed to extract the KdV equation from the basic equations of the model. Sagdeev potential, as well as the cnoidal wave solution of the KdV equation, has been discussed in detail. We have shown that the ion‐acoustic periodic (cnoidal) wave is formed only for values of the strength of nonextensivity (q). The q allowable range is shifted by changing the positron concentration (p) and the temperature ratio of electron to positron (σ). For all of the acceptable values of q, the cnoidal ion‐acoustic wave is compressive. Results show that ion‐acoustic wave is strongly influenced by the electron nonextensivity, the positron concentration, and the temperature ratio of electron to positron. In this work, we have investigated the effects of q, p, and σ on the characteristics of the ion‐acoustic periodic (cnoidal) wave, such as the amplitude, wavelength, and frequency.     

Rogue wave triplets in an ion-beam dusty plasma with superthermal electrons and negative ions

A new dust ion-acoustic wave structure called ‘Rogue wave triplets’ is investigated in an unmagnetized plasma consisting of stationary negatively charged dust grains, charged positive and negative ions, and electrons obeying kappa distribution, which is penetrated by an ion beam. The reductive perturbation theory is used to derive the nonlinear Schrödinger equation governing the dynamics as well as the modulation of wave packets. The rogue wave triplets which are composed of three separate Peregrine breathers can be generated in the modulation instability region. It has been suggested that a laboratory experiment be performed to test the theory presented here.     

Korteweg-de Vries方程的准孤立子解及其在离子声波中的应用

应用推广的tanh函数展开法,给出了Korteweg-de Vries方程具有准孤立子行为的两组孤子-椭圆周期波解,其中一组为新解.推导了均匀磁化等离子体中描述离子声波动力学行为的Korteweg-de Vries方程,发现电子分布、离子电子温度比、磁场大小、磁场方向对离子声准孤立子的波形具有显著影响.     

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.     

一维非线性声波传播特性

针对一维非线性声波的传播问题进行了有限元仿真和实验研究. 首先推导了一维非线性声波方程的有限元形式, 含有高阶矩阵的非线性项导致声波具有波形畸变、谐波滋生、基频信号能量向高次谐波传递等非线性特性. 编制有限元程序对一维非线性声波进行了计算并对仿真得到的畸变非线性声波信号进行处理, 分析其传播性质和物理意义. 为验证有限元计算结果, 开展了水中的非线性声波传播的实验研究, 得到了不同输入信号幅度激励下和不同传播距离的畸变非线性声波信号. 然后对基波和二次谐波的传播性质进行详细讨论, 分析了二次谐波幅度与传播距离和输入信号幅度的变化关系及其意义, 拟合出二次谐波幅度随传播距离变化的方程并阐述了拟合方程的物理意义. 结果表明, 数值仿真信号及其频谱均与实验结果有较好的一致性, 证实计算方法和结果的正确性, 并提出了具有一定物理意义的二次谐波随传播距离变化的简单数学关系. 最后还对固体中的非线性声波传播性质进行了初步探讨. 本研究工作可为流体介质中的非线性声传播问题提供理论和实验依据.     

Lower order three-dimensional Burgers equation having non-Maxwellian ions in dusty plasmas

The dust acoustic(DA) shock wave with dust charge fluctuations, non-Maxwellian ions, and non-isothermal electrons is studied theoretically. The perturbation technique is employed to derive the lower order three-dimensional(3D) Burgers equation, and shock wave solution is explored by the tan-hyperbolic method. The effects of flat trapped and trapped electron distributions in the presence of Maxwellian and non-Maxwellian ions on characteristics shock waves are observed. The temperature ratio of non-Maxwellian ion temperature and non-isothermal electron temperature is found to play an important role in forming the shock-like structure.     

非线性LC电路方程的显式精确行波解

理论上考察了具有耗散的非线性LC电路中的行波. 借助于作者最近发展的精确求解非线性偏微分方程的扩展的双曲函数方法解析地研究了模拟非线性电路中冲击波的四阶耗散非线性波动方程. 一致地获得了丰富的显式精确解析行波解, 包括精确冲击波解和奇异的行波解, 和三角函数有理形式的周期波解. 关键词： LC电路')" href="#">非线性LC电路 非线性耗散波动方程 冲击波 周期波     

Multi-dimensional quasi-simple waves in weakly dissipative flows

A multi-dimensional simple wave formalism is employed to formulate a multi-dimensional quasi-simple wave for a weakly dissipative fluid. This is a natural but nontrivial generalization of the so-called unidirectional quasi-simple wave. The method is more close to multi-orders analysis which is different from the standard perturbation method. Detailed solving up to the second order is presented for a 2D sound simple wave. A new 2D Burgers equation is derived for the wave phase. It essentially differs from the known 2D generalizations of the Burgers equation, e.g., from the Zabolotskaya-Khokhlov equation. The derived equation is investigated in the framework of group analysis of differential equations. Multi-parameter families of its exact solutions are constructed. Simplest solutions are chosen for analysis of their physical relevance in the initial variables.     

On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method

In this paper, we mainly study the time-space fractional strain wave equation in microstructured solids. He’s variational method, combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation. The main advantage of the variational method is that it can reduce the order of the differential equation, thus simplifying the equation, making the solving process more intuitive and avoiding the tedious solving process.Finally, the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method. The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics.     

有限磁场作用下等离子体背景中的切伦可夫不稳定性研究

 较高密度的相对论电子束注入等离子体中将会形成离子通道，在考虑了离子通道的影响下，推导出圆柱波导中更普遍的色散方程，并计算出考虑离子通道和不考虑离子通道效应时的色散关系及电磁波的增长率。