平方反比律有心力场中经典轨道问题的另一种讲授方法

有心力场中质点动力学问题是理论力学教学中的典型课题之一.它有助加深学生对能量和角动量这两个概念及其守恒原理的理解.同时这个课题在天文学和物理学中也有重要实际意义. 这部分内容的一般教学体系是首先阐明质点在有心力场中运动的基本性质,然后写出质点在径向与横向的动力学方程以及能量与角动量的守恒方程,接着说明完整求解运动规律[r=r(t)与θ=θ(t)]的主要步骤.至此问题虽然形式上解决了,但由于所涉及的数学运算特别是积分结果t=t(r)在反演上的困难,一般教材并不按此步骤处理有关问题.人们更感兴趣的是轨道问题.讨论轨道问题的基本…     

双温度氩-氮等离子体热力学和输运性质计算

获得覆盖较宽温度和压力范围内的等离子体热力学和输运性质是开展等离子体传热和流动过程数值模拟的必要条件.本文通过联立Saha方程、道尔顿分压定律以及电荷准中性条件求解等离子体组分;采用理想气体动力学理论计算等离子体热力学性质;基于Chapman-Enskog方法求解等离子体输运性质.利用上述方法计算了压力为0.1, 1.0和10.0 atm (1 atm=101325 Pa),电子温度在300—30000 K范围内,非局域热力学平衡(电子温度不等于重粒子温度)条件下氩-氮等离子体的热力学和输运性质.结果表明压力和非平衡度会影响等离子体中各化学反应过程,从而对氩-氮等离子体的热力学及输运性质有较大的影响.在局域热力学平衡条件下,计算获得的氩-氮等离子体输运性质和文献报道的数据符合良好.     

空气放电非平衡等离子体的模拟计算

基于空气放电非平衡等离子体动力学,对空气放电进行了数值计算,分析了放电后等离子体中的主要粒子（N2(v6),N2(A3),O2(a1),O和O3）数密度随起始温度、电子数密度和约化场强的变化趋势。计算结果表明,随着初始温度的升高,空气放电产生的粒子数密度增加。温度为300 K时,放电产生的O原子数密度最大值约为4.90×7 cm-3,而当温度升高到400 K和500 K时,O原子数密度的最大值则相应地增加到5.2×1010 cm-3和5.51×1010 cm-3。约化场强的影响与温度类似,其中氮气的振动激发态N2(v6)数密度随约化场强的变化幅度不明显。电子数密度增加,粒子数密度大幅增加,氮分子的激发态N2(A3)粒子数密度与电子数密度保持严格的线性关系。     

速度函数v(t)与时间变量t的定义域分析

1 问题的提出 质点运动学中,变加速直线运动条件下速度大小的求解是重要内容之一.由于速度在物体运动过程中是时间t的函数,求解时往往先通过求其运动方程x=x(t),再由运动方程x(t)对时间t求导,得出任一时刻的速度v(t).v=v(t)是时间t的函数,在t≥0的时域内v(t)有定义.但在某些特殊情况下,求得的速度v(t)会产生与实际物理现象不符的情况,给初学者造成误解.如一长为5 m的梯子,顶端斜靠在竖直的墙面上,设t=0时,顶端离地面4 m,当顶端以2 m/s的速度沿墙面匀速下滑时.求在t=3 s时,下端的速度[1].     

关于氢等离子体光谱谱线迭合问题

本文首先求解了电子在级数型势场中的定态薛定谔方程条件是r→∞时V(r)→0;t≤2。得到决定电子定态能级和波函数的几个公式。作为这些公式的应用,文中以完全电离等离子体为例,利用德拜势讨论了氢等离子体光谱谱线的加宽和谱线的迭合问题。     

各向异性、弱相对论性等离子体的一般色散关系的计算

在处理等离子体加热与不稳定性问题时,其核心是写出色散方程并求解出色散关系。本文给出了在有不均匀磁场、不均匀等离子体密度分布(如TOKAMAK中的等离子体)下,电磁波几乎角向射入具有各向异性、弱相对论性麦克斯韦分布的等离子体的一般色散方程和求解的程序。在等离子体中很重要的的双指标F_ij函数可展开成单指标的F_i函数,进而用等离子体色散函数求值。并发现从F_I采用F_ij的递推关系求诸F_ij函数的值的方法,因误差太大不能采用。     

HL-2Aװ�����������˵��о�

用密度调制的方法研究了等离子体中粒子输运问题。采用了注入脉冲式补充送气和超声分子束两种不同的密度调制方法。在HL-2A装置常规欧姆放电的情况下,运用有限差分法和Nagashima矩阵技术,求解了粒子平衡方程。计算出了粒子的输运系数(对流速度v和扩散系数D)。研究了粒子输运系数与等离子体线平均密度之间的关系。实验结果表明,在欧姆放电的情况下,等离子体芯部的粒子对流速度方向始终是向内的,并且密度低时,粒子输运系数(粒子扩散系数D和对流速度v)较大;密度高时,粒子输运系数较小。     

AC等离子体辅助CH4低温氧化的分子激发作用

本文采用实验测量和数值模拟结合的方法,对AC放电下He/CH4/O2混合气中激发态对甲烷裂解和低温氧化的动力学贡献进行研究。基于HP-Mech,增加反应物的放电机理以及激发态参与的化学反应及其驰豫反应,建立CH4低温氧化机理。采用化学反应动力学求解器CHEMKIN中的两段式Plasma-PSR模型模拟放电过程及化学反应过程。该动力学模型能较好地预测反应物的消耗和主要产物的生成,反应路径分析表明激发态物质CH4(v),O2(v),O2(a^1△g)等通过链式反应CH4(v)+OH→CH3+H2O,O2(v)+H→OH+O,O2(a^1△g)+H→OH+O促进活性自由基和产物的生成。     

������ŵЭǿ���ܶ��Ŷ��Լ���������Ӱ���ʵ���о�

利用静电探针阵列对HL-2A边缘等离子体径向和极向速度进行了测量,获得了最后闭合磁面附近湍流的雷诺协强〈(v)r(v)θ〉以及(v)r和(v)θ间相位差的剖面.实验表明,虽然(v)r、(v)θ的幅值对雷诺协强的大小会有影响,但雷诺协强的变化趋势主要取决于二者相位差的变化;另一方面,欧姆放电以及不同电子回旋加热功率L模放电条件下的实验结果显示,密度扰动引起的粒子输运所带来的极向动量输运的贡献与雷诺协强项对极向动量输运的贡献是可比的.这表明在分析湍流引起的动量输运时必须考虑粒子输运的贡献.     

旋度概念的从头构建法

通过基本的途径,没有利用斯托克斯公式,导出矢量场环量面密度的计算公式.指出同一点处矢量场f(r,t)绕不同轴的环量面密度不同,Δ×f的大小等于环量面密度的最大值,Δ×f的方向沿着环量面密度取最大值时回路所缠绕的轴的方向,绕n轴的环量面密度等于Δ×f沿n轴的分量.这样的一个矢量场Δ×f叫做f(r,t)的旋度.并且指出计算矢量场沿无穷短线段的线积分时人们常犯的错误.     

Kinetic equations for autocorrelation functions in dilute gases

We show that in the case of a dilute gas of neutral particles kinetic equations for autocorrelation functions such as $$\left\langle {\hat f\left( {r,v,t} \right)\hat f\left( {r\prime v\prime ,t\prime } \right)} \right\rangle ,where\hat f\left( {r,v,t} \right) = \sum {_{i = 1}^N } \delta \left( {r - r_i \left( t \right)} \right)\delta \left( {v - v_i \left( {tt} \right)} \right)$$ , can be obtained in a very simple manner by the use of the truncated BBGKY hierarchy. The resulting equations correspond to the low-density limit of the results of van Leeuwen and Yip. Moreover, the derivation does not make use of the Bogoliubov adiabatic approximation, and therefore includes non-Markovian effects which can be important in describing light scattering from gases and the collisional narrowing of atomic dipole radiation. The resulting equations in the long-wavelength limit correspond to the non-Markovian Boltzmann equation for the self-correlation part and the non-Markovian, linearized Boltzmann equation for the total autocorrelation function.     

Transport Equations of Plasma in a Curvilinear Magnetic Field

The problem of transport equations of a collisional plasma in a curvilinear magnetic field is studied. Two main approaches to this problem are presented: that based on using the Boltzmann kinetic equation and the drift kinetic equation approach. In the frame of the first approach a multimoment transport equation set is found which is more general than the transport equation sets of Braginskii and Grad. The tensor equations of this set are described in an arbitrary curvilinear coordinate system. This allow to use these equations in problems of a plasma confined in toroidal magnetic configurations. Simplification of the multimoment transport equation set in the case of high magnetic field is performed. In the frame of the drift kinetic equation approach, a generalization of the drift transport equations derived earlier by the authors (Zh. Eksp. Teor. Fiz. 83 (1982) 139) is given.     

Solving the Boltzmann equation in a 2-D-configuration and2-D-velocity space for capacitively coupled RF discharges

A new kinetic scheme, the generalized Monte Carlo flux (GMCF) method, provides the electron particle distribution function in phase space, f(ν, μ, r, z, t) (ν: speed, μ: velocity angle, r: radial position, z: axial position, and t: time), for solving the Boltzmann equation in modeling capacitively coupled RP discharges. For a simulation with spatial- and temporal-varying fields in RF discharges, the GMCF method handles the collision terms of the Boltzmann equation by using one transition matrix to compute the collision transition between velocity space cells. An anti-diffusion flux transport scheme is developed to overcome the numerical diffusion in the velocity and configuration spaces. The major advantages of the GMCF method are the increase in resolution in the tail of distribution functions and the decrease of computation time. The GMCF calculation results in terms of microscopic electron distribution function and macroscopic quantities of density, electric field and ionization rate, are presented for RF discharges and compared with other kinetic and fluid simulation and experimental results. The effects of the induced radial electric field in the sheath close to the radial wall in a cylindrically symmetric parallel-plate geometry are discussed     

生物质在闪速加热条件下的挥发特性研究

生物质快速热裂解技术是实现生物质液化的重要手段。研究在闪速加热条件下(达到104K／s)生物质的热挥发特性对于热裂解装置的设计非常重要。在等离子体加热的层流炉上对于几种典型的生物质材料,包括玉米秸秆、麦秸、稻壳、椰子壳等,进行了实验研究,获得了它们热挥发的活化能、反应频率因子等。研究发现,在闪速加热条件下,生物质热挥发的动力学参数与升温速率无关。     

稠密气体中的输运现象和方位势氩的粘滞率和热导率

建议用推广的恩斯柯克方程(14),讨论稠密气体中的输运现象。指出空间关联函数Y(r)可以从状态方程的维里展开求得。文中给出了计算方位势稠密气体的粘滞率和热导率的公式以及计算关联函数的方法。用得到的结果,计算了温度为173K和348K的氩的粘滞率和温度为183K和348K的氩的热导率。在高密度区,计算结果与实验测定的符合程度,较之现有理论,有明显的改进。 关键词：     

A hybrid fluid–kinetic neutral model based on a micro–macro decomposition in the SOLPS-ITER plasma edge code suite

We present a hybrid fluid–kinetic model for the hydrogenic atoms in the plasma edge that is implemented in SOLPS-ITER. A micro–macro decomposition of the kinetic equation leads to a fluid model with a continuity and parallel momentum equation (implemented in B2.5) coupled to a kinetic correction equation (implemented in EIRENE). We assess the hybrid model for a high recycling fixed background plasma. The hybrid approach leads to a reduction of the Central Processing Unit(CPU) time required to obtain the same statistical error as the full kinetic Monte Carlo (MC) simulation with approximate factors of 1.7, 4.9, and 1.9 for the particle, parallel momentum, and electron energy source, respectively. However, there is an increase in CPU time for the ion energy source. By comparing the results with our in-house plasma edge code, we conclude that the hybrid performance can be improved by adapting some default MC features in EIRENE.     

Kinetic two-dimensional modeling of inductively coupled plasmasbased on a hybrid kinetic approach

In this paper, we present a two-dimensional (2-D) kinetic model for low-pressure inductively coupled discharges. The kinetic treatment of the plasma electrons is based on a hybrid kinetic scheme in which the range of electron energies is divided into two subdomains. In the low energy range the electron distribution function is determined from the traditional nonlocal approximation. In the high energy part the complete spatially dependent Boltzmann equation is solved. The scheme provides computational efficiency and enables inclusion of electron-electron collisions which are important in low-pressure high-density plasmas. The self-consistent scheme is complemented by a 2-D fluid model for the ions and the solution of the complex wave equation for the RF electric field. Results of this model are compared to experimental results. Good agreement in terms of plasma density and potential profiles is observed. In particular, the model is capable of reproducing the transition from on-axis to off-axis peaked density profiles as observed in experiments which underlines the significant improvements compared to models purely based on the traditional nonlocal approximation     

Self-diffusion in fluids with weak long-range forces

Diffusion of a test particle in a homogeneous classical fluid with weak long-range forces is studied. The dominant mean-field effect (Vlasov's theory) vanishes for symmetry reasons. Dynamical phenomena follow then from fluctuations of the effective potential energy felt by the propagating particle. The kinetic equation corresponding to this mechanism is derived with the use of the multiple-time-scale method. Its structure resembles very much that of the (linearized) Balescu-Lenard equation of hot plasma theory. It is shown that the kinetic equation holds only if no phase transition occurs in the system. The thermalization of the diffusing particle and the high-temperature and Lorentz gas limits are discussed.     

Scaling in Rate-Changeable Birth and Death Processes with Random Removals

We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.     

Non-equilibrium statistical mechanics in the general theory of relativity: II. Linear fields in a kinetic approximation

The first paper in this series introduced a new, manifestly covariant approach to non-equilibrium statistical mechanics in classical general relativity. The object of this second paper is to apply that formalism to the evolution of a collection of particles that interact via linear fields in a fixed curved background spacetime. Given the viewpoint adopted here, the fundamental objects of the theory are a many-particle distribution function, which lives in a many-particle phase space, and a many-particle conservation equation which this distribution satisfies. By viewing a composite N-particle system as interacting one- and (N ? 1)-particle subsystems, one can derive exact coupled equations for appropriately defined reduced one- and (N ? 1)-particle distribution functions. Alternatively, by treating all the particles on an identical footing, one can extract an exact closed equation involving only the one-particle distribution. The implementation of plausible assumptions, which constitute straightforward generalizations of standard non-relativistic “kinetic approximations”, then permits the formulation of an approximate kinetic equation for the one-particle distribution function. In the obvious non-relativistic limit, one recovers the well-known Vlasov-Landau equation. The explicit form for the relativistic expression is obtained for three concrete examples, namely, interactions via an electromagnetic field, a massive scalar field, and a symmetric second rank tensor field. For a large class of interactions, of which these three examples are representative, the kinetic equation will admit a relativistic Maxwellian distribution as an exact stationary solution; and, for these interactions, an H-theorem may be proved.