Vlasov方程的数值求解

研究环形加速器中的纵向微波不稳定性,发展了Vlasov方程在(J,φ)坐标下用正交多项式展开的数值计算程序,并把它用于对微波不稳定性的初步研究.     

全相对论性Vlasov－Maxwell方程的解析解

本文给出了全相对论性Ｖｌａｓｏｖ－Ｍａｘｗｅｌｌ方程的解析解。该解是Ｓｗａｄｅｓｈ［１］结果的推广，它既适用于高温聚变等离子体，也适用于有相对论漂移速度的等离子体。     

巨共振激发的相对论效应

在相对论量子场论（ＱＨＤ）的框架下,得到了相对论线性Ｖｌａｓｏｖ方程．依此计算了球形核１６Ｏ、４０Ｃａ、９０Ｚｒ及２０８Ｐｂ的巨偶极共振的强度函数分布．结果表明,相对论效应是不可忽视的．计算得到的巨共振中心能量稍高于非相对论线性Ｖｌａｓｏｖ方程给出的对应值,与实验结果比较都有较好的符合．对计算结果作了简要的讨论,发现核子有效质量和平均场自旅轨道耦合力对巨共振能量有重要影想． In the framework of relativistic quantum hadron dynamical (QHD) theory,under semiclassical approximation and taking into vacuum fluctuation, a relativistic Vlasov equation (RVE) has been derived. Using RVE and considering other relativistic effects, we have studied the isovector dipole giant resonances built on ground state in spherical nuclei.The main results show that the resonance energies for each multipole are larger than those obtained from the non-relativistic classical Vlasov approach...     

非旋转银河系的重力不稳定性

银河系中星体分布的重力不稳定性在天文物理是个熟知的问题.尝试以加速器物理的方法初步分析了这个现象, 得到非旋转银河系在它的大小超过某阈值时会呈现不稳定现象的结论,而此阈值与银河系的质量密度有关.     

△粒子的相对论BUU方程

在与核子相对论BUU方程相统一的框架内,利用闭合时间回路格林函数方法导出了△粒子的相对论BUU方程,并同时给出平均场与碰撞项的解析表达式.结果表明,核子与△粒子的BUU方程是相互联立的.     

全相对论性Vlasov—Maxwell方程的解析解

本文给出了全相对论性Ｖｌａｓｏｖ－Ｍａｘｗｅｌｌ方程的解析解。该解是Ｓｗａｄｅｓｈ＾［＾１＾］结果的推广，它既适用于高温聚变等离子体，也适用于有相对论漂移速度的等离子体。     

相对论动力学方程的一个简单例解

采用在牛顿力学中常用的方法,用一种简洁的数学形式给出了一维运动情形下受恒力作用的粒子的相对论动力学方程的一个例解,详细讨论了相对论粒子的加速度、速度和运动方程与牛顿力学中对应物理量的区别和联系.     

相对论Dirac方程中矩阵维数的证明

利用Ｄｉｒａｃ方程中α，β矩阵的代数性质，构成Ｄｉｒａｃ群，再用群的性质，证明α，β矩阵一定是４×４矩阵，进而找出Ｐａｕｌｉ－Ｄｉｒａｃ表象中α，β矩阵的具体表示形式。     

狭义相对论中没有“矛盾方程”

根据洛伦兹变换把两个惯性系的坐标原点的时空坐标从一个坐标系变换到另一坐标系,从相对运动的角度说明洛伦兹变换是自洽的,运动物体上发生的自然过程比起静止物体的过程延缓了,并且两个坐标系中的观察者都认为对方的时钟变慢,是“动钟变慢”而非“动钟变快”,不会导致“矛盾方程”,不能混淆同一事件的变换规律与两个事件的变换结果．     

电子束能量沉积的相对论Fokker-Planck方程的计算方法

针对相对论电子束在高密度等离子体中的能量沉积过程,建立三维动量空间中快电子能量沉积的相对论Fokker-Planck方程的可计算物理模型,构造数值算法并研制数值模拟程序.通过与解析模型和蒙特卡罗模拟相比较,验证数值方法和程序的可靠性.在二维动量空间的模拟基础上,通过计算能量区间为0.5 MeV~3.5 MeV的快电子在背景密度为300 g·cm^-3的氘氚等离子体中的能量沉积过程,发现由于碰撞效应使平均散射角趋近平衡,三维动量空间计算快电子连续射程和穿透深度与二维结果基本一致.     

Landau damping in a bounded magnetized plasma column

The damping decrement of Landau damping and the effect of thermal velocity on the frequency spectrum of a propagating wave in a bounded plasma column are investigated.The magnetized plasma column partially filling a cylindrical metallic tube is considered to be collisionless and non-degenerate.The Landau damping is due to the thermal motion of charge carriers and appears whenever the phase velocity of the plasma waves exceeds the thermal velocity of carriers.The analysis is based on a self-consistent kinetic theory and the solutions of the wave equation in a cylindrical plasma waveguide are presented using Vlasov and Maxwell equations.The hybrid mode dispersion equation for the cylindrical plasma waveguide is obtained through the application of appropriate boundary conditions to the plasma-vacuum interface.The dependence of Landau damping on plasma parameters and the effects of the metallic tube boundary on the dispersion characteristics of plasma and waveguide modes are investigated in detail through numerical calculations.     

Relativistic BBGKY Theory and Collision Integral of Generalized Boltzmann Equation in a Relativistic Magnetized Plasma

Usually, only Coulomb interactions between charged particles which are independent of time are considered in BBGKY theory of a nonrelativistic plasma. In relativistic case, the induced electromagnetic forces between charged particles which are dependent on time obviously should be considered. A Lorentz-covariant generalized n-time Liouville equation for classical plasma is established. A convenient form applicable to the laboratory frame of this equation is also given. The relativistic BBGKY hierarchy is developed in which both Coulomb and electromagnetic forces between particles are included. A method for solving the relativistic pair correlation equation is given in polarization approximation. A new formula for calculating collision integral in terms of discrete particle Green functions is given. A number of generalized Boltzmann equations for relativistic plasmas are derived.     

Relativistic Landau quantization in the spiral dislocation spacetime

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime.We show that analytical solutions to the Dirac equation can be obtained,where the spectrum of energy corresponds to the relativistic Landau levels.We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.     

Landau damping of longitudinal oscillation in ultra- relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.     

Higher-order Hamiltonian fluid reduction of Vlasov equation

From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson bracket of this model from the Poisson bracket of the Vlasov equation, and we discuss the associated Casimir invariants.     

介子束缚态相对论本征方程的非微扰重整化

介子结合态本征方程中δ相互作用可用T矩阵进行非微扰重整化,深入理解重整化的一些基本问题:物理结果与重正化点的选取无关,T矩阵非微扰重整化的物理实质. Nonperturbative T-matrix renormalization of the relativistic eigen equation for meson mass spectra is described and the expressions for eigen mass spectra and eigen wave functions are given.     

Multi-moment advection scheme for Vlasov simulations

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one-and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.     

The Relativistic Boltzmann Equation and Two Times

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter τ. The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of τ. If t(τ) increases with τ, the worldline may be associated with a normal particle, but if it is decreasing in τ, it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time.