相对论磁化等离子体的广义玻尔兹曼方程碰撞项

本文采用Ｋｌｉｍｏｎｔｏｖｉｃｈ方法导出了相对论磁化等离子体的广义玻尔兹曼方程碰撞项，计算出带电粒子间的感应电磁力对碰撞项的贡献。     

考虑二维效应和相对论效应时低杂波电流驱动部分模拟结果

本文介绍低杂波电流驱动模拟计算编码中福克－普朗克方程的数值求解。考虑了螺距角散射造成的高垂直温度效应（二维效应）和相对论效应。同时．福克－普朗克方程中包括了描述尾部电子约束的项。数值结果表明，二维效应和相对论效应的加入均能提高电流驱动效率。驱动电流随尾部电子约束改善而增加。     

△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.     

在非相对论框架中导出泡利方程——经典电动力学与量子力学不一致之一例

在非相对论框架内,从非相对论薛定谔方程出发,将自由电子的非相对论哈密顿算符开方,推出了自由的两分量泡利旋量满足的动力学方程;进而在经典外电磁场中,利用最小耦合原理,推出了在外电磁场中非相对论电子满足的泡利方程.在此基础上,讨论经典电动力学与量子力学不一致之处,并从群表示论和量子化对粒子的自旋进行了分析.     

重离子碰撞两体关联输运理论Ⅲ.半经典近似下的数值计算

为了验证由相干单粒子波函数和两体关联动力学所建立的非相对论条件下的重离子碰撞两体关联输运理论的有效性,利用没有碰撞项的量子分子动力学,即时间相关的Hartree-Fock方法的经典近似,实现了两体关联输运理论在半经典近似下的数值计算.计算结果表明:这种两体关联输运理论的确能够有效地描述重离子碰撞过程中的输运和耗散过程.     

托卡马克等离子体不同运行模式下的电子回旋波电流驱动

在给定等离子体密度分布下，从电子、离子的能量方程出发，根据不同运行模式下等离子体的热传导率不同，分别求出了中心负剪切模式，常规剪切H模式和L模式下的等离子体温度分布，然后通过求解波迹方程与相对论情况下的Fokker-Planck方程，分别计算了这些模式下的电子回旋波电流驱动和波功率沉积.得到在中心负剪切下，驱动电流最大，驱动效率最高，功率沉积和电流分布区间跨度大；在常规剪切H模式下，驱动电流较小，分布区间跨度比较窄，驱动效率相对较低；在常规剪切L模式，驱动电流效率最低，分布区间跨度也非常集中. 关键词： 托卡马克 电子回旋波电流驱动 中心负剪切 常规剪切     

有限β环形等离子体二维漂移波本征模方程

本文从略去碰撞项的漂移动力方程出发,利用同心圆截面托卡马克位形,在m_e/m_i≤β<<1的条件下(m_i及m_e分别是离子和电子的质量),导出了有限β环形等离子体二维本征模方程。所得方程可以用来研究二维低频漂移波及高m气球模的稳定性。     

快点火中相对论电子束能量沉积的动理学研究

针对相对论快电子束在高密度压缩芯区等离子体中的能量沉积过程开展物理建模、程序研制和数值模拟研究。从等离子体粒子碰撞的基本物理出发,综合考虑了高能电子与背景等离子体之间的短程两体碰撞过程和长程集体效应,建立了相对论Fokker-Planck动理学模型,通过采用球谐展开的方法,推导得到了适于数值求解的方程形式并根据方程特点开展相应的数值算法研究及程序研制并完成了物理考核,对快点火能量沉积的典型物理算例进行了模拟研究,并针对即将在神光Ⅱ升级装置上开展的快点火物理实验进行了初步的物理分析。     

快点火中相对论电子束能量沉积的动理学研究

针对相对论快电子束在高密度压缩芯区等离子体中的能量沉积过程开展物理建模、程序研制和数值模拟研究。从等离子体粒子碰撞的基本物理出发,综合考虑了高能电子与背景等离子体之间的短程两体碰撞过程和长程集体效应,建立了相对论Fokker-Planck动理学模型,通过采用球谐展开的方法,推导得到了适于数值求解的方程形式并根据方程特点开展相应的数值算法研究及程序研制并完成了物理考核,对快点火能量沉积的典型物理算例进行了模拟研究,并针对即将在神光Ⅱ升级装置上开展的快点火物理实验进行了初步的物理分析。     

无穷深势阱中相对论粒子的矩阵元及其经典近似

对于无穷深势阱中自旋为０(满足Klein-Gordon方程)和自旋为1/2(满足Dirac方程)的相对论粒子, 分别计算了坐标、动量以及速度算符的矩阵元. 在大量子数极限下, 这些矩阵元给出相应的经典物理量(这里是狭义相对论中的有关量), 并且满足正确的经典关系. 从而表明, Heisenberg对应原理对这样的相对论体系也适用. 关键词： 无穷深势阱 Klein-Gordon方程 Dirac方程 Heisenberg对应原理     

Relativistic entropy and related Boltzmann kinetics

It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fixes univocally the entropy of the system, which turns out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect to its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitly remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativistic Boltzmann equation, obeys the H-theorem and predicts a stationary stable distribution, presenting power law tails in the high-energy region. The ensued relativistic kinetic theory preserves the main features of the classical kinetics, which recovers in the c \( \rightarrow\) ∞ limit.     

Collisional relaxation of superthermal electrons generated by relativistic laser pulses in dense plasma

Energy relaxation of the hot electron population generated by relativistic laser pulses in overdense plasma is analyzed for densities ranging from below to 1000 times solid density. It is predicted that longitudinal beam-plasma instabilities, which dominate energy transfer between hot electrons and plasma at lower densities, are suppressed by collisions beyond solid density. The respective roles of collisional energy transfer modes, i.e., direct collisions, diffusion, and resistive return current heating, are identified with respect to plasma density. The transition between the kinetic and the collisional regimes and scalings of collisional process are demonstrated by a fully integrated one-dimensional collisional particle simulation.     

Kinetics of the isotropic expansion of a uniform electron-photon plasma

An analysis is performed of the main stages in the expansion of an electron-photon plasma with collisional processes taken into account. A relativistic Fokker-Planck equation for the electrons in the Compton stage of the expansion is derived from the general covariant kinetic equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 53–57, September, 1982.     

Kinetic theory of radiation in non-equilibrium relativistic plasmas

Many-particle QED is applied to kinetic theory of radiative processes in many-component plasmas with relativistic electrons and non-relativistic heavy particles. Within the framework of non-equilibrium Green’s function technique, transport and mass-shell equations for fluctuations of the electromagnetic field are obtained. We show that the transverse field correlation functions can be decomposed into sharply peaked (non-Lorentzian) parts that describe resonant (propagating) photons and off-shell parts corresponding to virtual photons in plasmas. Analogous decompositions are found for the longitudinal field correlation functions and the correlation functions of relativistic electrons. As a novel result a kinetic equation for the resonant photons with a finite spectral width is derived. The off-shell parts of the particle and field correlation functions are shown to be essential to calculate the local radiating power in relativistic plasmas and recover the results of vacuum QED. The influence of plasma effects and collisional broadening of the relativistic quasiparticle spectral function on radiative processes is discussed.     

Normal modes of a relativistic quantum plasma; The one-component plasma

The normal modes of a relativistic electron gas are studied on the basis of the Boltzmann-Vlasov kinetic equation via a projection operator formalism. A general framework is constructed in which the fully relativistic Vlasov self-consistent force term appears as a symmetric operator acting in the Hilbert space of one-particle states. The plasma-dynamical equations are obtained by projecting onto the subspace consisting of the charge, energy and momentum densities, plus the nonconserved current density. The eigenmodes of these equations include two transverse and two longitudinal plasma modes, and one damped heat mode. They are explicitly calculated up to second order in the wave vector and to first order in the collision frequency.     

Moment Systems Derived from Relativistic Kinetic Equations

In this paper, we are interested in the derivation of macroscopic equations from kinetic ones using a moment method in a relativistic framework. More precisely, we establish the general form of moments that are compatible with the Lorentz invariance and derive a hierarchy of relativistic moment systems from a Boltzmann kinetic equation. The proof is based on the representation theory of Lie algebras. We then extend this derivation to the classical case and general families of moments that obey the Galilean invariance are also constructed. It is remarkable that the set of formal classical limits of the so-obtained relativistic moment systems is not identical to the set of classical moments quoted in Ref. 21 and one could use a new physically relevant criterion to derive suitable moment systems in the classical case. Finally, the ultra-relativistic limit is considered.     

Kinetic theory of the plasma-dynamical modes and the transport coefficients of a relativistic plasma

The kinetic equation of an inhomogeneous relativistic plasma, consisting of an electron gas and a radiation field, is studied with particular regard to its eigenvalues in the hydrodynamical limit. The treatment is classical for the particles and quantum-mechanical for the field oscillators.After a suitable regularization, the eigenvalues are obtained by a perturbation theory through second order in the strength of the gradients. It is shown that these eigenvalues are in exact correspondence with the macroscopic relativistic plasma-dynamical modes. The important role played by the Vlassov operator in building up the peculiar structure of these modes is underlined. From a comparison of the macroscopic and microscopic eigenvalues we obtain general expressions for the thermal conductivity, the shear viscosity and the bulk viscosity of a relativistic plasma. The contribution of the radiation field to these quantities is a noteworthy feature of these expressions.     

Stability of the Relativistic Maxwellian in a Collisional Plasma

The relativistic Landau-Maxwell system is the most fundamental and complete model for describing the dynamics of a dilute collisional plasma in which particles interact through Coulombic collisions and through their self-consistent electromagnetic field. We construct the first global in time classical solutions. Our solutions are constructed in a periodic box and near the relativistic Maxwellian, the Jüttner solution.Acknowledgements The research is supported in part by NSF grants.     

Kinetic Thomas-Fermi solutions of the Gross-Pitaevskii equation

Approximate solutions of the Gross-Pitaevskii (GP) equation, obtained upon neglection of the kinetic energy, are well known as Thomas-Fermi solutions. They are characterized by the compensation of the local potential by the collisional energy. In this article we consider exact solutions of the GP-equation with this property and definite values of the kinetic energy, which suggests the term “kinetic Thomas-Fermi” (KTF) solutions. Despite their formal simplicity, KTF-solutions can possess complex current density fields with unconventional topology. We point out that a large class of light-shift potentials gives rise to KTF-solutions. As elementary examples, we consider one-dimensional and two-dimensional optical lattice scenarios, obtained by means of the superposition of two, three and four laser beams, and discuss the stability properties of the corresponding KTF-solutions. A general method is proposed to excite two-dimensional KTF-solutions in experiments by means of time-modulated light-shift potentials.