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.     

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。     

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...     

硬球势中相对论费米气体的热力学性质

用量子统计与数值模拟相结合的方法,在广义外势中相对论费米系统的热力学量的基础上,研究硬球势中相对论费米气体的热力学性质.得到了考虑相对论效应时系统的内能和热容量的解析表达式,分析了相对论效应对内能和热容量的影响.研究表明:与非相对论比较,相对论费米气体的内能和热容量更高;相对论特征量越大,热容量的转折温度越低;随着温度的升高,特征量越大,内能就越大.     

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.     

UF_6分子价轨道相对论效应的理论电子动量谱学研究

用非相对论、标量相对论和二分量相对论三种不同的密度泛函方法对UF_6分子的电子结构进行了量子化学计算,并利用编写的程序计算出了三种方法下各个价轨道的电子动量谱,比较了三种方法计算的价轨道能级及动量分布的差异.结果表明,相对论效应不仅使UF_6的能级劈裂和移动,而且对部分价轨道电子动量分布有显著的影响.     

等离子体湍流能量传输的尺度相关性

对于空间环境中近乎无碰撞的等离子体,可采用Vlasov方程进行理论描述,基于Vlasov方程,讨论了等离子体湍流能量传输和耗散的过程:由亚格子应力引起的尺度间的能量传输,电场做功,压强张量做功(压强张量与速度梯度张量的相互作用).通过混合Vlasov-Maxwell(HVM)数值模拟,进一步研究了能量传输通道之间的联系...     

强流相对论电子束双腔纵向自调制研究

当强流相对论电子束在类双腔速调管系统中传输时，会发生自调制现象. 利用这一现象可以 在无微波注入的情况下得到较好的微波输出，这是一种由强流相对论效应引起的自激振荡. 利用这一原理有可能研制出一类新型的微波器件. 对强流相对论电子束在这种物理机制作用 下发生起振的条件及传输机理进行了理论分析，并进行了数值模拟. 优化结果显示，利用4k A, 500kV的强流相对论电子束，可得到099GHz，800MW的微波输出，效率约40％. 关键词： 强流相对论电子束 自调制 反馈机制 数值模拟     

探测二茂铁外价轨道(e,2e)反应中的扭曲波效应

利用第三代高效率电子动量谱仪,分别在600和1500 eV两种不同入射电子能量下获得了二茂铁(ferrocene)分子外价轨道的电离能谱和电子动量谱的相关实验结果.并利用非相对论与标量相对论密度泛函方法计算出了二茂铁的重叠型和交错型两种不同构象的理论动量谱.两种构象的外价轨道一一对应,理论电子动量谱基本一样.对二茂铁的外价轨道,在低动量区观测到了强烈的扭曲波效应,这与这些轨道主要由铁原子的3d轨道构成有关.通过相对论和非相对论计算结果的比较,表明相对论效应对于二茂铁的外轨道动量分布几乎没有影响. 关键词： 二茂铁分子 电子动量谱 相对论效应 扭曲波效应     

相对论修正对麦克斯韦-玻耳兹曼分布律的影响

在本文中,分别推导了低速情形（E≈m0c^2＋p^2/2m0）和一般情形（E=√p^2c^2＋m0^2c^4）下考虑相对论修正的动量分布表达式和速率分布表达式,发现低速情形下修正后的动量分布形式与不考虑修正的动量分布在形式上一致,而速率分布形式发生了改变;对一般情形的动量分布函数和速率分布函数进行了数值模拟并对结果进行了必要讨论．我们发现当β减少时整个动量分布曲线向大动量区域延伸,当β较大,即温度较低使得p〈1时,一般情形将近似为低速情形．     

A conservative scheme for the relativistic Vlasov–Maxwell system

A new scheme for numerical integration of the 1D2V relativistic Vlasov–Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the cell at the beginning of each time step, we successfully integrate the system with no artificial loss of particles. Furthermore, splitting the equations into advection and interaction parts, the method conserves the sum of the kinetic energy of particles and the electromagnetic energy. Three test problems, the gyration of particles, the Weibel instability, and the wakefield acceleration, are solved by using our scheme. We confirm that our scheme can reproduce analytical results of the problems. Though we deal with the 1D2V relativistic Vlasov–Maxwell system, our method can be applied to the 2D3V and 3D3V cases.     

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.     

Relativistic Magnetosonic Solitary Wave in Magnetized Multi-Ion Plasma

In the presence of an applied uniform magnetic field Bo, the properties of 2-dimensional （2D） magnetosonic solitary waves of relativistic amplitude in the plasma containing electron, light ions He^＋, and heavy ions O＋ are presented. In the weakly relativistic limit, a Kadomtsev Petviashvili （KP） equation is derived by reductive perturbation method. We give the N-soliton solution of the KP equation and find dromion solutions of a potential of the physical field. The interaction law of the dromions is obtained, which shows there is no exchange of energy, momentum, and angular momentum before and after interaction of the dromions except for phase shifts.     

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.     

Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system

Semi-Lagrangian (SL) methods have been very popular in the Vlasov simulation community , , , , , ,  and . In this paper, we propose a new Strang split SL discontinuous Galerkin (DG) method for solving the Vlasov equation. Specifically, we apply the Strang splitting for the Vlasov equation [6], as a way to decouple the nonlinear Vlasov system into a sequence of 1-D advection equations, each of which has an advection velocity that only depends on coordinates that are transverse to the direction of propagation. To evolve the decoupled linear equations, we propose to couple the SL framework with the semi-discrete DG formulation. The proposed SL DG method is free of time step restriction compared with the Runge–Kutta DG method, which is known to suffer from numerical time step limitation with relatively small CFL numbers according to linear stability analysis. We apply the recently developed positivity preserving (PP) limiter [37], which is a low-cost black box procedure, to our scheme to ensure the positivity of the unknown probability density function without affecting the high order accuracy of the base SL DG scheme. We analyze the stability and accuracy properties of the SL DG scheme by establishing its connection with the direct and weak formulations of the characteristics/Lagrangian Galerkin method [23]. The quality of the proposed method is demonstrated via basic test problems, such as linear advection and rigid body rotation, and via classical plasma problems, such as Landau damping and the two stream instability.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

A generalized quantum kinetic equation for models of relativistic nuclear dynamics

Zubarev’s method of non-equilibrium statistical operator is applied to problems of relativistic kinetic theory. Within this method, a generalized relativistic quantum kinetic equation for the relativistic Wigner function is derived with taking into account the drift term of the Vlasov type and the collision integral of the second order in particle interaction. It is shown that this result holds as well for gauge invariant theories in the case of slowly changing fields. An advantage of the developed approach is exemplified by the consideration of relativistic nuclear matter within the Walecka and Nambu-Jona-Lasinio models. Typical relativistic effects like retardation, spin degrees of freedom and antiparticle evolution are taken into consideration.     

Wavefunctions for Particles with Arbitrary Spin

By solving rigorously the relativistic wave equations derived from Bargmann-Wigner equation for arbitrary spin,the relativistic wavefunctions in momentum representation for particles with arbitrary spin are deduced.     

On the filamentation instability in degenerate relativistic plasmas

The filamentation instability of the electromagnetic (EM) beam in an underdense plasma with high level of degeneracy is examined by means of the momentum equation, continuity equation and Maxwell's equations. It has been demonstrated that the instability develops for weakly as well as strongly relativistic degenerate plasma and arbitrary strong amplitude of EM beams.     

Phase-space moment-equation model of highly relativistic electron-beams in plasma-wakefield accelerators

We formulate a new procedure for modelling the transverse dynamics of relativistic electron beams with significant energy spread when injected into plasma-based accelerators operated in the blow-out regime. Quantities of physical interest, such as the emittance, are furnished directly from solution of phase space moment equations formed from the relativistic Vlasov equation. The moment equations are closed by an Ansatz, and solved analytically for prescribed wakefields. The accuracy of the analytic formulas is established by benchmarking against the results of a semi-analytic/numerical procedure which is described within the scope of this work, and results from a simulation with the 3D quasi-static PIC code HiPACE.