包含辐射阻尼效应的束流纵向微波不稳定性研究

 包含束团辐射阻尼效应的Fokker-Planck方程是比较完备地描述粒子运动状态的束团分布方程。在Fokker-Planck方程的基础上采用微扰展开方法对纵向微波不稳定性的发生机制及过程进行了分析，并且根据计算结果，研究了辐射阻尼效应对纵向微波不稳定性的影响。在计算中包含了静态的势阱畸变效应。计算结果表明，包含辐射阻尼效应的纵向微波不稳定性阈值高于没有辐射阻尼效应的不稳定性阈值。     

格点规范理论中Fokker-Planck方程的平均场解

将格点规范理论中的演化分布函数逐步地分解为单链变量分布函数的乘积,我们得到了Fokker-Planck方程的平均场近似解.     

空间电荷阻抗和纵向束团定态解

回顾了加速器的阻抗模型,讨论了空间电荷阻抗和管道壁阻的高频衰减特性.从Vlasov?Maxwell方程出发提出了当存在类似空间电荷阻抗时,在任意外场、任意分布下,束团定态分布的一般解法,并以两种重要分布为例,给出重离子加速器强流参数下的定态分布.解得的定态分布可以进一步应用于稳定性分析和计算机模拟计算.由定态分布的求解得出了对束团中的朗道阻尼和稳定性研究非常重要的纵向“色散”函数.     

非均匀分布纵向耦合束不稳定性的研究

利用Vlasov方程研究了非均匀分布情形下的纵向多束团不稳定性.当束团均匀分布时,由该方法所得到的结果与ZAP程序给出的结果一致;对于非均匀分布的情形,由该分析解得到的结果与模拟跟踪方法所得到的结果接近.     

球坐标动量空间下相对论Vlasov方程的数值算法

针对相对论Vlasov方程动量区间跨度大、难以计算的困难,将相对论Vlasov方程在球坐标动量空间中进行数值求解.对相对论Vlasov方程球坐标动量空间构造4阶非分裂守恒型数值格式.数值模拟相对论Landau阻尼问题并与解析理论进行比较,验证数值模型和算法的有效性.对激光等离子体相互作用进行初步模拟分析,表明通过采用球坐标下的动量空间,可在相对较少动量网格情形下,获得与粒子模拟可相互验证的结果.     

束团伸长效应的理论研究

 论述了束团伸长效应现有理论的不足和困难。在强流条件下，用统计力学理论解出粒子纵向分布函数，从而将目前关于束团伸长现象的平衡理论和微波不稳定性理论用统一的形式加以描述。并且在理论上证明了束团伸长效应在本质上是多束团效应，指出了窄带阻抗对束团伸长效应的重要贡献。     

非线性漂移的Fokker-Planck方程的非定态解

本文用格林函数方法讨论Fokker-Planck方程的非定态问题,将标度理论的“标度区”和“最终时区”统一考虑。在标度理论的头两个时区,所得结果与标度理论的解一致。当t→∞时,所得的非定态解趋于Fokker-Planck方程的定态解,解决了标度区分布函数在稳定点发散的问题,避免了“标度区”和“最终时区”对接的困难。 关键词：     

有相对论效应的二维Fokker-Planck程序包的开发与应用

求解没有相对论效应的Fokker-Planck方程的程序包已于2002年完成。求解有相对论效应的Fokker-Planck方程的程序包，由意大利引进，该程序包是反跳平均的，考虑了捕获电子效应、各种不同加热模式下的准线性扩散系数。可用于描述托卡马克辅助加热情形的等离子体粒子的动力学过程，能够计算环形几何下电子和离子的分布函数，包含了波加热，中性束注入，粒子损失等效应。对HL-1M装置和HL-2A装置的实验数据分析非常有用。     

用二维含时Fokker-Planck方程分析Tokamak中α粒子的输运

按分布函数的定义不同,描述高能带电粒子在等离子体中输运的-Planck方程有不同的形式。从数值计算的观点出发对两种不同形式的Fokker-Planck方程作了比较和评价,并指出Fokker-Planck碰撞项可解释为速度空间的对流扩散项。在此基础上用有限差分方法求解二维(速度一维,几何一维)含时Fokker-Planck方程,编制了计算程序CAPT,并将其应用于α粒子的输运研究。最后计算了典型的Tokamak D-T聚变堆参数下α粒子的损失,并给出了堆内α粒子的分布及损失α粒子的速度分布。     

BEPC上离子引起的耦合束团不稳定性分析

对在北京正负电子对撞机(BEPC)上观测到的由离子引起的电子束二极耦合束团不稳定性的实验数据作了分析处理,给出了这种二极耦合束团不稳定性的边带.首先用离子俘获的线性两束流理论定量计算了离子引起的二极耦合束团不稳定性发生的阈值束流流强和不稳定性的增长时间,然后用基于束流–离子强弱作用模型的模拟程序跟踪了在实验情况下束流与离子的相互作用过程,跟踪结果成功地再现了离子引起的二极耦合束团不稳定性边带,并给出了比较合理的不稳定性增长时间.     

Short-time correlations of many-body systems described by nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations

Analytical expressions for short-time correlation functions, diffusion coefficients, mean square displacement, and second order statistics of many-body systems are derived using a mean field approach in terms of nonlinear Fokker–Planck equations and Vlasov–Fokker–Planck equations. The results are illustrated for the Desai–Zwanzig model, the nonlinear diffusion equation related to the Tsallis statistics, and a Vlasov–Fokker–Planck equation describing bunch particles in particle accelerator storage rings.     

A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma

The interaction of intense lasers with solid matter generates a hot plasma state that is well described by the Vlasov–Fokker–Planck equation. Accurate and efficient modeling of the physics in these scenarios is highly pertinent, because it relates to experimental campaigns to produce energy by inertial confinement fusion on facilities such as the National Ignition Facility. Calculations involving the Vlasov–Fokker–Planck equation are computationally intensive, but are crucial to proper understanding of a wide variety of physical effects and instabilities in inertial fusion plasmas. In this topical review, we will introduce the background physics related to Vlasov–Fokker–Planck simulation, and then proceed to describe results from numerical simulation of inertial fusion plasma in a pedagogical manner by discussing some key numerical algorithm developments that enabled the research to take place. A qualitative comparison of the techniques is also given.     

Numerical approximation of the Vlasov–Maxwell–Fokker–Planck system in two dimensions

A numerical method is developed for solving the Vlasov–Maxwell–Fokker–Planck system in two spatial dimensions. This system of equations is a model for a collisional plasma in the presence of a self consistent electromagnetic field. The numerical procedure is a type of deterministic particle method and is an extension to include the full electromagnetic field of the approximation method of Wollman and Ozizmir [S. Wollman, E. Ozizmir, Numerical approximation of the Vlasov–Poisson–Fokker–Planck system in two dimensions, J. Comput. Phys. 228 (2009) 6629–6669]. In addition, the long time asymptotic behavior of solutions is studied. It is determined that the solution to the Vlasov–Maxwell–Fokker–Planck system converges to the same steady state solution as that for the Vlasov–Poisson–Fokker–Planck system.     

Landau Damping for the Linearized Vlasov Poisson Equation in a Weakly Collisional Regime

In this paper, we consider the linearized Vlasov–Poisson equation around an homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a parameter \({\varepsilon }\) in front of the collision operator which will tend to 0. Moreover, we study two cases of collision operators, linear Boltzmann and Fokker–Planck. We prove a result of Landau damping for those equations in Sobolev spaces uniformly with respect to the collision parameter \({\varepsilon }\) as it goes to 0.     

The Linearized Vlasov and Vlasov–Fokker–Planck Equations in a Uniform Magnetic Field

Journal of Statistical Physics - We study the linearized Vlasov equations and the linearized Vlasov–Fokker–Planck equations in the weakly collisional limit in a uniform magnetic field....     

Covariant formulation of non-equilibrium statistical thermodynamics

The Fokker Planck equation is considered as the master equation of macroscopic fluctuation theories. The transformation properties of this equation and quantities related to it under general coordinate transformations in phase space are studied. It is argued that all relations expressing physical properties should be manifestly covariant, i.e. independent of the special system of coordinates used. The covariance of the Langevin-equations and the Fokker Planck equation is demonstrated. The diffusion matrix of the Fokker Planck equation is used as a contravariant metric tensor in phase space. Covariant drift vectors associated to the Langevin- and the Fokker Planck equation are found. It is shown that special coordinates exist in which the covariant drift vector of the Fokker Planck equation and the usual non-covariant drift vector are equal.The physical property of detailed balance and the equivalent potential conditions are given in covariant form. Finally, the covariant formulation is used to study how macroscopic forces couple to a system in a non-equilibrium steady state. A general fluctuation-dissipation theorem for the linear response to such forces is obtained.     

Similarity solutions of the Fokker–Planck equation with time-dependent coefficients

In this work, we consider the solvability of the Fokker–Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker–Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker–Planck equations are presented, and their properties analyzed.     

Solution of Fokker Planck equations with and without manifest detailed balance

Previous work on Fokker Planck equations with manifest detailed balance is generalized to include also the case without manifest detailed balance. The two cases are unified by exhibiting a general time reversal transformation with respect to which any Fokker Planck equation satisfies detailed balance, provided its steady state distribution exists. We also introduce a new method for solving some Fokker Planck equations with nonvanishing steady state drift by analytic continuation of the solution of a hermitian eigenvalue problem.