Vlasov-kinetic computer simulations of electrostatic waves in dusty plasmas: an overview of recent results

A series of numerical simulations based on a recurrence-free Vlasov kinetic model using kinetic phase point trajectories are presented. Electron-ion plasmas and three-component (electron-ion-dust) dusty or complex plasmas are considered, via independent simulations. Considering all plasma components modeled through a kinetic approach, the linear and nonlinear behavior of ion-acoustic excitations is investigated. Maxwellian and kappa-type (superthermal) distribution functions are assumed, as initial conditions, in separate simulations for the sake of comparison. The focus is on the parametric dependence of ion-acoustic waves on the electron-to-ion temperature ratio and on the dust concentration. © 2014 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.

Direct Vlasov simulations of electron-attracting cylindrical Langmuir probes in flowing plasmas

Current collection by positively polarized cylindrical Langmuir probes immersed in flowing plasmas is analyzed using a non-stationary direct Vlasov-Poisson code. A detailed description of plasma density spatial structure as a function of the probe-to-plasma relative velocity U is presented. Within the considered parametric domain, the well-known electron density maximum close to the probe is weakly affected by U. However, in the probe wake side, the electron density minimum becomes deeper as U increases and a rarified plasma region appears. Sheath radius is larger at the wake than at the front side. Electron and ion distribution functions show specific features that are the signature of probe motion. In particular, the ion distribution function at the probe front side exhibits a filament with positive radial velocity. It corresponds to a population of rammed ions that were reflected by the electric field close to the positively biased probe. Numerical simulations reveal that two populations of trapped electrons exist: one orbiting around the probe and the other with trajectories confined at the probe front side. The latter helps to neutralize the reflected ions, thus explaining a paradox in past probe theory.

A Kinetic Vlasov Model for Plasma Simulation Using Discontinuous Galerkin Method on Many-Core Architectures

Thesis (Ph.D.)--University of Washington, 2016-03

Multiscale Schemes for the BGK--Vlasov--Poisson System in the Quasi-Neutral and Fluid Limits. Stability Analysis and First Order Schemes

This paper deals with the development and the analysis of asymptotically stable and consistent schemes in the joint quasi-neutral and fluid limits for the collisional Vlasov-Poisson system. In these limits, the classical explicit schemes suffer from time step restrictions due to the small plasma period and Knudsen number. To solve this problem, we propose a new scheme stable for choices of time steps independent from the small scales dynamics and with comparable computational cost with respect to standard explicit schemes. In addition, this scheme reduces automatically to consistent discretizations of the underlying asymptotic systems. In this first work on this subject, we propose a first order in time scheme and we perform a relative linear stability analysis to deal with such problems. The framework we propose permits to extend this approach to high order schemes in the next future. We finally show the capability of the method in dealing with small scales through numerical experiments.

Free vibration of rectangular plates of arbitrary thickness

Free vibration of thick rectangular plates is investigated by using the “method of initial functions” proposed by Vlasov. The governing equations are derived from the three-dimensional elastodynamic equations. They are obtained in the form of series and theories of any desired order can be constructed by deleting higher terms in the infinite order differential equations. The numerical results are compared with those of classical, Mindlin, and Lee and Reismann solutions.

Free vibration of rectangular plates of arbitrary thickness with one or more edges clamped

Frequencies of free vibration of rectangular plates of arbitrary thickness, with different support conditions, are calculated by using the Method of Initial Functions (MIF), proposed by Vlasov. Sixth and fourth order MIF theories are used for the solution. Numerical results are presented for three square plates for three thickness ratios. The support conditions considered are (i) three sides simply supported and one side clamped, (ii) two opposite sides simply supported and the other two sides clamped and (iii) all sides clamped. It is found that the results produced by the MIF method are in fair agreement with those obtained by using other methods. The classical theory gives overestimates of the frequencies and the departures from the MIF results increase for higher modes and larger thickness ratios.

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

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 .

原子核巨共振温度变化机制

我们利用流体动力学宏观理论与HF微观理论对同位旋标量多极巨共振能量随温度的变化机制做了讨论。首先用流体动力学方法导出了同位旋标量多极巨共振能量随温度变化的一般关系式。公式表明巨共振能量随温度的变化受制于热核体积膨胀和核子平均动能增加两个因素之间的竟争，它们分别使共振能减小和增加。接着又用Skyrme-HF方法得到了核半径系数和核子平均动能随温度变化的关系式。最后得到同位旋标量多极巨共振能量随温度变化的一个简单关系式。体积膨胀和核子平均动能增加这两种因素的影响大体互相抵消，最终导致热核同位旋标量多极巨共振能量基本不随温度变化。我们用Boltzmann-Nordherin-Vlasov方程数值计算和分析了重离子反应中单极巨共振OMR的形成与衰减。为了系统地比较入射能、碰撞参数对不同反应系统GMR的形成与衰减的影响，我们计算了不同条件下不同重离子反应系统的四极矩、动能和单极矩随时间的演化。计算表明，1)GMR能量与入射能和碰撞参数无关，仅仅是核子数的函数。2) 入射能愈大GMR形成稍有提前，GMR振幅也越大但OMR振幅衰减越快GMR消亡越早。3) 碰撞参数越大GMR振幅越小GMR消亡越早。4) GMR在40fm/c左右形成，依照入射能和碰撞参数的不同在200到400fm/c后消亡，入射能愈大或碰撞参数愈大GMR消亡越早。概括地讲，GMR能量是核子数的光滑函数，与入射能或激发能无关；入射能越大GMR振幅越大，GMR形成时间稍早但衰减和消亡更快。我们用经典唯象输运模型和量子输运模型讨论了核系统扩张过程中OQR模式的密度涨落并用它们来模拟系统的集体行为。我们讨论了集体坐标Q与集体动量P的涨落随时间的演化。计算显示集体变量Q的涨落发展主要取决于通过随机驱动力引入的初始统计涨落，统计涨落与量子涨落行为相似。在核系统扩张阶段耗散与涨落机制对于动量分布的影响是重要的。量子涨落在初值中已经存在，对于低温系统，量子涨落所起的作用尤为重要，它能够缩短涨落达到特定值的临界时间，从而在动力学对称性破缺中发挥重要作用。由于量子涨落的作用，处于spinodal状态的核系统将更早地分解。我们也讨论了双核系统GDR的形成与性质，还探讨了GDR宽度随温度变化的机制。

重离子同步加速器SIS中的束团纵向稳定性理论、测量和模拟

本论文中的工作是在德国重离子研究中心（GSI）和中国科学院近代物理研究所的联合培养计划下完成的。论文以GS工的重离子同步加速器SIS为主要研究对象，就其强流运行及为GSI最近批准的新项目而升级的纵向动力学方面进行了研究和探讨。该项工作对于在建的大科学工程兰州重离子储存环HIRFL-CSR有借鉴意义。在GSI的新项目国际重离子、反质子加速器科学研究装置的蓝图中，现有的重离子同步加速器S工S将作为前级提升束流的强度和能量。束团的纵向稳定性是保证可靠的强流运行所必须回答的问题，包括以下内容，在本文中分别进行了探索和解答：纵向的重离子加速器环境阻抗模型；在可能的阻抗条件下束流线性稳定性；在阻尼及不稳定性效应下束流相空间分布的演化行为和结果（发射度增长、粒子丢失等）及其内在机制；对不稳定性和束流相空间稀释效应进行控制的可能性。不同流强下束流纵向相空间测量，这是本论文工作的一个重要基础。自洽的Vlasov束团模型（任意外场加空间电荷效应下的束流匹配）和实际运行中的非理想捕获过程（有限的高频电压上升时间，对应不同的绝热系数），作为任何束团运行和稳定性研究的前提分别在论文中得到了厘清。解析方面的工作包括定态和微扰理论，即将线性Vlasov方程应用于束团，并在适当的近似下得到简洁的解析方程。经过重新推导，得到了修正的Sachrer积分方程，使之在强空间电荷效应下的仍然适用，由此得到了线性稳定图。编写调试成功了PIC（particle-in-cell）算法的模拟程序，和线性理论相互校验，并与己得到的实验结果进行了对比，对实际运行中复杂过程进行了模拟，并研究了不稳定性发展后期非线性阶段。线性理论，模拟和实验结果有很好的一致性。在SIS实验中观察到一种流强相关的束团相干模式演化现象，该现象揭示出束团中朗道阻尼条件，这与束团稳定性密切相关。对空间电荷抑制朗道阻尼效应及发射度增长进行了细致研究。提出用快反馈装置控制相空间稀释的思路。线性理论和模拟的结果都预言，在阻性阻抗和空间电荷阻抗存在下，藕合束不稳定性是515多束团强流运行的潜在威胁。阻性阻抗来自管壁及加速器部件的有效导电性或特殊共振结构，或直接来自频率偏置的高频腔。阻抗补偿或特殊的束团操作可以用来控制桃合束不稳定性。

Fully kinetic simulation of ion acoustic and dust-ion acoustic waves

A series of numerical simulations is presented, based on a recurrence-free Vlasov kinetic model using kinetic phase point trajectories. All plasma components are modeled kinetically via a Vlasov evolution equation, then coupled through Poisson’s equation. The dynamics of ion acoustic waves in an electron-ion and in a dusty (electron-ion-dust) plasma configuration are investigated, focusing on wave decay due to Landau damping and, in particular, on the parametric dependence of the damping rate on the dust concentration and on the electron-to-ion temperature ratio. In the absence of dust, the occurrence of damping was observed, as expected, and its dependence to the relative magnitude of the electron vs ion temperature(s) was investigated. When present, the dust component influences the charge balance, enabling dust-ion acoustic waves to survive Landau damping even in the extreme regime where Te???Ti. The Landau damping rate is shown to be minimized for a strong dust concentration or/and for a high value of the electron-to-ion temperature ratio. Our results confirm earlier theoretical considerations and contribute to the interpretation of experimental observations of dust-ion acoustic wave characteristics.