Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

This paper describes an Adaptive Mesh and Algorithm Refinement (AMAR) methodology for multi-scale simulations of gas flows and the challenges associated with extending this methodology for simulations of weakly ionized plasmas. The AMAR method combines Adaptive Mesh Refinement (AMR) with automatic selection of kinetic or continuum solvers in different parts of computational domains. We first review the discrete velocity method for solving Boltzmann and Wang Chang–Uhlenbeck kinetic equations for rarefied gases. Then, peculiarities of AMR implementation with octree Cartesian mesh are discussed. A Unified Flow Solver (UFS) uses AMAR method with adaptive Cartesian mesh to dynamically introduce kinetic patches for multi-scale simulations of gas flows. We describe fluid plasma models with AMR capabilities and illustrate how physical models affect simulation results for gas discharges, especially in the areas where electron kinetics plays an important role. We introduce Eulerian solvers for plasma kinetic equations and illustrate the concept of adaptive mesh in velocity space. Specifics of electron kinetics in collisional plasmas are described focusing on deterministic methods of solving kinetic equations for electrons under different conditions. We illustrate the appearance of distinct groups of electrons in the cathode region of DC discharges and discuss the physical models appropriate for each group. These kinetic models are currently being incorporated into AMAR methodology for multi-scale plasma simulations.     

Well-posedness of continuum models for weakly ionized plasmas

Continuum fluid models of weakly ionized plasmas are useful in the design and control of plasma-assisted deposition and etching processes. The equations in these models are numerically stiff. Their stiffness is affected by the imposed boundary conditions. In this work, a DC discharge model is studied and the effect of the boundary conditions on the model solution is investigated. It is established, both analytically and numerically, that depending on the choice of boundary conditions the model may range from being ill-posed to being solvable with standard software. It is also established that excessive truncation error maybe present in numerical simulations which appear to qualitatively capture plasma structure. Accurate numerical simulations of the considered model, with alternate boundary conditions, are shown to capture many characteristics of a DC discharge, albeit at lower values of applied voltage than those reported in the literature. Finally, model shortcomings are discussed     

A remark on the drift dissipative instability of weakly ionized plasma

The author takes into account ion motion along the magnetic lines in the dispersion equation. It is shown that the drift branch of waves joins the ion acoustic branch in the weakly ionized plasma, too, and that the term describing this motion has a stabilizing effect. These results are independent on the relation of the wave length to the mean free path of the electrons.The author would like to express his sincere thanks to Dr. J. Václavík for his valuable comments.     

弱电离尘埃等离子体的介电张量研究

忽略磁场作用,通过求解含BGK碰撞项的Boltzmann方程和尘埃粒子充电方程导出了弱电离尘埃等离子体介电张量的表达式.证明了“冷”尘埃等离子体的纵向介电张量系数与横向介电张量系数相等.完善了弱电离尘埃等离子体电磁特性的理论模型. 关键词： 弱电离尘埃等离子体 Boltzmann方程 充电方程 介电张量     

Application of weakly ionized plasmas for materials sampling andanalysis

The use of weakly ionized plasmas as spectroscopic sources for materials sampling and analysis is reviewed. Plasma sources currently used for this purpose include direct-current and alternating-current plasmas, inductively coupled plasmas, microwave-induced plasmas, surface-wave plasmas, capacitively coupled plasmas, capacitive microwave plasmas, glow discharges, flowing afterglows, theta pinch discharges, exploding films and wires, and laser-produced plasmas. The authors give a summary of relevant characteristics of some of the plasma sources. Included are the source, common method of application, approximate detection limit for that method, applicability for solid sampling, susceptibility to matrix effects, approximate cost, and the most common usage for the method     

Asymptotic evolution of weakly collisional Vlasov-Poisson plasmas

We study the role of (weak) numerical diffusion on the long time evolution of the Vlasov-Poisson plasma. We consider the classical problem of phase space vortex formation by particle trapping. We show that the asymptotic macroscopic state is not independent of diffusion even if the dissipative length scale is much shorter than any characteristic physical length scale of the system.     

弱电离大气等离子体电子能量分布函数的理论研究

使用球谐展开的方法求解玻尔兹曼方程,得到了弱电离大气等离子体(79％氮气和21％的氧气)的电子能量分布函数(EEDF).发现当约化电场较小时(E/N＜100 Td),EEDF在2-3 eV急剧下降,在此情况下,高能尾部比麦氏分布要小;当约化电场增加,E/N＞ 400 Td,分布函数趋近于麦氏分布;当约化电场进一步增加,E/N＞ 2000 Td,EEDF的高能尾部(超过200 eV)相对于麦氏分布增加,在高频场作用下,EEDF更倾向于麦氏分布.当ω》vm时,有效电子温度只依赖于E/ω,而与碰撞频率无关;当ω《vm时,有效电子温度只依赖于E/N,与微波频率无关.与一些单原子分子等离子体中电子-电子碰撞在电离度大于10-6时就会影响EEDF不同,空气等离子体中,只有当电离度大于0.1％时,电子-电子碰撞才会对EEDF有明显影响.     

Dissipation of energy of low-frequency waves in a weakly ionized gas

The properties of low-frequency waves in a slightly ionized gas are discussed on the basis of the Boltzmann transport and Maxwell equations. Special attention is paid to decay mechanisms forcing the gas to thermal equilibrium. It is shown that the collisional exchange of energy between ions and neutral atoms may considerably influence the dispersion equations of several modes of oscillations.The author wishes to thank Mrs. E. Dosoudilová for executing the numerical computations.     

Incoherent scattering of electromagnetic waves by a weakly ionized plasma layer

Institute of Theoretical Physics of the Ukrainian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 12, pp. 1327–1341 December, 1990     

Physical implication of two problems in transition prediction of boundary layers based on linear stability theory

Up to now,the most widely used method for transition prediction is the one based on linear stability theory.When it is applied to three-dimensional boundary layers,one has to choose the direction,or path,along which the growth rate of the disturbance is to be integrated.The direction given by using saddle point method in the theory of complex variable function is seen as mathematically most reasonable.However,unlike the saddle point method applied to water waves,here its physical meaning is not so obvious,as the frequency and wave number may be complex.And on some occasions,in advancing the integration of the growth rate of the disturbance,up to a certain location,one may not be able to continue the integration,because the condition for specifying the direction set by the saddle point method can no longer be satisfied on the basis of continuously varying wave number.In this paper,these two problems are discussed,and suggestions for how to do transition prediction under the latter condition are provided.     

Transport of microparticles in weakly ionized gas-discharge plasmas under microgravity conditions

Measurements of effective structural (pair correlation function) and transport (diffusion constant) characteristics of the system of microparticles in dc and rf gas-discharge plasmas under microgravity conditions are reported. The comparison between these measurements and numerical simulations is used for complex plasma diagnostics.     

Effects of dimples on laminar boundary layers

A series of direct numerical simulations of the flow past a flat plate with two and eight rows of dimples in a staggered arrangement is carried out. The Reynolds number based on the boundary layer thickness and freestream velocity near the inflow plane is 1000 and the dimples are spherical with a depth to diameter ratio of 0.1. The incoming flow is laminar and the boundary layer thickness before the dimples is half the dimple depth. At this low Reynolds number the flow is expected to remain laminar over a smooth flat plate. The presence of the dimples triggers instabilities that cause significant momentum transport. It is shown that the shear layer that forms as the flow separates over the first two rows of dimple becomes unstable and sheds coherent vortex sheets. The vortex sheets become unstable and are transformed into packets of horseshoe vortices. When these vortices evolve over a flat plate or over a series of dimples the flow dynamics are very different with important changes in momentum transport across the boundary layer.     

Propagation of dust-acoustic waves in weakly ionized plasmas with dust-charge fluctuation

For an unmagnetized partially ionized dusty plasma containing electrons, singly charged positive ions, micron-sized massive negatively charged dust grains and a fraction of neutral atoms, dispersion relations for both the dust-ion-acoustic and the dustacoustic waves have been derived, incorporating dust charge fluctuation. The dispersion relations, under various conditions, have been exhaustively analysed. The explicit expressions for the growth rates have also been derived. International Conference on the Frontiers of Plasma Physics and Technology, 9–14 December 2002, Bangalore, India.