Structure of a microparticle crystal in a radio-frequency discharge plasma

By employing the particle-in-cell method we study the distributions of the electric field strength and of the electron and ion concentrations in the microparticle crystal in the electrode sheath in a radio-frequency discharge in helium. The coordinates and charges of the microparticles are found from the balance condition for the forces acting on the particles and the balance of electron and ion fluxes to the particles. With periodic boundary conditions introduced, we investigate the three-dimensional problem for the unit cell of the microparticle crystal. We examine the dependence on gas pressure and discharge voltage of the main crystal parameters: the critical particle separation (at which a phase transition from a monolayer crystal to a double-layer crystal occurs), the particle potentials, and the distances between the layers in the double-layer crystal. We obtain the critical values of the friction coefficient for the particles in the gas, i.e., values below which the crystal becomes unstable against the development of particle oscillations in the transverse direction, and compare the experimental data on crystal structure and stability with the theoretical results. Finally, we set up an approximate model that makes it possible to calculate the main parameters of the microparticle crystal. Zh. éksp. Teor. Fiz. 115, 877–893 (March 1999)     

Anomalous capacitive sheath with deep radio-frequency electric-field penetration

A novel nonlinear effect of anomalously deep penetration of an external radio-frequency electric field into a plasma is described. A self-consistent kinetic treatment reveals a transition region between the sheath and the plasma. Because of the electron velocity modulation in the sheath, bunches in the energetic electron density are formed in the transition region adjacent to the sheath. The width of the region is of order V(T)/omega, where V(T) is the electron thermal velocity, and omega is the frequency of the electric field. The presence of the electric field in the transition region results in a collisionless cooling of the energetic electrons and an additional heating of the cold electrons.     

气体放电阴极鞘层氩离子的自洽蒙特卡罗模拟

建立了气体放电阴极鞘层离子的自洽蒙特卡罗模拟模型,考虑了离子与中性原子的电荷交换碰撞和弹性散射,用到了精确依赖于离子能量的电荷交换和动量输运截面。模拟了氩离子在阴极鞘层中的运动,得到了不同气压下自治电场分布,离子的能量分布和角分布,发现:离子由鞘层边界向阴极运动过程中,离子能量分布的高能部分逐渐增大,角分布向小角度部分压缩,鞘层中的强电场加速和聚焦了离子;在鞘层边界附近的电场呈非线性。     

Determination of sheath parameters by test particles upon local electrode bias and plasma switching

Equilibrating gravitation by electric forces, microparticles can be confined in the plasma sheath above suitably biased local electrodes. Their position depends on the detailed structure of the plasma sheath and on the charge that the particles acquire in the surrounding plasma, that is by the electron and ion currents towards it. Bias switching experiments reveal how the charge and equilibrium position of the microparticle change upon altered sheath conditions. Above a critical bias, the particle is subject to an additional downward acceleration that cannot be explained solely by gravity and ion drag. This acceleration can be attributed to a positive charging of the particle induced by extreme out-of-equilibrium conditions of the plasma sheath in its surroundings: locally the plasma sheath can be completely deprived of electrons by means of the bias. We observe similar particle behaviors also in the afterglow of the discharge for a persisting bias voltage on the electrode: damped oscillation into a new equilibrium or (accelerated) fall according to the bias. The observed particle dynamics in locally tailored plasma sheath environments directly monitors changes in electric field structures and plasma density profiles.     

Rotation of a single vortex in dusty plasma

A single vortex is obtained in radio-frequency capacitive discharge in argon gas. The dust subsystem is confined in the horizontal plane with an asymmetrical saw structure placed on the lower electrode. The vortex rotates as a whole along the long side of the saw-teeth. Asymmetry of the saw structure plays an important role in the rotation of the vortex. Nonzero curl of the total force resulting from the local ion flow and the electric field in the plasma sheath could be attributed to the persistent rotation of vortex.     

尘埃颗粒在射频等离子体鞘层中的非线性共振现象的理论研究

一种自洽的理论模型用于研究尘埃颗粒在射频鞘层中垂直方向的非线性共振现象.利用射频鞘层动力学模型，研究了鞘层电场和尘埃颗粒的充电过程.考虑作用在尘埃颗粒上的各种作用力(如重力、电场力、离子拖拽力、中性气体摩擦力及探针的扰动力)，并通过数值求解颗粒运动方程，模拟了该尘埃颗粒在探针扰动下的非线性振荡过程.所得结果不仅很好地再现了最近的实验观察，同时还发现这种非线性振动过程与等离子体参数、施加的射频偏压的功率、探针的扰动电位和位置等有着密切的联系. 关键词： 射频鞘层 尘埃颗粒 尘埃充电 非线性共振 迟滞     

Interaction between glow discharge plasma and dust particles

The effect of dust particle concentration on gas discharge plasma parameters was studied through development of a self-consistent kinetic model which is based on solving the Boltzmann equation for the electron distribution function. It was shown that an increase in the Havnes parameter causes an increase in the average electric field and ion density, as well as a decrease in the charge of dust particles and electron density in a dust particle cloud. Self-consistent simulations for a wide range of plasma and dust particle parameters produced several scaling laws: these are laws for dust particle potential and electric field as a function of dust particle concentration and radius, and the discharge current density. The simulation results demonstrate that the process of self-consistent accommodation of parameters of dust particles and plasma in condition of particle concentration growth causes a growth in the number of high-energy electrons in plasma, but not to depletion of electron distribution function.     

Effect of Parallel-Plate Geometry on Mode Transition Behavior in Argon Microplasmas: Two-Dimensional Simulation

A two-dimensional self-consistent fluid model is employed to investigate radio-frequency process parameters on the plasma properties in Ar microdischarges. The neutral gas density and temperature balance equations are taken into account. We mainly investigate the effect of the electrode gap on the spatial distribution of the electron density and electron temperature profiles, due to a mode transition from the regime(secondary electrons emission is responsible for the significant ionization) to the regime(sheath oscillations and bulk electrons are responsible for sustaining discharge) induced by a sudden decrease of electron density and electron temperature.The pressure, radio-frequency sources frequency and voltage effects on the electron density are also elaborately investigated.     

射频等离子体鞘层动力学模型

在流体力学方程的基础上建立了一种自洽的无碰撞射频等离子体鞘层动力学模型.这种自洽性包含两个方面:一方面,由于考虑了瞬时鞘层电场对离子运动的影响,因此该模型适用于描述任意频率段的射频鞘层演化过程;另一方面,在模型中采用等效电路方法来自洽地确定极板上的瞬时电位与瞬时鞘层厚度之间的关系.采用数值方法模拟出鞘层的瞬时厚度及极板的瞬时电位变化、鞘层内离子密度和电场强度等物理量的时空变化.结果表明,当射频场的频率小于或等于离子等离子体频率时,离子流密度明显地随时间变化 关键词： 射频 离子 鞘层 流体力学     

Levitation and dynamics of a collection of dust particles in afully ionized plasma sheath

Examines the dynamics of a collection of charged dust particles in the plasma sheath above a large body in a fully ionized space plasma when the radius of the large body is much larger than the sheath thickness. The dust particles are charged by the plasma, and the forces on the dust particles are assumed to be from the electric field in the sheath and from gravitation only. These forces will often act in opposite directions and may balance, making dust suspension and collection possible. The dust particles are supplied by injection or by electrostatic levitation. The ability of the sheath to collect dust particles, will be optimal for a certain combination of gravitation and plasma and dust particle parameters. In a dense dust sheath, the charges on the dust particles contribute significantly to the total space charge, and collective effects become important. These effects will reduce the magnitude of the sheath electric field strength and the charge on the dust particles. As dust particles are collected, the dust sheath is stretched and the largest dust particles may drop out, because the sheath is no longer able to suspend them. In a tenuous dust sheath, the inner layer, from the surface and about one Debye length thick, will be unstable for dust particle motion, and dust will not collect there. In a dense dust sheath, collective effects will decrease the thickness of this inner dust-free layer, making dust collection closer to the surface possible. By linearization of the force and current equations, the necessary and sufficient conditions for a stable dust sheath are found. The authors consider conditions which resemble those of planetary system bodies, but the results may also be of relevance to some laboratory plasmas     

外加磁场对碰撞射频鞘层离子能量分布的影响

采用双流体模型,数值研究入射到射频鞘层偏压电极上的离子能量分布.研究结果表明：磁场在改变离子运动状态的同时,调控着基板上的离子能量分布,使之在垂直基板方向和平行基板方向间转移. 关键词： 等离子体 射频 鞘层 磁场     

Self-Consistent expansion of a layer of electrons in the field of intrinsic space charge against the background of a neutral gas

The dynamics of self-consistent expansion of an electron layer under the action of the electric force of intrinsic space charge and friction force is investigated. The expansion of the electron layer occurs against the background of a neutral gas, which gives rise to the friction force opposing the motion of electrons. One-dimensional motion of electrons is considered for plane, cylindrical, and spherical symmetries. Exact analytic solutions are obtained to the linear system of hydrodynamic equations of plasma for electrons with a self-consistent electric field.     

Effects of gas pressure on plasma characteristics in dual frequency argon capacitive glow discharges at low pressure by a self-consistent fluid model

A self-consistent fluid model for dual radio frequency argon capacitive glow discharges at low pressure is established.Numerical results are obtained by using a finite difference method to solve the model numerically, and the results are analyzed to study the effect of gas pressure on the plasma characteristics. It shows that when the gas pressure increases from 0.3 Torr(1 Torr = 1.33322×10~2 Pa) to 1.5 Torr, the cycle-averaged plasma density and the ionization rate increase;the cycle-averaged ion current densities and ion energy densities on the electrodes electrode increase; the cycle-averaged electron temperature decreases. Also, the instantaneous electron density in the powered sheath region is presented and discussed. The cycle-averaged electric field has a complex behavior with the increasing of gas pressure, and its changes take place mainly in the two sheath regions. The cycle-averaged electron pressure heating, electron ohmic heating, electron heating, and electron energy loss are all influenced by the gas pressure. Two peaks of the electron heating appear in the sheath regions and the two peaks become larger and move to electrodes as the gas pressure increases.     

Self-consistent hybrid model for a stratified positive column of a low pressure glow discharge

The stratification of a positive column of a low-pressure glow discharge in inert gases has been studied with the help of a self-consistent hybrid model. The model is based on the solution of a nonlocal kinetic Boltzmann equation for the electron distribution function, a nonstationary drift-diffusion equation for the ions, and the Poisson equation for the electric field. Spatial electron and ion density distributions and the electric field distribution in the positive column were obtained. The converged solution of the model gives a self-consistent resonant strata length L and the value and the form of the modulated plasma parameters. An unexpected surprising result was obtained: for a given potential drop in the positive column of a low-pressure glow discharge, a self-consistent spatially modulated striation-like electric field does not lead to the resonant increasing of the ionization frequencies in the discharge as compared with a constant electric field with the same potential drop. Usually, it was assumed that, in spatially modulated field distributions, all the parameters in a striated plasma will be more pronounced and have a resonant form. The text was submitted by the authors in English.     

One-Dimensional Fluid Model for Dust Particles in Dual-Frequency Capacitively Coupled Silane Discharges

A self-consistent fluid model, which incorporates density and flux balances of electrons, ions, neutrals and nanoparticles, electron energy balance, and Poisson＇s equation, is employed to investigate the capacitively coupled silane discharge modulated by dual-frequency electric sources. In this discharge process, nanoparticles are formed by a successive chemical reactions of anion with silane. The density distributions of the precursors in the dust particle formation are put forward, and the charging, transport and growth of nanoparticles are simulated. In this work, we focus our main attention on the influences of the high-frequency and low-frequency voltage on nanoparticle densities, nanoparticle charge distributions in both the bulk plasma and sheath region.     

Numerical modeling of low-pressure RF plasmas

A particle-in-cell simulation is used to model the plasma generated in a parallel plate RF reactor at low pressure. Nonperiodic boundary conditions are used, and the electric field and particle motion are obtained by finite-difference methods leading to the self-consistent creation of sheaths on the boundaries. Model cross sections are used to describe collisions between particles. Ionization is included, and the plasma is maintained by fast electrons generated in the RF sheaths. Most of the power dissipation is due to the acceleration of ions in the time-average sheath fields. At high applied voltage, the power dissipation is described well by the power law P∝V^5/2. Simple scaling laws for the density and plasma potential are obtained. The effect of ion mass and charge-exchange colisions on the ion energy spectrum collected by the electrodes is examined. The ion loss rate drops in the presence of charge-exchange collisions, and this leads to an increase in the density. The collisions also markedly alter the ion energy distribution function     

Microparticles in a collisional Rf plasma sheath under hypergravity conditions as probes for the electric field strength and the particle charge

We used microparticles under hypergravity conditions, induced by a centrifuge, in order to measure nonintrusively and spatially resolved the electric field strength as well as the particle charge in the collisional rf plasma sheath. The measured electric field strengths demonstrate good agreement with the literature, while the particle charge shows decreasing values towards the electrode. We demonstrate that it is indeed possible to measure these important quantities without changing or disturbing the plasma.     

Axial magnetostatics of a ring current in a Kerr field

The electromagnetic fields generated by a ring current around a Kerr black hole have been found. The acceleration of a charged particle by a force electric field along the rotation axis is investigated in the constructed model, as applied to the astrophysics of quasars.