Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath     

Simulation study of the sheath region of a processing plasma with two-temperature electrons and charged nanoparticles

A four-fluid model is used to investigate the structure of a dusty plasma sheath with two species of electrons, i.e., cold and hot electrons. Numerical results show that, in the presence of hot electrons, regular fluctuations are developed in the spatial profiles of the sheath potential and number densities of the plasma and dust nanoparticles. The amplitude and spatial period of the fluctuations depend on the hot electron parameters. The sheath width shows a non-monotonic dependence on the temperature and number density of the hot electrons, as well as the density and Mach number of the nanoparticles.     

具有非广延分布电子的碰撞等离子体磁鞘的结构

很多关于等离子体鞘层的研究工作都是基于电子满足经典的麦克斯韦速度分布函数,而等离子体中的粒子具有长程电磁相互作用,使用Tsallis提出的非广延分布来描述电子更为恰当.本文建立一个具有非广延分布电子的碰撞等离子体磁鞘模型,理论推导出受非广延参数q影响的玻姆判据,离子马赫数的下限数值会随着参数q的增大而减小.经过数值模拟,发现与具有麦克斯韦分布(q=1)电子的碰撞等离子体磁鞘对比,具有超广延分布(q<1)和亚广延分布(q>1)电子的碰撞等离子体磁鞘的结构各有不同,包括空间电势分布、离子电子密度分布、空间电荷密度分布.模拟结果显示非广延分布的参数q对碰撞等离子体磁鞘的结构具有不可忽略的影响.希望这些结论对相关的天体物理、等离子体边界问题的研究有参考价值.     

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.     

甚高频激发容性耦合氩等离子体的电子能量分布函数的演变

甚高频激发的容性耦合等离子体由于离子通量和能量的相对独立可控而受到人们的关注. 本文采用朗缪尔探针诊断技术测量了40.68 MHz激发的容性耦合Ar等离子体的特性(如电子能量概率分布、电子温度和密度等)随宏观参量的演变情况. 实验结果表明, 电子能量概率分布随着气压的增加从双麦克斯韦分布逐步转变为单麦克斯韦分布并最终演变为Druyvesteyn分布, 而射频激发功率的增加促进了低能电子布居数的增强; 在从等离子体放电中心移向边界的过程中, 低能电子的布居数显著下降, 而高能电子的布居则有所上升; 放电极板间距的变化直接导致了等离子体中电子加热模式的转变. 另外, 我们也对等离子体中的高低能电子密度和温度的分配情况进行了讨论.     

等离子体中热阴极鞘层的结构

结合热阴极电子发射理论和等离子体鞘层流体方程研究了热阴极附近存在虚阴极结构时的等离子体鞘层问题,采用Sagdeev势的方法讨论了鞘层解和广义Bohm判据.结果表明,不同于普通的Bohm鞘,由于热阴极附近存在大量发射电子,影响整个等离子体鞘层结构,使得进入鞘层的离子临界Mach数不是独立的常数,而是与鞘层电位降等参数有关的物理量.临界Mach数随着鞘层电位降（从鞘边缘到虚阴极）先增大后降低,并且随着热阴极温度的升高单调增大.此外,在平板模型下有相当可观的残余热发射电子越过虚阴极鞘层进入等离子体. 关键词： 鞘层 热阴极发射 Bohm判据     

Matching an RF sheath model to a bulk plasma model

In this paper, we present a combined plasma-sheath model designed for the study of high density discharges, or other systems with thin sheaths. Sheaths in high density plasmas are typically less than 1 mm in thickness. When modeling multidimensional discharges, fully resolving the sheaths can be prohibitively expensive computationally, especially when RF power is coupled capacitively into the discharge. However, the sheath impedance often strongly affects instantaneous and period-averaged plasma potential, which in turn can strongly influence crucial processing characteristics such as the ion energy and angular distributions impacting surfaces. In the combined plasma-sheath model we present, the sheaths are treated independently from the plasma region, and different length scales are employed for each. The Godyak-Sternberg sheath model [Phys. Rev. A, 42, 2299 (1990)] is used to represent the sheaths. The bulk plasma portion of the discharge is represented using a fluid model. Boundary conditions at the plasma-sheath interfaces transfer information dynamically between the sheath and bulk plasma portions of the model. Results from the combined plasma-sheath model are compared to results from a discharge model that fully resolves the sheaths, with generally good to excellent agreement     

Simulation of radio-frequency atmospheric pressure glow discharge in γ mode

The existence of two diffe1：ent discharge modes has been verified in an rf （radio-frequency） atmospheric pressure glow discharge （APGD） by Shi [J. Appl. Phys. 97, 023306 （2005）]. In the first mode, referred to as a mode, the discharge current density is relatively low and the bulk plasma electrons acquire the energy due to the sheath expansion. In the second mode, termed γ mode, the discharge current density is relatively high, the secondary electrons emitted by cathodc under ion bombardment in the cathode sheath region play an important role in sustaining the discharge. In this paper, a one-dimensional self-consistent fluid model for rf APGDs is used to simulate the discharge mechanisms in the mode in helium discharge between two parallel metallic planar electrodes. The results show that as the applied voltage increases, the discharge current becomes greater and the plasma density correspondingly increases, consequentially the discharge transits from the a mode into the γ mode. The high collisionality of the APGD plasma results in significant drop of discharge potential across the sheath region, and the electron Joule heating and the electron collisional energy loss reach their maxima in the region. The validity of the simulation is checked with the available experimental and numerical data.     

Effect of Cathode and Anode Voltage on an Ion Sheath Thickness in a Magnetically Confined Diffusion Plasma

This article reports about the ion sheath thickness variation occurring in front of a negatively biased plate immersed in the target plasma region of a double plasma device. The target plasma is produced due to the local ionization of neutral gas by the high energetic electrons coming from the source region (main discharge region). It is observed that for an increase in cathode voltage (filament bias voltage) in the source region, the ion flux into the plate increases. As a result, the sheath at the plate contracts. Again, for an increase in source anode voltage (magnetic cage bias), the ion flux to the plate decreases. As a result, the sheath expands at the plate. The ion sheath formed at the separation grid of the device is found to expand for an increase in cathode voltage and it contracts for an increase in the anode voltage of the main discharge region. One important observation is that the applied anode bias can control the Bohm speed of the ions towards the separation grid. Furthermore, it is observed that the ion current collected by the separation grid is independent of changes in plasma density in the diffusion region but is highly dependent on the source plasma parameters. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

双频容性耦合等离子体相分辨发射光谱诊断

采用相分辨发射光谱法, 对双频容性耦合纯Ar和不同含O₂量的Ar-O₂混合气体放电等离子体的鞘层激发模式进行了探究. 在射频耦合电源上极板的鞘层区域处观察到两种电子激发模式: 鞘层扩张引起的电子碰撞激发模式和二次电子引起的电子碰撞激发模式; 并发现这两种激发模式均受到低频射频电源周期的调制. 在纯Ar放电等离子体中, 两种激发模式的激发轮廓相似; 而在Ar-O₂混合气放电等离子体中, 随着含O₂量的增加, 二次电子的激发轮廓变弱. 此外, 利用相分辨发射光谱法对不同含O₂量的Ar-O₂混合气放电下Ar的 750.4 nm谱线的平均低频电源周期轴向分布进行了研究, 得到了距耦合电源上极板约3.8 mm处为双频容性耦合射频等离子体的鞘层边界. 关键词： 双频容性耦合等离子体 等离子体鞘层 发射光谱     

Kinetic simulations of argon dusty plasma afterglow including metastable atom kinetics

The afterglow of a dusty plasma of rf discharge in argon is simulated by the particle-in-cell-Monte Carlo collision (PIC-MCC) method. The experimental observation that heavy dust contamination of plasma leads to an anomalous increase in the electron density at the beginning of afterglow is explained by release of electrons from the dust surface. Under the assumption that the floating potential of particles is in equilibrium with plasma conditions, the fast cooling of electrons in afterglow plasma due to a rapid escape of hot electrons from the volume leads to a decrease in the magnitude of the floating potential and hence to a loss of charge by dust. The intensive desorption of electrons from nanoparticles is the origin of anomalous behavior of the electron density. At the next stage of afterglow, when the electrons become cool, the plasma decay is defined by ambipolar diffusion. The effect of metastable argon atoms is also considered. Additional ionization due to metastable atom collisions affects the electron temperature but does not change the behavior of the electron density qualitatively.     

Effect of Discharge Plasma Potential on Diffusion Plasma Parameters Controlled by a Mesh Grid in a Double Plasma Device

The plasma region under investigation is separated from the discharge region by a mesh grid. Plasma potential and electron number densities and electron temperatures under bi‐Maxwellian approximation for electron distribution function of the multi‐dipole argon plasma are measured. The cold electrons in the diffusion region are produced by local ionization. The hot electrons are the ionizing electrons behaving as Maxwellian. The electron trapping process in the discharge region is produced by potential well due to positive plasma potential with respect to the anode and by a repulsive grid. The dependence of ratios of the density of the hot to the cold electrons N_E (=N_eh/N_ec) and hot to cold electron temperature T(=T_eh/T_ec) in the diffusion region on the depth of the potential well has been investigated. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

等离子体鞘层附近尘埃颗粒特性的数值模拟

为了研究尘埃等离子体中尘埃颗粒以及鞘层中粒子密度分布等特性,对尘埃颗粒存在条件下等离子体鞘层结构的采取数值模拟.采用稳态无碰撞的尘埃等离子体鞘层模型,对玻姆判据、尘埃颗粒的荷电性质、平板鞘层区域的电势分布及鞘层内粒子分布特性进行了系统的数值模拟研究.计算结果显示,鞘层边缘尘埃颗粒数密度的增加、尘埃温度的升高,将引起孤立尘埃颗粒对电子吸附能力的减弱,集体效应也受到一定程度的影响;二者同时对离子玻姆速度以及鞘层厚度的增加都有着极大的促进作用.鞘层电势在靠近下极区处降落迅速,主要聚集在接近阴极极板的鞘层区域,各种微粒数密度的空间分布满足准中性条件.     

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.     

电子和负离子的反射运动对碰撞电负性磁鞘的影响

研究了鞘层中电子和负离子的反射运动对碰撞电负性磁鞘玻姆判据和鞘层结构的影响.通过理论推导得到了考虑鞘层中电子和负离子的反射运动时鞘层玻姆判据表达式,并通过数值模拟得到了电子和负离子采用玻尔兹曼模型和反射运动模型时离子马赫数的下限随参数的变化曲线以及鞘层中带电粒子密度的分布曲线.结果表明,电子和负离子的反射运动模型和玻尔兹曼模型离子马赫数的上限完全相同,下限表达式不同,反射运动模型中下限还与基板电势有关,且随着基板电势值的增加而增大,达到与玻尔兹曼分布中相同值后保持不变,随着鞘边负离子浓度和温度的不同达到最大值的速度不同;离子马赫数的下限在玻尔兹曼和反射运动模型中都随鞘边负离子浓度的增加和温度的降低而减小,只是在反射运动模型中的最大值要小;两种模型中离子马赫数的下限都随鞘边电场的增加而增加,但在玻尔兹曼模型中增加得更快最终值更大;两种模型离子马赫数的下限都随碰撞参数或磁场角度的增加而降低,但在玻尔兹曼模型中降低更快,随着碰撞参数或者磁场角度的增加两种模型中离子马赫数的下限趋于一致;当基板电势值较小时,电子和负离子的反射运动对鞘层结构影响较大,当基板电势值较大时电子和负离子反射运动对鞘层中带电粒子密度分布的影响很小.     

Nonlinear dynamics of radio frequency plasma processing reactorspowered by multifrequency sources

The source frequency has a strong influence on plasma characteristics in RF discharges. Multiple sources at widely different frequencies are often simultaneously used to separately optimize the magnitude and energy of ion fluxes to the substrate. In doing so, the sources are relatively independent of each other. These sources can, however, nonlinearly interact if the frequencies are sufficiently close. The resulting plasma and electrical characteristics can then be significantly different from those due to the sum of the individual sources. In this paper, a plasma equipment model is used to investigate the interaction of multiple frequency sources in capacitively and inductively coupled RF excited plasmas. In capacitively coupled systems, we confirmed that the plasma density increases with increasing frequency but also found that the magnitude of the DC bias and DC sheath voltage decreases. To produce a capacitively coupled discharge having a high plasma density with a large DC bias, we combined low and high frequency sources. The plasma density did increase using the dual frequency system as compared to the single low frequency source. The sources, however, nonlinearly interacted at the grounded wall sheath, thereby shifting both the plasma potential and DC bias. In inductively coupled plasmas (ICP), the frequency of the capacitive substrate bias does not have a significant effect on electron temperature and density. The DC bias and DC sheath voltage at the substrate were, however, found to strongly depend on source frequency. By using additional RF sources at alternate locations in ICP reactors, it was found that the DC bias at the substrate was varied without significantly changing other plasma parameters, such as the substrate sheath potential     

Theoretical analysis of electron acoustic shock waves in magnetized superthermal plasma with electron beam

We have analysed the small-amplitude non-linear electron acoustic shock waves by taking into account the effects of electron beam in magnetized plasma. Satellite observations in different regions of the Earth's magnetosphere have shown that the electrostatic solitary waves are generally associated with electron or/and ion beams. The nonlinear Korteweg-de-Vries Burgers (KdVB) equation has been derived by considering the basic fluid equations and dissipation effects. The nonlinear coefficient of KdVB equation comes out to be negative. Only dip-shaped potential structures are reported here. For the parameters discussed in this paper, we did not find positive polarity shocks. This could be due to the restrictions on the plasma parameters since we are using the fixed densities of the cold, hot, and beam electrons as observed by the Viking satellite in the auroral region. In this paper, the importance of the cold electron to hot electron temperature in conjunction with the beam speed is pointed out. Increase in beam density, kinematic viscosity, and magnetic field results in increase in the amplitude while the increase in hot electron concentration and superthermality leads to decrease in potential. The numerical analysis is presented for the parameters corresponding to the observation of burst b event by Viking satellite in the dayside auroral zone of the earth's magnetosphere.     

ANALYSIS OF DUAL FREQUENCY CONFINED CAPACITIVELY COUPLED PLASMA AT LOW POWER

Confined dual frequency hydrogen plasma discharge has been investigated with microwave interferometer method and radial profiles are taken by Abel inversion technique. Dual radio-frequency sources, operating at 27.12MHz and 1.94MHz, are coupled to each other through the plasma. 27.12MHz RF power is used to enhance plasma density and 1.94MHz power is used to enhance ion acceleration energy to the electrode. Radial density profiles has been taken for comparing the effects of low frequency source that the secondary RF source causes reduction in plasma density due to the sheath expansion. Instead radial density profile is assumed as flat by most of the models, there is about 2.5eV of potential drop occurs from centre to boundary at 40W of primary source power. It has been observed that increasing sheath width (increasing the secondary source power to primary source power) reduces the bulk plasma volume and makes potential profile flattening in y direction. While the high frequency power is dissipated by electrons in the bulk plasma; low frequency power is mostly dissipated by ions in the sheath region. Using both high and low frequency power, we may control plasma density and ion acceleration energy to the electrode simultaneously.     

Modeling of plasma behavior in a plasma electrode Pockels cell

We present three interrelated models of plasma behavior in a plasma electrode Pockels cell (PEPC). In a PEPC, plasma discharges are formed on both sides of a thin, large-aperture electro-optic crystal (typically KDP). The plasmas act as optically transparent, highly conductive electrodes, allowing uniform application of a longitudinal field to induce birefringence in the crystal. First, we model the plasma in the thin direction, perpendicular to the crystal, via a one-dimensional fluid model. This yields the electron temperature and the density and velocity profiles in this direction as functions of the neutral pressure, the plasma channel width, and the discharge current density. Next, me model the temporal response of the crystal to the charging process, combining a circuit model with a model of the sheath which forms near the crystal boundary. This model gives the time-dependent voltage drop across the sheath as a function of electron density at the sheath entrance. Finally, we develop a two dimensional MHD model of the planar plasma, in order to calculate the response of the plasma to magnetic fields. We show how the plasma uniformity is affected by the design of the current return, by the longitudinal field from the cathode magnetron, and by fields from other sources. This model also gives the plasma sensitivity to the boundary potential at which the top and bottom of the discharge are held. We validate these models by showing how they explain observations in three large Pockels cells built at Lawrence Livermore National Laboratory