Fluid Model of a Sheath Formed in Front of an Electron Emitting Electrode Immersed in a Plasma with Two Electron Temperatures

The formation of a sheath in front of a negatively biased electrode (collector) that emits electrons is studied by a one‐dimensional fluid model. Electron and ion emission coefficients are introduced in the model. It is assumed that the electrode is immersed in a plasma that contains energetic electrons. The electron velocity distribution function is assumed to be a sum of two Maxwellian distributions with two different temperatures, while the ions and the emitted electrons are assumed to be monoenergetic. The condition for zero electric field at the collector is derived. Using this equation the dependence of electron and ion critical emission coefficients on various parameters ‐ like the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons ‐ is calculated for a floating collector. A modification of the Bohm criterion due to the presence of hot and emitted electrons is also given. The transition between space charge limited and temperature limited electron emission for a current‐carrying collector is also analyzed. The critical potential, where this transition occurs, is calculated as a function of several parameters like the Richardson emission current, the ratio between the hot and cool electron density, the ratio between hot and cool electron temperature and the initial velocity of secondary electrons. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

二次电子分布函数对绝缘壁面稳态鞘层特性的影响

由于缺乏详细的理论计算和实验结果,在研究绝缘壁面稳态流体鞘层特性时,通常假设壁面出射的总二次电子服从单能分布(0)、半Maxwellian分布等.在单能电子轰击壁面的详细二次电子发射模型基础上,采用Monte Carlo方法统计发现:当入射电子服从Maxwellian分布时,绝缘壁面发射的总二次电子服从三温Maxwellian分布.进而,采用一维稳态流体鞘层模型进行对比研究,结果表明:二次电子分布函数对鞘边离子能量、壁面电势、电势及电子/离子密度分布等均具有明显影响;总二次电子服从三温Maxwellian分布时,临界空间电荷饱和鞘层无解,表明随着壁面总二次电子发射系数的增加,鞘层直接从经典鞘层结构过渡到反鞘层结构.     

Emission of Ions from a Nonequilibrium Plasma

A model of a plasma ion emitter is considered for two types of velocity distribution of plasma electrons: the sum of two Maxwellian velocity distributions with different temperatures and the sum of a Maxwellian distribution and a directed flux. Criteria for the formation of a plasma emission surface are derived. The effect of the parameters of the electron distribution on the magnitude of the perturbation of the quasi-neutral emitting plasma by the external electric field of the negative electrode and on the emission current density is considered. A comparison with the Bohm case is performed.     

射频辉光放电CH4等离子体中电子的能量分布

通过求解Lorentz简化的玻尔兹曼方程,得到射频放电CH₄等离子体中电子的能量分布函数.求解过程中使用一个简化的射频电场模型代替泊松方程求解放电电场.共计包含6类环境气体及27种电子碰撞反应.通过EEDF对等离子体中的电子反应率系数、电子平均能量、电子的传输率系数等进行求解分析.结果表明,在等离子体鞘层区域电子能量具有Maxwell分布形式,在正柱区域具有Druyvesteyn分布形式.最高电子能量和最大反应率系数出现在鞘层区域.电子的迁移率系数和扩散率系数随射频周期的演化时空分布不均匀.     

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.     

Floating Sheath Potentials in Non-Maxwellian Plasmas

The floating sheath potential in a plasma having a Maxwellian electron distribution function is e?>s = -kTe 1n (a/b)/2 where Te is the electron temperature, a is the ratio of electron temperature to ion temperature, and b is the ratio of electron mass to ion mass. This expression is derived by equating the flux of electrons and ions to a surface in the plasma. Only electrons initially having an energy greater than -e?s flow to the surface. These electrons are in the tail of the distribution, a region that differs significantly from a Maxwellian in many plasmas. An analysis is performed where the sheath potential is solved for using a two-temperature model for the electron distribution function. The two-temperature model accurately describes the distortion from a Maxwellian in the tail of the distribution function. The magnitude of the sheath potential calculated with the two-temperature distribution is significantly smaller than that obtained using a Maxwellian distribution, a result of the reduction in the relative abundance of energetic electrons in the tail of the distribution.     

Dust particles in collisionless plasma sheath with arbitrary electron energy distribution function

Dust particles often appear in industrial plasmas as undesirable product of the plasma-wall interactions. Large particles of several micrometers in diameter are concentrated in a thin layer (the sheath) above the lower electrode of the rf driven parallel plate device, where the electric force is strong enough to compensate particle’s gravity. Experimental and theoretical uncertainties are significantly increased in the plasma sheath. Common models of dust charging in the plasma sheath suppose the Maxwellian electron energy distribution function (EEDF) in conjunction with a flux of cold ions satisfying classical Bohm criterion at the sheath edge. In this paper we generalize this model to arbitrary EEDF with adapted Bohm criterion. We limit our considerations to collisionless or slightly collisional plasma, where the EEDF inside the sheath is expressed through the EEDF in the plasma bulk. Derived theoretical formulas are incorporated into numerical model, describing collisionless radio frequency (rf) plasma sheath together with the electrical charge, various kinds of forces, balancing radius and oscillation frequency of particles.     

Arc spot ignition caused by sheath instability

The transition from the stationary and homogeneous state of the collision-free space charge sheath between plasma and wall to a strongly inhomogeneous and instationary state with are spots is initiated by local enhancement of power supply from the plasma, connected with increasing electron emission. The general relations between surface emissivity, net current density, sheath potential, and power density in such “active” boundary layers are derived, taking the feedback of emitted electrons on the plasma parameters into account, as far as necessary. Joule heat generation is taken into account. The decisive effect of the transition is the rapidly increasing yield of thermo-field electron emission. Conditions and possible paths to sheath instability and arc spot formation are discussed     

Effects of Energetic Electrons on Collector and Source Potentials in a Finite Ion Temperature Plasma

Formation of the potential in a two-electron-temperature plasma region facing a floating collector was studied theoretically with a kinetic plasma-sheath model and by electrostatic particle simulation. The electrons were described by truncated full Maxwellian velocity distribution functions and the ions by an accelerated half-Maxwellian velocity distribution function. The collector potential and the plasma source sheath or presheath potential drop were evaluated as functions of the hot to cool electron temperature ratio and the hot electron density ratio using Vlasov and Poison equations. The results showed that the presheath potential drop varied continuously with electron composition ratio for lower values of the electron temperature ratio, while for higher values in a narrow composition ratio range, triple values of the potential were found. Of the two physically acceptable values, the lower was characterized by the cool electrons and the higher by the hot electrons. It is anticipated that a current-free double layer structure is formed in the plasma system between these two potential regions. The collector floating potential, as a function of electron composition ratio, is mainly dominated by the hot electrons, since already a small value of hot electron current is sufficient to compensate the ion saturation current. In order to complete the theoretical investigation we also study the hydrogen plasma system with the XPDP1 particule-in-cell simulation code composed at Berkeley. At certain plasma parameter values formation of a double layer structure was observed. The potential Values on the upper and lower side of the double layer, as well as that of the collector floating potential, corresponded very well to the calculated values. On the upper side the plasma was composed of ions, accelerated through the source sheath potential drop, and electrons consisting of cool full Maxwellian and hot truncated full Maxwellian populations. On the lower side only hot electrons and ions additionally accelerated through the double layer were found.     

Effect on Landau damping rates for a non-Maxwellian distribution function consisting of two electron populations

In many physical situations where a laser or electron beam passes through a dense plasma,hot low-density electron populations can be generated,resulting in a particle distribution function consisting of a dense cold population and a small hot population.Presence of such low-density electron distributions can alter the wave damping rate.A kinetic model is employed to study the Landau damping of Langmuir waves when a small hot electron population is present in the dense cold electron population with non-Maxwellian distribution functions.Departure of plasma from Maxwellian distributions significantly alters the damping rates as compared to the Maxwellian plasma.Strong damping is found for highly nonMaxwellian distributions as well as plasmas with a higher density and hot electron population.Existence of weak damping is also established when the distribution contains broadened flat tops at the low energies or tends to be Maxwellian.These results may be applied in both experimental and space physics regimes.     

Self-consistent structure of a dc discharge with a closed hall current in crossed electric and magnetic fields

A dc glow discharge with a closed Hall current in crossed electric and magnetic fields in helium is investigated. It is shown that the main features of an unmagnetized dc discharge [1] (such as the separation of the discharge into a space charge sheath and a quasineutral plasma, the formation of a cathode fall region and a negative glow, the appearance of a region with a reversed electric field producing a potential well for low-energy electrons and resulting in the formation of a Faraday dark space, and the formation of three pronounced groups of electrons in the electron distribution function) are also retained in a discharge in crossed fields. It is found that the sheath length is almost independent of the magnetic field, while the length of the negative glow region decreases appreciably with increasing magnetic field. The measured electron distribution function agrees well with the nonlocal theory, according to which the current in the Faraday dark space is carried by the intermediate electrons that are not trapped in the potential well and the energies of which are lower than the first excitation energy.     

Influence of electron energy distribution on helium recombining plasma diagnostics using line emissions

The influence of electron energy distribution on helium recombining plasma diagnostics is investigated using a helium collisional‐radiative model. The population densities of excited helium atoms are calculated for Maxwellian and non‐Maxwellian distribution plasma cases. In the case of the Maxwellian distribution plasma, the electron temperature and electron density determined by the Boltzmann plot method agree well with the input plasma parameters. On the other hand, it is indicated that the electron temperature and electron density are significantly underestimated in the bi‐Maxwellian distribution plasma case, even though the density of the hot electron components is three orders smaller than that of the bulk electrons. This result indicates that in a non‐Maxwellian helium recombining plasma, evaluation of the particle balance based on line emissions from excited helium atoms would be difficult because the reaction rate of atomic and molecular processes is strongly dependent on the electron temperature and density.     

LEAD螺旋波射频等离子体电子能量分布函数的测量

通过电压扫描探针测量了LEAD装置螺旋波射频等离子体伏安特性曲线和电子能量分布函数,并对等离子体基本参数剖面如电子温度、密度、等离子体电位和鞘电位降系数等进行了计算.实验发现在LEAD装置半径5cm以内的位置电子能量分布函数都遵循麦克斯韦分布.而在半径7cm附近,即与射频源线圈处于相同径向位置,电子能量呈现出典型的双麦...     

Hot Ion Production in a Modified Penning Discharge

Ions with Maxwellian energy distributions and kinetic temperatures up to seven keV have been observed in a modified Penning discharge. Investigation of the plasma revealed two distinct spoke-like concentrations of charge, consisting respectively of ions and electrons, rotating with different velocities in the sheath between the plasma and the anode ring. Theoretical expressions are derived for the frequency of the ion and electron spoke rotation, for the ion kinetic temperature resulting from the ion spoke velocity, and for the ion heating efficiency. An extensive series of experimental measurements were made to check these theoretical expressions, and approximate agreement was obtained. It is shown that the ion kinetic temperature in the modified Penning discharge scales according to the relation Vi ~ Vani1/4/B1/2 where Va is the applied anode voltage, ni is the ion density in the sheath, and B is the magnetic field strength. The observed data demonstrate that the ion heating efficiency can be as high as several tens of percent.     

尘埃颗粒与等离子体鞘层相互作用的数值模拟

通过求解一维稳态的尘埃等离子体鞘层模型,得到了等离子体鞘层势、正离子密度、电子密度和尘埃颗粒密度随一维横向的分布,Bohm判据及鞘层边界无量纲Bohm速度随尘埃密度的变化曲线,尘埃颗粒的带电量和尘埃密度的关系,尘埃颗粒的温度对尘埃颗粒自身在鞘层中分布的影响。结果表明,随着尘埃密度的增加,鞘层的厚度在减小,鞘层内的电子密度在下降,而且尘埃颗粒的带电量也在逐渐减少;随着尘埃温度的增加,鞘层的厚度减小,电子密度下降,而且鞘层附近的尘埃颗粒在逐渐增多。     

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.     

Stochastic electron heating in a capacitive RF discharge withnon-Maxwellian and time-varying distributions

In capacitively coupled radio frequency discharges, the electrons gain and lose energy by reflection from oscillating, high voltage sheaths. When time-averaged, this results in stochastic heating, which at low pressure is responsible for most of the electron heating in these discharges. Previous derivations of stochastic heating rates have generally assumed that the electron distribution is a time-invariant, single-temperature Maxwellian, and that the sheath motion is slow compared to the average electron velocity, so that electrons gain or lose a small amount of energy in each sheath reflection. Here we solve for the stochastic heating rates in the opposite limit of fast sheath motion and consider the applicability of the slow and fast sheath equations in the intermediate region. We also consider the effect of a two-temperature Maxwellian distribution on particle balance and the effect of a time-varying temperature on the heating rates and densities     

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.     

Heat flow through a plasma sheath in the presence of secondary electron emission from plasma‐wall interaction

The formation of a plasma sheath in front of a negative wall emitting secondary electron is studied by a one‐dimensional fluid model. The model takes into account the effect of the ion temperature. With the secondary electron emission (SEE ) coefficient obtained by integrating over the Maxwellian electron velocity distribution for various materials such as Be, C, Mo, and W, it is found that the wall potential depends strongly on the ion temperature and the wall material. Before the occurrence of the space‐charge‐limited (SCL ) emission, the wall potential decreases with increasing ion temperature. The variation of the sheath potential caused by SEE affects the sheath energy transmission and impurity sputtering yield. If SEE is below SCL emission , the energy transmission coefficient always varies with the wall materials as a result of the effect of SEE , and it increases as the ion temperature is increased. By comparison of with and without SEE , it is found that sputtering yields have pronounced differences for low ion temperatures but are almost the same for high ion temperatures.     

碰撞对两种正离子的电负性磁鞘影响的数值研究

建立包括两种正离子的电负性磁鞘的流体模型,利用四阶龙格库塔法数值求解描述一维稳态等离子体鞘层的方程组,考察离子与中性粒子碰撞对一维稳态等离子体鞘层的影响.结果表明:鞘边Ar⁺与He⁺的含量比值与碰撞参数对离子马赫数的取值范围都有影响.鞘边负离子含量越少,碰撞对鞘层中带电粒子密度的影响越明显.并且随碰撞参数的加大,鞘层中电子、负离子的密度下降越快,两种正离子的密度则呈现不同的波动变化.鞘边负离子含量越多,碰撞对鞘层中两种正离子的速度影响就越明显.此外,碰撞参数越大对鞘边δ越大的鞘层中的带电粒子密度影响越大.