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)     

Spatial Distribution of Energetic Electrons during Magnetic Reconnection

Electron acceleration by the inductive electric field near the X point in magnetic reconnection is an important generation mechanism for energetic electrons. Particle simulations have revealed that most of energetic electrons reside in the magnetic field line pileup region, and a depletion of energetic electrons can be found near the centre of the diffusion region [Phys. Plasmas, 13 (2006) 012309]. We report direct measurement of energetic electron in and around the ion diffusion region in near-Earth tail by the cluster, and our observations confirm the above predictions: a depletion of the high-energy electron fluxes is detected near the centre of the diffusion region. At the same time, the plasma temperature has a similar profile in the diffusion region. .     

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.     

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.     

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.     

Control of the Interface Between Electron‐Hole and Electron‐Ion Plasmas: Hybrid Semiconductor‐Gas Phase Devices as a Gateway for Plasma Science

Coupling electron‐hole (e^–‐ h⁺) and electron‐ion plasmas across a narrow potential barrier with a strong electric field provides an interface between the two plasma genres and a pathway to electronic and photonic device functionality. The magnitude of the electric field present in the sheath of a low temperature, nonequilibrium microplasma is sufficient to influence the band structure of a semiconductor region in immediate proximity to the solid‐gas phase interface. Optoelectronic devices demonstrated by leveraging this interaction are described here. A hybrid microplasma/semiconductor photodetector, having a Si cathode in the form of an inverted square pyramid encompassing a neon microplasma, exhibits a photosensitivity in the ～420–1100 nm region as high as 3.5 A/W. Direct tunneling of electrons into the collector and the Auger neutralization of ions arriving at the Si surface appear to be facilitated by an n ‐type inversion layer at the cathode surface resulting from bandbending by the microplasma sheath electric field. Recently, an npn plasma bipolar junction transistor (PBJT), in which a low temperature plasma serves as the collector in an otherwise Si device, has also been demonstrated. Having a measured small signal current gain h_fe as large as 10, this phototransistor is capable of modulat‐ing and extinguishing the collector plasma with emitter‐base bias voltages <1 V. Electrons injected into the base when the emitter‐base junction is forward‐biased serve primarily to replace conduction band electrons lost to the collector plasma by secondary emission and ion‐enhanced field emission in which ions arriving at the base‐collector junction deform the electrostatic potential near the base surface, narrowing the potential barrier and thereby facilitating the tunneling of electrons into the collector. Of greatest significance, therefore, are the implications of active, plasma/solid state interfaces as a new frontier for plasma science. Specifically, the PBJT provides the first opportunity to control the electronic properties of a material at the boundary of, and interacting with, a plasma. By specifying the relative number densities of free (conduction band) and bound (valence band) electrons at the base‐collector interface, the PBJT's emitter‐base junction is able to dictate the rates of secondary electron emission (including Auger neutralization) at the semiconductor‐plasma interface, thereby offering the ability to vary at will the effective secondary electron emission coefficient for the base surface (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

氮气开关流柱形成过程的理论研究

使用蒙特卡罗-粒子模拟方法对氮气开关中的流柱形成过程进行模拟, 并结合计算结果对其进行理论分析. 发现在流柱击穿发生前(即空间电荷场远小于本底电场), 等离子体的电离频率、电子平均能量及其迁移速度等都近似为常数, 因此可以解析求解电子数密度方程对等离子体的演化行为进行分析. 在击穿发生后, 随机碰撞过程会破坏初始等离子体区域分布的对称性, 并出现分叉的等离子体区域结构. 在放电过程中, 随着等离子体密度增加, 其内部基本保持电中性且电场不断减小, 靠近阴阳极两端电荷分离产生的净电荷密度不断增加, 场强也不断增加, 且靠近阳极端的电荷密度(绝对值)和场强都大于阴极端. 通过改变极板间电压发现, 平均电子能量随极板间场强增加而增加, 电子迁移速度随着场强近似线性增加, 电离频率随场强的变化快慢介于E⁴与E⁵之间.     

Effect of sheath potential on electromagnetic radiation emitted from the rear surface of a metallic foil target

In ultra-intense laser--matter interactions, intense electric fields formed at the rear surface of a foil target may have strong influences on the motion of energetic electrons, and thereby affect the electromagnetic emissions from the rear surface, usually ascribed to transition radiation. Due to the electric fields, transition radiation occurs twice and bremsstrahlung radiation also happens because the electrons will cross the rear surface twice and have large accelerations. In the optic region, transition radiation is dominant. The radiation spectrum depends on the electric field only when the electrons are monochromatic, and becomes independent of the electric field when the electrons have a broadband momentum distribution. Therefore, in an actual experiment, the electric field at the rear surface of a foil could not be studied just with the measurement of optic emissions. In the terahertz region, both bremsstrahlung and transition radiations should be taken into account, and the radiation power could be enhanced in comparison with that without the inclusion of bremsstrahlung radiation. The frequency at which the maximum terahertz radiation appears depends on the electric field.     

Simulation of laser–plasma interactions and fast-electron transport in inhomogeneous plasma

A new framework is introduced for kinetic simulation of laser–plasma interactions in an inhomogeneous plasma motivated by the goal of performing integrated kinetic simulations of fast-ignition laser fusion. The algorithm addresses the propagation and absorption of an intense electromagnetic wave in an ionized plasma leading to the generation and transport of an energetic electron component. The energetic electrons propagate farther into the plasma to much higher densities where Coulomb collisions become important. The high-density plasma supports an energetic electron current, return currents, self-consistent electric fields associated with maintaining quasi-neutrality, and self-consistent magnetic fields due to the currents. Collisions of the electrons and ions are calculated accurately to track the energetic electrons and model their interactions with the background plasma. Up to a density well above critical density, where the laser electromagnetic field is evanescent, Maxwell’s equations are solved with a conventional particle-based, finite-difference scheme. In the higher-density plasma, Maxwell’s equations are solved using an Ohm’s law neglecting the inertia of the background electrons with the option of omitting the displacement current in Ampere’s law. Particle equations of motion with binary collisions are solved for all electrons and ions throughout the system using weighted particles to resolve the density gradient efficiently. The algorithm is analyzed and demonstrated in simulation examples. The simulation scheme introduced here achieves significantly improved efficiencies.     

Transition region between a nonequilibrium plasma and a negative electrode

A model is developed that describes the transition region between a quasineutral plasma and a planar negative electrode and in which the electron velocity distribution is represented as the sum of two Maxwellian distributions with different temperatures or as the sum of a Maxwellian distribution and distribution corresponding to an electron beam directed toward the electrode. Criteria for the formation of a sheath of positive space charge and a secondary plasma in the transition region are derived. An analysis is made of the dependence of the structure of the transition region on the parameters of the electron distribution, the space charge density distribution in the sheath, and the density of the ion current to the electrode. The criteria obtained are compared with the Bohm criterion.     

Magnetic-dipole vortex generation by propagation of ultraintense and ultrashort laser pulses in moderate-density plasmas

A magnetic-dipole vortex is generated in the behind of an ultraintense and ultrashort laser pulse in a near critical density plasma. The vortex is self-sustained by its magnetic field pressure which expels background electrons, and resulting sheath field accelerates electrons to drive high amplitude electric current inside the vortex. The electron energy spectra shows nonthermal distribution with relatively high energy. The vortex is stable for a long period since it is in the electromagnetic equilibrium, whose structure and characteristics are explained by a simple analytical model.     

Simulations of plasma formation in the cathode sheath of an efficient excimer lamp

Based on the available experimental data and computer simulations, analytical approximations of the quantities characterizing electron multiplication in the cathode sheath are proposed. The critical electric field is found above which runaway electrons are observed. Using the approximations proposed, the dependences of the plasma parameters (the electron and ion densities and currents and the electric field strength) on the distance from the cathode are analyzed. Simple formulas for the total current, the cathode sheath thickness, and the cathode potential drop as functions of the electric field on the cathode surface are derived.     

Effect of driving frequency on electron heating in capacitively coupled RF argon glow discharges at low pressure

A one-dimensional(1D) fluid model on capacitively coupled radio frequency(RF) argon glow discharge between parallel-plates electrodes at low pressure is established to test the effect of the driving frequency on electron heating. The model is solved numerically by a finite difference method. The numerical results show that the discharge process may be divided into three stages: the growing rapidly stage, the growing slowly stage, and the steady stage. In the steady stage,the maximal electron density increases as the driving frequency increases. The results show that the discharge region has three parts: the powered electrode sheath region, the bulk plasma region and the grounded electrode sheath region. In the growing rapidly stage(at 18 μs), the results of the cycle-averaged electric field, electron temperature, electron density, and electric potentials for the driving frequencies of 3.39, 6.78, 13.56, and 27.12 MHz are compared, respectively. Furthermore,the results of cycle-averaged electron pressure cooling, electron ohmic heating, electron heating, and electron energy loss for the driving frequencies of 3.39, 6.78, 13.56, and 27.12 MHz are discussed, respectively. It is also found that the effect of the cycle-averaged electron pressure cooling on the electrons is to "cool" the electrons; the effect of the electron ohmic heating on the electrons is always to "heat" the electrons; the effect of the cycle-averaged electron ohmic heating on the electrons is stronger than the effect of the cycle-averaged electron pressure cooling on the electrons in the discharge region except in the regions near the electrodes. Therefore, the effect of the cycle-averaged electron heating on the electrons is to "heat" the electrons in the discharge region except in the regions near the electrodes. However, in the regions near the electrodes, the effect of the cycle-averaged electron heating on the electron is to "cool" the electrons. Finally, the space distributions of the electron pressure cooling the electron ohmic heating and the electron heating at 1/4 T, 2/4 T, 3/4 T, and 4/4 T in one RF-cycle are presented and compared.     

Nonstationary macroparticle charging in an arc plasma jet

The charging of liquid metal macroparticles in the rarified part of a vacuum arc plasma jet is studied. The sheath in the vicinity of the macroparticle is collisionless and the problem with different Debye length to macroparticle radius ratios is analyzed. Maxwellian velocity distribution functions with different temperatures for the electrons and ions in an arbitrary ratio are allowed in the model. By solving the equation for the electric field together with the equation for ion and electron flux, the charging time and the near electric field of the macroparticles were calculated. The kinetics of the macroparticle charging are controlled by the ion and electron flux to the macroparticle, which depend on the potential distribution in the sheath. The potential falls off slower than 1/r² in the case of the large Debye length to macroparticle radius ratio, and falls off more rapidly than 1/r² in the other case. The charge which accumulates on a macroparticle at distances of about 10 cm from a 100-Å cathode is about 10^-16 C and the charging time is about 10^-5 s. The influence of the plasma drift velocity on the macroparticle charging is small. The model presented here agrees well with an experimental study of macroparticle repulsion from biased substrates     

DC column plasma kinetics in a longitudinal magnetic field

The cylindrical column plasma of a neon dc glow discharge under the influence of a weak longitudinal magnetic field is studied. An extended, fully self-consistent model of the column plasma has been used to determine the kinetic quantities of electrons, ions and excited atoms, the radial space charge field, and the axial electric field for given discharge conditions. The model includes a nonlocal kinetic treatment of the electrons by solving their spatially inhomogeneous kinetic equation, taking into account the radial space charge field and the axial magnetic field. The treatment is based on the two-term expansion of the velocity distribution and comprises the determination of its isotropic and anisotropic components in the axial, radial, and azimuthal direction. A transition from a distinctly nonlocal kinetic behavior of the electrons in the magnetic-field-free case to an almost local kinetic behavior has been found by increasing the magnetic field. The establishment of the electron cyclotron motion around the column axis increasingly restricts the radial electron energy transport and reduces the radial ambipolar current. The complex interaction of these transport phenomena with the alterations in the charge carrier production leads finally to a specific variation of the electric field components. The axial field increases by applying weak magnetic fields, however, decreases with increasingly higher magnetic fields. At higher magnetic fields, the radial space-charge field is considerably reduced     

电子温度对霍尔推进器等离子体鞘层特性的影响

采用二维粒子模拟方法研究了霍尔推进器通道中电子温度对等离子体鞘层特性的影响, 讨论了不同电子温度下电子数密度、鞘层电势、电场及二次电子发射系数的变化规律. 结果表明: 当电子温度较低时, 鞘层中电子数密度沿径向方向呈指数下降, 在近壁处达到最小值, 鞘层电势降和电场径向分量变化均较大, 壁面电势维持一稳定值不变, 鞘层稳定性好; 当电子温度较高时, 鞘层区内与鞘层边界处电子数密度基本相等, 而在近壁面窄区域内迅速增加, 壁面处达到最大值, 鞘层电势变化缓慢, 电势降和电场径向分量变化均较小, 壁面电势近似维持等幅振荡, 鞘层稳定性降低; 电子温度对电场轴向分量影响较小; 随电子温度的增大, 壁面二次电子发射系数先增大后减少. 关键词： 霍尔推进器 等离子体鞘层 电子温度 粒子模拟     

Comments on "On asymptotic matching and the sheath Edge"

In Sternberg and Godyak (2003), the authors claim that the sheath edge obtained through asymptotic matching is the edge of the electron free ion sheath characterized by Godyak's "strong" electric field |E|=kT/sub e//(e/spl lambda//sub D/). I present a careful re-analysis of the same problem and show that the paper is incorrect. The "intermediate region" of asymptotic analysis has an extremely narrow validity range in potential space and does not contain the ion-electron sheath. Consequently, in asymptotic theory, the sheath edge is uniquely defined by the transition from the quasi-neutral plasma to the ion-electron sheath. It may equivalently be characterized by the Bohm criterion or by a "medium" electric field |E|/spl sim/kT/sub e//(eL/sup 3/5//spl lambda//sub D//sup 2/5/) mediating between strong sheath fields |E|/spl sim/kT/sub e//(e/spl lambda//sub D/) and weak plasma fields |E|/spl sim/kT/sub e//(eL).     

Model of plasma sheath region using variable particle weights

The interaction of low temperature plasma with a probe is studied in this contribution. We would like to describe the transport of charged particles through the sheath region. A model of this sheath region is created. In the model we describe ions and electrons by molecular dynamics, with Monte Carlo method for collisions. This model is one dimensional in space and two dimensional in the velocity space and was modified for planar, spherical and cylindrical geometry. To reduce the number of particles, we introduced variable weights of particles. This approach enables to speed up the algorithm and to correctly compute the values of the electric current.     

Sheath thickness evaluation for collisionless or weakly collisionalbounded plasmas

The widely used Child-Langmuir law for sheath thickness evaluation in semi-infinite collisionless plasmas makes the assumptions of quasi-neutrality (n_e=n_i) and zero electric field intensity E=0 at the sheath edge, as well as applying the Bohm criterion for ions entering the sheath. However, through a whole region fluid model, Poisson's equation has been solved numerically for the steady-state solution through the sheath and presheath without these assumptions. With the sheath edge defined, as in the Child-Langmuir law, at the place where the ion velocity is equal to the Bohm velocity, the sheath thickness of a bounded collisionless or weakly collisional plasma has been found with this model in some cases to be much larger than that obtained with the Child-Langmuir Law. The sheath thickness discrepancy is significant under conditions found in low pressure high density plasma (HDP) tools for plasma processing. Results presented indicate that the sheath thickness is very sensitive to the electric field and space charge density at the sheath edge. The electric field and space charge density can be successfully estimated by an intermediate scale matching method, and are used to derive a modified expression for the potential in the sheath that can be solved numerically for sheath thickness. With these results, the matching problem, arising when sheath and plasma are modeled separately, can be overcome     

Energetic electron emission from a ferroelectric sample during incomplete surface discharge

In this paper, the results of simplified analytical modeling and particle-in-cell numerical simulations of plasma formation and propagation along the surface of a ferroelectric sample under the application of a negative driving pulse to the rear solid electrode are presented. These models allow one to reproduce the main characteristics of the incomplete discharge. In particular, it is shown that the experimentally observed energetic electrons are related to the secondary emission electron acceleration in the sheath between the plasma and the ferroelectric surface. Also, simulation results show that secondary electron emission significantly decreases the surface plasma density while increasing its propagation velocity and that high desorption rate of the neutrals is required to sustain surface plasma formation.