Electron cyclotron resonance in a weakly magnetized radio-frequency inductive discharge

The evolution of the electron energy distribution function (EEDF) over a weak magnetic field range is investigated in magnetized radio-frequency (rf) inductive discharges under a collisionless regime where an anomalous skin effect and electron cyclotron resonance (ECR) can occur. A significant change in the low-energy range of the EEDF is found in the ECR condition during the evolution. The observed result reveals the low-energy electrons are efficiently heated by the rf ECR in the presence of the anomalous skin effect. The calculated result of the electron distribution based on kinetic theory is in good agreement with the experiment.     

高功率微波单一气体及混合气体击穿特性

综合考虑高功率微波对电子的加速过程以及电子与气体分子的碰撞过程,建立了单一气体与混合气体击穿过程的蒙特卡罗仿真模型,编写了三维蒙特卡罗仿真程序(3D-MCC)。针对单一气体Ar和N2以及混合气体N2/O2展开研究,仿真了气体雪崩击穿电子云形成过程,对比分析了不同气体电子能量分布函数随压强的变化规律。发现了Ar击穿特性受电子能量分布函数影响较大,而N2击穿特性受电子能量分布函数影响较小。通过分析平均电子能量以及电子密度随时间的变化过程,得到了Ar和N2击穿时间,并通过与流体模型计算得到的击穿时间比对分析验证了3D-MCC模型的正确性。在真空腔体内开展了S波段高功率微波大气击穿实验,测量得到了场强为6.38 kV/cm时不同压强下的大气击穿时间。通过在辐射源与真空腔体之间增加聚焦透镜,大大减小了壁效应的影响,并且采用模型仿真得到的大气击穿时间与实验结果吻合较好。     

Substantiation of the two-temperature kinetic model by comparing calculations within the kinetic and fluid models of the positive column plasma of a dc oxygen discharge

Results from kinetic and fluid simulations of the positive column plasma of a dc oxygen discharge are compared using commercial CFDRC software (), which enables one to perform numerical simulations in an arbitrary 3D geometry with the use of both the fluid equations for all the components (fluid model) and the kinetic equation for the electron energy distribution function (kinetic model). It is shown that, for both the local and nonlocal regimes of the formation of the electron energy distribution function (EEDF), the non-Maxwellian EEDF can satisfactorily be approximated by two groups of electrons. This allows one to take into account kinetic effects within the conventional fluid model in the simplest way by using the proposed two-temperature approximation of the nonequilibrium and nonlocal EEDF (2T fluid model).     

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     

Electron energy distribution function in a hollow-cathode glow discharge in mixtures of nitrogen with electronegative gases

The electron energy distribution function (EEDF) in a hollow-cathode glow discharge in mixtures of nitrogen with electronegative gases is investigated. It is shown that small admixtures of SF₆ or CCl₄ to nitrogen significantly increase the number of electrons in the energy range 2–6 eV, which corresponds to the inverse part of the EEDF. In nitrogen with small admixtures of F₂ or NF₃, the EEDF differ slightly from that calculated for pure nitrogen. The EEDF in these mixtures substantially depends on electron attachment to electronegative gas molecules.     

Hysteresis transition between diffuse and constricted modes of dc discharge in argon

The results of theoretical studies of hysteresis transition between the diffuse and constricted modes of a dc glow discharge in argon are presented. It has been shown that the experimentally observed hysteresis of the current voltage characteristic (CVC) at the transition from the constricted to the diffuse mode is caused by the nonlocal formation of the electron energy distribution function (EEDF) while taking into account the heterogeneity of radial fields, namely, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region. The effect of the non-local formation of the EEDF has been described approximately by introducing the effective temperature of the high-energy part of the EEDF and solving the equation for the radial profile of the high-energy part of the EEDF.     

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.     

Short-pulse high-power microwave breakdown at high pressures

The fluid model is proposed to investigate the gas breakdown driven by a short-pulse(such as a Gaussian pulse) highpower microwave at high pressures.However,the fluid model requires specification of the electron energy distribution function(EEDF);the common assumption of a Maxwellian EEDF can result in the inaccurate breakdown prediction when the electrons are not in equilibrium.We confirm that the influence of the incident pulse shape on the EEDF is tiny at high pressures by using the particle-in-cell Monte Carlo collision(PIC-MCC) model.As a result,the EEDF for a rectangular microwave pulse directly derived from the Boltzmann equation solver Bolsig+ is introduced into the fluid model for predicting the breakdown threshold of the non-rectangular pulse over a wide range of pressures,and the obtained results are very well matched with those of the PIC-MCC simulations.The time evolution of a non-rectangular pulse breakdown in gas,obtained by the fluid model with the EEDF from Bolsig+,is presented and analyzed at different pressures.In addition,the effect of the incident pulse shape on the gas breakdown is discussed.     

Numerical simulation of super-short pulsed discharge in Helium with particle-in-cell Monte--Carlo collisions technique

This paper reports that a simulation of glow discharge in pure helium gas at the pressure of 1.333×10³ Pa under a high-voltage nanosecond pulse is performed by using a one-dimensional particle-in-cell Monte Carlo collisions (PIC--MCC) model. Numerical modelling results show that the cathode sheath is much thicker than that of anode during the pulse discharge, and that there exists the phenomenon of field reversal at relative high pressures near the end of the pulse, which results from the cumulative positive charges due to their finite mobility during the cathode sheath expansion. Moreover, electron energy distribution function (EEDF) and ion energy distribution function (IEDF) have been also observed. In the early stage of the pulse, a large amount of electrons can be accelerated above the ionization threshold energy. However, in the second half of the pulse, as the field in bulk plasma decreases and thereafter the reverse field forms due to the excessive charges in cathode sheath, although the plasma density grows, the high energy part of EEDF decreases. It concludes that the large volume non-equilibrium plasmas can be obtained with high-voltage nanosecond pulse discharges.     

Electron Energy Distribution Function Extraction Using Integrated Step Function Response and Regularization Methods

Recently, electron energy distribution function (EEDF) extraction techniques have been evaluated using regularized solutions to the integral problem. These techniques do not assume any mathematical representation of the EEDF and solve the integral problem for any function that best represents the EEDF. Also, unlike the more widely used point-by-point extraction of the second-derivative relationship, the integrated relationship between electron current and the EEDF is used, instead of a relatively small fraction of the integrated data in the point-by-point method. In this paper, the electron current for an arbitrary distribution function is derived, assuming that the distribution is a sum of step functions representing such a function. This technique for EEDF extraction is validated by adding noise to numerically generated data and using a regularized least squares (RLS) method to calculate the original function by solving for the individual step function contribution to the total electron current. Comparisons are then made between the expected and the reconstructed solution to evaluate its accuracy with respect to EEDF reconstruction and integrated normalization of the electron density.      

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.     

Determination of the electron energy distribution in a plasma from the first and second derivatives of the probe current

An approach to the reconstruction of the electron energy distribution function (EEDF) as the sum of the second derivative of the electron current to the probe and some value proportional to its first derivative is proposed (hereafter we mean derivatives with respect to voltage). Solutions to model problems for typical electron distributions in a plasma show that this approach lowers the systematic error of EEDF reconstruction by several times in comparison with the conventional techniques using Langmuir and diffusion probes. The approach is applicable in a wide range of the ratio of the probe radius to the free path of electrons. It can be used for the determination of fast nonequilibrium electron distribution in neon discharge afterglow and also for the evaluation of the Maxwellian electron temperature in the low-energy range of nitrogen discharge afterglow.     

Modeling of the electrostatic corona discharge reactor

A model is presented for the electrostatic corona discharge reactor (ECDR) in a pin-plate configuration. The main objective is to describe the fundamental chemistry and physics governing the discharge behavior and to predict the ECDR performance under various operating conditions. The electric field strength is estimated assuming a space-charge-free field. A two-term spherical harmonic expansion is used to solve the Boltzmann equation for the electron energy distribution function (EEDF) and calculate the electron-molecule reaction rates using collision cross-section data. Species continuity equations are solved for the dry and wet air systems to predict ozone and NO_x at various feed flow rates (1630, 4890, 14, 670 cm/s) and an applied voltage of 10 kV. Among the various results reported, it is noted that the calculations indicate the Maxwell EEDF cannot be used because it overpredicts the electron-molecule rate coefficients by several orders of magnitude     

Electron temperature in a decaying krypton plasma in the presence of a low electric field

The influence of low electric fields on the average electron energy in an afterglow krypton plasma is studied by means of probe diagnostics and theoretical analysis. It is shown that, when the average electron energy is lower than the energy corresponding to the minimum scattering transport cross section, the degree of plasma ionization substantially affects the shape of the electron energy distribution function (EEDF). The nonequlibrium character of the EEDF results in the density dependence of the coefficient of ambipolar diffusion, which leads to a change in the radial profile of the charged particle density, an increase in the drop in the ambipolar potential across the plasma, and an increase in the rate of diffusive plasma decay. These effects substantially enhance the diffusive cooling of electrons, which is probably a decisive factor influencing the electron energy balance in high-Z noble gases.     

Non-Maxwellian electron energy distribution function in He,He/Ar,He/Xe/H<Subscript>2</Subscript> and He/Xe/D<Subscript>2</Subscript> low temperature afterglow plasma

Experimental studies of the electron energy distribution function “EEDF” under well defined conditions in flowing afterglow plasma, using a Langmuir probe are reported. The EEDF is measured in He₂ ⁺ and Ar⁺ dominated plasmas and in XeH⁺ and XeD⁺ dominated recombining plasmas. He is used as a buffer gas at medium pressures in all experiments (1600 Pa, 250 K). The deviation of the measured EEDF from Maxwellian distribution is shown to depend on plasma composition and on the processes governing the plasma decay. The influence of energetic electrons produced during the plasma decay on the body and tail of the EEDF is observed. The mechanism of energy balance in afterglow plasma is discussed.     

Validity of the two-term Boltzmann approximation employed in the fluid model for high-power microwave breakdown in gas

The electron energy distribution function （EEDF）, predicted by the Boltzmann equation solver BOLSIG＋ based on the two-term approximation, is introduced into the fluid model for simulating the high-power microwave （HPM） breakdown in argon, nitrogen, and air, and its validity is examined by comparing with the results of particle-in-cell Monte Carlo collision （PIC/MCC） simulations as well as the experimental data. Numerical results show that, the breakdown time of the fluid model with the Maxwellian EEDF matches that of the PIC/MCC simulations in nitrogen; however, in argon under high pressures, the results from the Maxwellian EEDF were poor. This is due to an overestimation of the energy tail of the Maxwellian EEDF in argon breakdown. The prediction of the fluid model with the BOLSIG＋ EEDF, however, agrees very well with the PIC/MCC prediction in nitrogen and argon over a wide range of pressures. The accuracy of the fluid model with the BOLSIG＋ EEDF is also verified by the experimental results of the air breakdown.     

Calculation of parameters of krypton plasma excited by electron beam with additional heating by high-frequency electric field

The electron energy-distribution functions, the rates of plasmochemical reactions, and the densities of various plasma components have been calculated for a microwave discharge (f = 1000 MHz, P = 100–700 mW) in krypton plasma (p = 0.5 atm) excited by an electron beam with an energy of 12 keV. It has been found that the heating by a microwave field shifts the peak of the electron energy-distribution function (EEDF) from 0.5 to 2 eV, which leads to higher rates of reactions with excitation thresholds lying near the EEDF peak. As a result, the population of excited levels increases by two to three times.     

Effect of molecular nitrogen on the electron mobility in a mixture of argon and optically excited sodium vapor

A parametric study of the electron energy distribution function (EEDF) and the electron mobility in the mixture Na + Ar + N₂ is carried out. An analysis is made of the conditions that obtain in a photoplasma when the detachment of the mean electron energy from the neutral gas temperature is due to superelastic collisions (collisions of the second kind) with excited sodium atoms. The case of low ionization of the medium at low vibrational temperatures of the ground state of the nitrogen molecules is considered. To find the EEDF a numerical solution of the Boltzmann transport equation is carried out. It is found that in the indicated mixture the presence of nitrogen leads to a depletion of the EEDF in the region of efficient vibrational excitation of the molecules and promotes the formation of inversion in the EEDF ∂f(ɛ)/∂ɛ>0 in the energy range corresponding to the Ramsauer minimum in the cross section of elastic collisions of electrons with the argon atoms. It is shown that the nonequilibrium character of the EEDF leads to a complicated dependence of the electron mobility on the partial ratios of the components of the mixture, the degree of ionization of the medium, and the population of the resonantly excited sodium atoms. Zh. Tekh. Fiz. 69, 14–19 (April 1999)     

沿面闪络流体模型电离参数粒子模拟确定方法

介绍了粒子模拟确定高功率微波介质沿面闪络击穿流体模型相关电离参数的方法.对粒子模拟方法 (包括带电粒子动力学方程、次级电子发射以及蒙特卡罗碰撞模型)和流体整体模型方法 (包括连续性方程和能量守恒方程)做了简介.基于自编的1D3V粒子模拟-蒙特卡罗碰撞程序给出了在高(低)气压、不同气体种类以及不同微波场强和微波频率下流体模型电离参数的粒子模拟结果,包括电离频率、击穿时间、平均电子能量、电子能量分布函数类型.研究结果表明:平均电子能量与电子能量分布函数类型关系不大;中低气压下,电子能量接近Maxwell分布,电子能量分布函数类型对电离参数几乎没有影响;中高气压下,电子能量分布函数类型对电离参数有重要影响,其依赖系数X趋于高阶形式.不同气体的电子能量分布函数类型不同,需要利用粒子模拟对电子能量分布函数类型进行标定.同时,电子能量分布函数依赖系数与微波场强和频率也有关系,其随微波场强增加而增大,随微波频率增加而减小.在给定考察范围(微波场强在7 MV/m以下,微波频率在40 GHz以内),中低气压下,平均电子能量随微波场强增加而迅速增大,电离频率随微波场强增加先增大后降低,平均电子能量随微波频率增加而降低,电离频率随微波频率增加先增加后降低;高气压下,平均电子能量随微波场强增加而缓慢增大,电离频率随微波场强增加而增大,微波频率对平均电子能量和电离频率影响不大.