基于流体模型和非平衡态电子能量分布函数的高功率微波气体击穿研究

用流体模型研究高功率微波气体击穿时, 电子能量分布函数常被假设为麦克斯韦分布形式, 此假设可能将给模拟结果带来较大的误差. 通过求解玻尔兹曼方程, 得到非平衡状态下的电子能量分布函数. 分别将上述两类分布函数引入到流体模型中, 对氩气击穿进行了数值模拟. 结果表明, 基于非平衡分布函数得到的击穿时间与粒子模拟结果符合得很好, 而当平均电子能量较低时, 麦克斯韦分布函数的高能尾部导致了较短的击穿时间. 最后, 采用非平衡分布函数计算了不同压强下的氩气击穿阈值, 发现其与实验结果基本符合. 关键词： 微波气体击穿 电子能量分布函数 流体模型 玻尔兹曼方程     

Heating mechanism in one-dimensional bounded magnetized inductively coupled plasma

A self-consistent nonlocal kinetic model has been established to investigate the electron heating mechanism in an one-dimensional bounded magnetized inductively coupled plasma (MICP) under low pressures. The interaction function of electrons with rf electric field and electron energy distribution function (EEDF) are determined by solving the linearized Boltzmann equation incorporating with the Maxwell equations. The numerical results show that the presence of the direct-current (dc) magnetic field plays an important role in the EEDF and high-energy electrons are efficiently heated by the Azbel–Kaner resonances under the anomalous skin-effect conditions.     

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.     

A phase-space particles motion scheme for electron kineticsimulation

A phase-space particle motion scheme (PSPMS) for electron kinetic simulation is proposed. This scheme is based on the convenient representation of electron motion in phase space using the particles method. PSPMS offers the possibility of calculating the electron energy distribution function (EEDF) much faster than by conventional methods. PSPMS electron calculation is shown to match convective scheme and Monte Carlo simulations of swarms in the uniform electric field and the cathode fall (CF). PSPMS may be used for a self-consistent model of low-pressure glow discharge construction     

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.     

Kinetic two-dimensional modeling of inductively coupled plasmasbased on a hybrid kinetic approach

In this paper, we present a two-dimensional (2-D) kinetic model for low-pressure inductively coupled discharges. The kinetic treatment of the plasma electrons is based on a hybrid kinetic scheme in which the range of electron energies is divided into two subdomains. In the low energy range the electron distribution function is determined from the traditional nonlocal approximation. In the high energy part the complete spatially dependent Boltzmann equation is solved. The scheme provides computational efficiency and enables inclusion of electron-electron collisions which are important in low-pressure high-density plasmas. The self-consistent scheme is complemented by a 2-D fluid model for the ions and the solution of the complex wave equation for the RF electric field. Results of this model are compared to experimental results. Good agreement in terms of plasma density and potential profiles is observed. In particular, the model is capable of reproducing the transition from on-axis to off-axis peaked density profiles as observed in experiments which underlines the significant improvements compared to models purely based on the traditional nonlocal approximation     

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.     

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.     

射频感应耦合Ar-N2等离子体物理特性的Langmuir探针测量及理论研究

分别通过Langmuir探针测量和动力学模型模拟方法研究了射频感应耦合Ar-N₂等离子体中电子能量分布、电子温度、电子密度等物理量随N₂含量的变化规律.实验研究结果表明：电子能量分布呈现出非Maxwell型分布,并由双温分布向三温分布过渡;电子温度在不同的气压下随N₂含量的增加呈现出不同的变化规律.在放电气压小于1.3 Pa时,电子温度随N₂含量的增加而下降;当气压大于1.3 Pa时,电子温度随N₂关键词： 感应耦合等离子体 2混合气体放电')" href="#">Ar-N₂混合气体放电 电子能量分布 Langmuir探针     

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.     

Effects of nonlocal electron kinetics and transition from αto γ regime in an RF capacitive discharge in nitrogen

The electron kinetics and regime of operation of asymmetrically coupled RF (27-MHz) nitrogen discharges in two vessels with different interelectrode gaps over the range of 0.20-0.35 torr gas pressure are studied in terms of the electron energy distribution function (EEDF). The latter is measured by means of a computer-controlled data acquisition system, a Langmuir probe with cross-modulation second derivative technique applied. The experiments are performed with an axial resolution along the RF electric field and accompanied with a measurement of electrical discharge characteristics. The effects of local and nonlocal plasma response are considered. The transition between α and γ discharge regimes is registered by measuring the EEDF and its moments' changes with the increase of the RF discharge current density     

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.      

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.     

The influence of metastable atoms and the effect of the nonlocal character of the electron distribution on the characteristics of the positive column in an argon discharge

Commercial CFDRC software () is used to self-consistently simulate the plasma of the positive column (PC) of a dc discharge in argon. The software allows simulations in an arbitrary 3D geometry by using Poisson’s equation for the electric potential and fluid equations for the heavy components and by solving a nonlocal kinetic equation for electrons. It is shown that, in calculating the electron distribution function, the local approximation is almost always inapplicable under real conditions of a diffuse PC usually met in practice (pR<(5–10) cm Torr). The influence of metastable atoms, which can substantially affect the parameters of the PC plasma, is considered. It is shown that superelasic collisions play an important role in enriching the fast component of the electron distribution function and that the Penning ionization can result in an ascending volt-ampere characteristic of the positive column.     

Nonlocal phenomena in the positive column of a medium-pressure glow discharge

Commercial CFDRC software () is used to self-consistently simulate the plasma of the positive column (PC) of a medium-pressure dc discharge in argon. The software allows simulations in an arbitrary 3D geometry by using Poisson’s equation for the electric potential and fluid equations for the heavy components and by solving a nonlocal kinetic equation for electrons. It is shown that, in calculating the electron distribution function, the local approximation is almost always inapplicable not only at relatively low pressures (pR<1 cm Torr), but also at relatively high pressures (pR<10 cm Torr), i.e., under the real conditions of a diffuse PC usually met in practice. The use of the local approximation in solving the kinetic equation for electrons leads to significant errors in determining the main parameters of the PC. A paradoxical effect has been revealed: the peaks of the profiles of the excitation rates shift from the discharge axis toward the periphery as the pressure increases from low to medium values (1 cm Torr<pR<10 cm Torr). It is shown that the effect is related to the nonlocal character of the electron distribution function.     

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。     

射频低压等离子体电子能量分布函数的探针诊断

本文对于无内电极放电的射频低压等离子体,采用探针电流调制法,设计并建立了三探针诊断电子能量分布函数的测量系统,测量了压力在10^-3—10^-1Torr下氮气等离子体的电子能量分布函数。从理论和实验上研究了探针鞘层上射频干扰电压对测量电子能量分布函数的影响,给出了确定射频干扰值以及对射频干扰的影响进行修正的方法,并采用该方法对实验数据进行了修正,得到了正确的电子能量分布函数。根据所得到的电子能量分布函数计算的电子平均能量,与由探针伏安特性计算得到的电子平均能量相差不超过5％,该结果间接证明了本文实验测量系统的可靠性以及对射频干扰影响进行修正的正确性。     

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.     

Experimental investigation of nonlocality effects in the electron energy spectrum in an electronegative gas

The nonlocality of the electron energy distribution function (EEDF) in a dc discharge in oxygen is observed experimentally. A method is developed for measuring the isotropic part of the EEDF in a low-temperature plasma of electronegative gases. The radial dependence of the EEDF and the radial distributions of the electron density, the average electron energy, and the potential are determined. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 511–516 (10 April 1996)