Modeling of the nanoparticle coagulation in pulsed radio-frequency capacitively coupled C_2H_2 discharges

The role of pulse parameters on nanoparticle property is investigated self-consistently based on a couple of fluid model and aerosol dynamics model in a capacitively coupled parallel-plate acetylene(C2H2) discharge. In this model, the mass continuity equation, momentum balance equation, and energy balance equation for neutral gas are taken into account.Thus, the thermophoretic force arises when a gas temperature gradient exists. The typical results of this model are positive and negative ion densities, electron impact collisions rates, nanoparticle density, and charge distributions. The simulation is performed for duty ratio 0.4/0.7/1.0, as well as pulse modulation frequency from 40 k Hz to 2.7 MHz for pure C2H2 discharges at a pressure of 500 m Torr. We find that the pulse parameters, especially the duty ratio, have a great affect on the dissociative attachment coefficient and the negative density. More importantly, by decreasing the duty ratio, nanoparticles start to diffuse to the wall. Under the action of gas flow, nanoparticle density peak is created in front of the pulse electrode,where the gas temperature is smaller.     

Simulation of nanoparticle coagulation in radio-frequency C_2H_2/Ar microdischarges

The nanoparticle coagulation is investigated by using a couple of fluid models and aerosol dynamics model in argon with a 5% molecular acetylene admixture rf microdischarges,with the total input gas flow rate of 400 sccm.It co-exists with a homogeneous,secondary electron-dominated low temperature γ-mode glow discharges.The heat transfer equation and flow equation for neutral gas are taken into account.We mainly focused on investigations of the nanoparticle properties in atmospheric pressure microdischarges,and discussed the influences of pressure,electrode spacing,and applied voltage on the plasma density and nanoparticle density profiles.The results show that the characteristics of microdischarges are quite different from those of low pressure radio-frequency discharges.First,the nanoparticle density in the bulk plasma in microdischarges is much larger than that of low pressure discharges.Second,the nanoparticle density of 10 nm experiences an exponential increase as soon as the applied voltage increases,especially in the presheath.Finally,as the electrode spacing increases,the nanoparticle density decreased instead of increasing.     

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.     

Mode transition in dusty micro-plasma driven by pulsed radio-frequency source in C_2H_2/Ar mixture

Physical qualities of dusty plasma in the pulsed radio-frequency C_2H_2/Ar microdischarges are carefully investigated by a one-dimensional hydrodynamic model and aerosol dynamics model.Since the thermophoretic force has a great effect on the nanoparticle density spatial distribution,the neutral gas energy equation is taken into accounted.The effects of pulse parameters(dust ratio,modulation frequency) on the nanoparticle formation and growth process are mainly discussed.The calculation results show that,as the duty ratio increases,the mode transition from the sheath oscillation(a regime) to the secondary electron heating(7 regime) occurred,which is quite different from the conventional pulsed discharge.Moreover,the effect of modulation frequency on the width of sheath and plasma density is analyzed.Compared with the H_2CC~-ions,the modulation frequency effect on the nanoparticles density becomes more prominent.     

Momentengleichungen für Plasmen mit anisotropem Neutralgasdruck und anisotropem Ionendruck

Strongly non-Maxwellian and non-isotropic velocity distributions of the neutral atoms and of the ions occur in collisionless plasmas at high degrees of ionization, especially in gas discharges at low pressures and high current densities and in high temperature plasmas. The velocity distributions and the related velocity moments for the neutral gas and the ion gas are calculated. The influence of the magnetic fields on the ions is neglected. Especially, the pressure tensors and the heat flow tensors are investigated. The differential equations are given for the velocity moments of the velocity distribution. Additional terms occur in the equation of motion, if the pressure is non-isotropic and non-Cartesian coordinates are used. A heat flow tensor is evaluated that closes the system of differential equations for the neutral gas consistently and allows to rederive typical formulas of the molecular neutral gas flow. The heat flow tensor essentially determines the type of the differential equation system for the velocity moments. It is shown, that the neutral gas temperature is not constant across the plasma. Different statements deal with the heat flow tensor in the ion gas. In particular, non-vanishing ion temperature on the axis and a system of differential equations for the positive column under free-fall conditions are investigated. The inertia terms for the ion gas and the neutral gas must be taken into account in the pressure balance of the plasma.     

Experimentelle und theoretische Untersuchungen von Nichtgleichgewichtseffekten an stationären Heliumplasmen unter Normaldruck

Measurements and calculations of temperature, densities and field-strength-current-characteristics of cascaded arcs (0.15 and 0.3 cm radius) burning in Helium under normal pressure are reported. It is shown that the evaluation of measured arc data assuming Saha equilibrium is not in agreement with the detailed solution of the balance equations. The temperature of electrons and heavy particles as well as the density of electrons and neutrals must be determined as independent variables from the rate equation for ground state neutrals, from the equation of state, and from the energy balance of the electron gas and of the total plasma. The latter equation can be replaced by relations between measured intensities and the state variables. The deviations from Saha equilibrium are mainly caused by diffusion of neutral particles into the arc core and of charged particles into the opposite direction. The theoretical results derived from the balance equations are compared with spectroscopic line intensity and line width measurements. The agreement is good even if the equilibrium conditions are strongly violated.     

三种电极的大气压氩等离子体射流光学特性

采用铜片-单匝线圈电极、螺旋缠绕电极和双铜片电极3种结构的放电装置,以氩气作为工作气体,在正弦波激励下获得了大气压等离子体射流。利用电学方法测量了放电电流以及电荷量,并对放电脉冲和放电功率进行了研究;利用发射光谱法对射流的等离子体参量进行了空间分辨测量,并根据ArⅠ 763.5 nm和Ar Ⅰ 772.4 nm的光强计算了电子激发温度。结果发现：在外加电压的正负半周期内,电流脉冲的个数和幅值呈现非对称的变化趋势;随着外加电压的增加,3种结构电极的放电功率从1.7 W逐渐增加到6.0 W;在相同的外加电压情况下,电极面积越小,等离子体射流的长度越长;3种等离子体射流的电子激发温度在1 348.5~3 212.1 K之间,并且随着气体流量的增加,各位置的电子激发温度总体上呈下降趋势,而等离子体的电子密度呈上升趋势。实验结果表明：外加电压对放电功率有一定影响;射流长度与电极面积有关;气体流量对电子激发温度和电子密度的空间分布起重要作用。     

Numerical investigation of a fast-axial-flow CW CO2 laser

This paper presents the results of the calculation of the parameters of the active medium of a fast-axial-flow CO₂ laser using numerical methods in the framework of a one-dimensional approximation of the set of continuity equations, Bernoulli equation, equation of gas state, energy equation and multi-temperature rate equations with regard to diffusion for the gas flow in the cylindrical discharge tube. The spatial distribution of the small-signal gain and gas temperature along the gas flow direction have been calculated for a given set of initial conditions, namely, gas flow velocity, gas pressure and the tube diameter. In addition, the dependence of small-signal gain, the asymmetric stretch vibrational temperature of CO₂ (T₃) and the gas temperature on the discharge current were studied.     

Effect of electrode configuration on plasma spatial distribution and gas temperature in multi-arc plasma generator with three pairs of electrodes

In this paper, a novel nonthermal multi-arc plasma generator with three pairs of electrodes is presented to obtain large-volume plasma. The discharge behaviour of multi-arc is investigated through high-speed photography. Statistical process of the photographic images of arc discharge is used for analysis of the effect of electrode configuration on arc spatial distribution and fluctuation of plasma flow. Besides, the gas temperature is diagnosed by diatomic molecular OH fitting method. Results show that the electrode configuration has vital effect on the spatial distribution of plasma in discharge area. A relatively stable region with high luminance is obtained in the centre of the discharge area by adjusting the electrode arrangements, in which the plasma gas temperature in swirl flow field is higher than that in straight flow field in multi-arc generator. Furthermore, the fluctuation of plasma flow weakens in multi-arc generator with electrode configurations capable of producing swirl flow field.     

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设计了一个取样位置能在射频辉光放电等离子体电极间自由移动的取样装置,用质谱计测量了SiCl4等离子体的离子信号。提出了一种线性拟合的方法用于计算SiCl4等离子体的消耗率,利用测量的离子信号,计算出了SiCl4等离子体中SiCln(n=0~2)中性基团的空间分布。实验结果表明,可移动质谱取样装置的设计是合理的;用线性拟合方法得到的等离子体消耗率和中性基团的相对密度,比以前的方法得到的更精确。     

管板式大功率横流CO2激光横模测量及数值模拟

为了提高激光稳定性和激光加工质量,实验测量了大功率横流CO2激光横模,并理论分析了横模形成机理。针对大功率横流CO2激光器管板式电极结构,由麦克斯韦方程给出电场的横向分布,并通过数值计算得到了激光强度的横向分布。实验结果与数值模拟得到的激光能量分布基本一致。结果表明,在给定放电电压条件下,电极结构和气体流动速率决定了激光横模峰值大小,激光峰值的横向位置取决于气体流动的速率。     

Gas flow characteristics of argon inductively coupled plasma and advections of plasma species under incompressible and compressible flows

In this work, incompressible and compressible flows of background gas are characterized in argon inductively coupled plasma by using a fluid model, and the respective influence of the two flows on the plasma properties is specified. In the incompressible flow, only the velocity variable is calculated, while in the compressible flow, both the velocity and density variables are calculated. The compressible flow is more realistic; nevertheless, a comparison of the two types of flow is convenient for people to investigate the respective role of velocity and density variables. The peripheral symmetric profile of metastable density near the chamber sidewall is broken in the incompressible flow. At the compressible flow, the electron density increases and the electron temperature decreases. Meanwhile, the metastable density peak shifts to the dielectric window from the discharge center, besides for the peripheral density profile distortion, similar to the incompressible flow.The velocity profile at incompressible flow is not altered when changing the inlet velocity, whereas clear peak shift of velocity profile from the inlet to the outlet at compressible flow is observed as increasing the gas flow rate. The shift of velocity peak is more obvious at low pressures for it is easy to compress the rarefied gas. The velocity profile variations at compressible flow show people the concrete residing processes of background molecule and plasma species in the chamber at different flow rates. Of more significance is it implied that in the usual linear method that people use to calculate the residence time, one important parameter in the gas flow dynamics, needs to be rectified. The spatial profile of pressure simulated exhibits obvious spatial gradient. This is helpful for experimentalists to understand their gas pressure measurements that are always taken at the chamber outlet. At the end, the work specification and limitations are listed.     

Investigation of the glow and contracted discharge plasmas in nitrogen by coherent anti-Stokes Raman spectroscopy,optical interferometry,and numerical simulation

The translational temperature in the plasma of glow and contracted discharges is measured using the methods of coherent anti-Stokes Raman spectroscopy and optical interferometry. The current density in the discharge is determined by measuring the electron concentration with optical interferometry and emission spectroscopy. The distribution of nitrogen molecules over vibrational and rotational levels in the ground state, the electron energy distribution, and the time dependence of the gas temperature are numerically found based on a model including the homogeneous Boltzmann equation and balance equations for the concentrations of charged and excited particles and for the gas temperature. The dynamics of transition to the quasi-steady-state distribution of nitrogen molecules over vibrational levels is studied.     

Scaling laws for the spatial distributions of the plasma parameters in the positive column of a dc oxygen discharge

Comprehensive self-consistent simulations of the positive column plasma of a dc oxygen discharge are performed with the help of commercial CFDRC software (), which enables one to carry out computations in an arbitrary 3D geometry using fluid equations for heavy components and a kinetic equation for electrons. The main scaling laws for the spatial distributions of charged particles are determined. These scaling laws are found to be quite different in the parameter ranges that are dominated by different physical processes. At low pressures, both the electrons and negative ions in the inner discharge region obey a Boltzmann distribution; as a result, a flat profile of the electron density and a parabolic profile of the ion density are established there. In the ion balance, transport processes prevail, so that ion heating in an electric field dramatically affects the spatial distribution of the charged particles. At elevated pressures, the volume processes prevail in the balance of negative ions and the profiles of the charged particle densities in the inner region turn out to be similar to each other.     

Gasaufheizung und Energiebilanz einer stationären hochfrequenten Ringentladung in Edelgasen

Gasheating and Energy Balance of a Stationary High Frequency Ring Discharge in Rare Gases The energy balance of an inductively coupled high frequency (28,5 Mhz) discharge in a cylindrical vessel (11,2 cm diam.) in Ne, Ar, Kr, Xe at pressures between 0,1 and 10 Torr and at power inputs between 10 and 1000 W is investigated. The heat power transferred to the neutral gas in the stationary discharge is determined from the time behaviour of the neutral gas pressure in the afterglow period. The power measurements are completed by probe measurements of the electron density and energy distribution function. The measured electron energy distribution functions are maxwellian with a slight deficit electrons in the energy range of inelastic collisions. The electron temperatures show a rather low radial space dependence which can be explained on the basis of the local energy, balance by thermal conduction in the electron gas. The measured gas heating power is within the experimental error (factor 2) in agreement with calculations from the measured electron temperature and density under the assumption that the gas is heated by elastic electron-atom-collision only. A discussion of the energy balance for the total discharge indicates volume recombination losses of the ions which increase the density of the excited atoms and hence the energy losses by stepwise exitations.     

Potential of an insulated electrode in a high-energy electron flow under a gas pressure of 0.1–1.0 Pa

We analyze the variation of the floating potential of an insulated metallic electrode in a flow of electrons with an energy of up to 300 eV under a gas pressure of 0.1–1.0 Pa at a current density lower than 0.1 A/cm². It is shown that the dependence of the floating potential on the initial electron energy is non-monotonic; this fact is explained by the variation of the ratio of the ion current density to the density of fast electron current in the plasma. The balance of the electron and ion currents on the surface of an insulated electrode is ensured by the cutoff of the low-energy part of the electron flow at the level determined by the magnitude of the floating potential. The maximal value of the floating potential increases upon a decrease in the gas pressure; this is due to a decrease in the ion current density. The interval of energy variation in which the floating potential decreases from the maximal value (50–250 eV) to 5–6 eV increases with the electron current density and the gas pressure. The electrode material and the type of the gas do not noticeably affect the variation of the floating potential.     

Nonlinear standing waves in 2-D acoustic resonators

This paper deals with 2-D simulation of finite-amplitude standing waves behavior in rectangular acoustic resonators. Set of three partial differential equations in third approximation formulated in conservative form is derived from fundamental equations of gas dynamics. These equations form a closed set for two components of acoustic velocity vector and density, the equations account for external driving force, gas dynamic nonlinearities and thermoviscous dissipation. Pressure is obtained from solution of the set by means of an analytical formula. The equations are formulated in the Cartesian coordinate system. The model equations set is solved numerically in time domain using a central semi-discrete difference scheme developed for integration of sets of convection-diffusion equations with two or more spatial coordinates. Numerical results show various patterns of acoustic field in resonators driven using vibrating piston with spatial distribution of velocity. Excitation of lateral shock-wave mode is observed when resonant conditions are fulfilled for longitudinal as well as for transversal direction along the resonator cavity.     

Untersuchung des Nichtgleichgewichtszustandes an stationären Edelgasplasmen unter Normaldruck

It is shown that in wall stabilized rare gas arcs under normal pressure deviations from Saha-equilibrium occur. These deviations are very strong for Helium and Neon, smaller for Argon and Krypton discharges and are caused by diffusion of neutral and charged particles. A numerical method is described for the evaluation of temperature and density distributions from measured line intensities in the case of non-equilibrium, based on the balance equations of the arc plasma. Results are given for Neon, Argon and Krypton arcs of 0.15 and 0.3 cm radius. A simple validity condition for local thermal equilibrium in a plasma with diffusion effects is derived. The influence of non-equilibrium on the determination of transition probabilities is discussed.     

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N2-Ar射频放电等离子体广泛应用于微电子工业的刻蚀、氮化物薄膜的制备及金属表面氮化等技术领域。开发了N2-Ar混合气体容性耦合射频放电PIC/MC自洽模型,模型主要描述了e-,N2+,N+,Ar+等主要带电粒子的行为分布。等离子体的碰撞过程分别考虑了带电粒子(e-,N2+,N+,Ar+)与基态中性N2分子和Ar原子的21种碰撞反应过程。模拟结果表明,在纯N2及N2-Ar混合气体容性耦合射频放电中,各种带电粒子的数密度都在等离子体区达到最大值,且氮分子离子为主要粒子;在N2容性耦合射频放电中,加入10%氩气时,N+平均能量有所增加,在射频电极处两种氮离子(N2+,N+)高能粒子所占比例增加。本研究对认识N2-Ar射频放电等离子体过程微观机理具重要意义。