Nonstationary and Quasi-stationary Treatment of Distribution Anisotropy in the Temporal Relaxation of an Energetic Electron Group

A relaxation study of an electron group in collision dominated weakly ionized plasmas has been performed. The study is based on the two-term approximation of the Legendre polynomial expansion of the electron velocity distribution in the nonstationary Boltzmann equation. To overcome the limitation of the conventional quasi-stationary treatment of the distribution anisotropy, a very efficient solution approach of the nonstationary kinetic equation in two-term approximation has been developed which allows for a strict nonstationary treatment of the distribution anisotropy. By using this approach the temporal evolution of the isotropic and anisotropic distribution of the electrons has been investigated for a model plasma, which involves typical features of an inert gas plasma. A comparison of the results with corresponding ones obtained by applying the conventional approach under various parameter conditions clearly indicates a pronounced falsification of the real relaxation course by the latter approach.     

Electron Kinetics with Attachment and Ionization from Higher Order Solutions of Boltzmann's Equation

An appropriate approach is presented for solving the Boltzmann equation for electron swarms and nonstationary weakly ionized plasmas in the hydrodynamic stage, including ionization and attachment processes. Using a Legendre-polynomial expansion of the electron velocity distribution function the resulting eigenvalue problem has been solved at any even truncation-order. The technique has been used to study velocity distribution, mean collision frequencies, energy transfer rates, nonstationary behaviour and power balance in hydrodynamic stage, of electrons in a model plasma and a plasma of pure SF₆. The calculations have been performed for increasing approximation-orders, up to the converged solution of the problem. In particular, the transition from dominant attachment to prevailing ionization when increasing the field strength has been studied. Finally the establishment of the hydrodynamic stage for a selected case in the model plasma has been investigated by solving the nonstationary, spatially homogeneous Boltzmann equation in twoterm approximation.     

Modelling of Secondary Electron Impact on the Self-Consistent RF Bulk Plasma Description

The impact of a secondary electron beam, generated at the electrodes and accelerated in the sheaths, on the self-consistent treatment of the electron behaviour in an rf bulk plasma has been investigated by a parametric study. Source of electrons in the plasma are collisional ionization and secondary electron injection. Electrons are lost by ambipolar diffusion to the electrodes of a parallel plate rf discharge configuration. The non-stationary Boltzmann equation is used to determine self-consistently the rf field amplitude necessary for maintaining the steady-state rf bulk plasma as well as the time resolved behaviour of the electron energy distribution function and of all contributions to the electron particle and power balance, at given source rate and energy distribution of secondary electron injection.     

Spatially Homogeneous Modelling of a Stabilized XeCl* Laser Discharge

Recently an improved technique to create a stable and homogeneous discharge for pumping excimer laser plasmas has been proposed in [1]. This technique is based on the additional use of a stabilizing low-current preliminary discharge. For the study of such laser discharges a self-consistent spatially homogeneous model with the inclusion of the time-dependent Boltzmann equation for the electrons, of the rate equation system arising from the heavy particle and photon kinetics and of the electrical circuit equations has been employed. A brief presentation of important features of the comprehensive model is given. An iterative procedure to solve self-consistently the system of kinetic, rate and circuit equations has been generalized and applied to discharge conditions where a dominant electron-electron interaction occurs. Model calculations have been performed for typical XeCl* laser plasmas which operate according to the improved discharge technique. On this basis a detailed analysis of main features of this laser discharge is given and the impact of various parameters on significant characteristics of the discharge is calculated and discussed.     

ArF准分子激光系统的能量效率特性

为深入理解ArF准分子激光系统的运转机制,进而获得优化ArF准分子激光系统设计的理论及方向性指导,利用一维流体模型,以气体高压放电等离子体深紫外激光辐射过程为主要对象,研究了放电抽运ArF准分子激光系统的动力学特性,梳理了ArF准分子激光系统的能量传递过程,深入研究了等离子体放电机理,从能量沉积效率、ArF*粒子形成过程、激光输出三个方面,分析了动力学过程中影响能量效率的主要因素,提出了相应的改进优化措施.仿真结果表明,氟气及相关粒子在系统运转过程中有重要作用,工作气体中氟气的组分比例对能量效率影响较大,偏离最佳点会导致激光系统能量效率的下降.相关结论为ArF准分子激光系统的优化设计和稳定可靠运转提供了重要的理论参考依据.     

The Impact of Different CO Admixtures on the Electron Kinetics in Collision Dominated RF He/CO Bulk Plasmas

Electron energy distribution functions and mean collision frequencles for the uniform bulk plasma of established rf discharges in He/CO have been obtained by solving the time dependent Boltzmann equation. The results, which are of importance for plasma processing and laser technology, show that already small CO admixtures to He remarkably changes the periodic behaviour of the energy distribution of the electrons by drastical enhancement of the collisional energy dissipation effectiveness in the mixture. These changes can be interpreted on the basis of a lumped energy dissipation frequency in all electron collisions which is determined by the atomic data of the electron collision processes as well as by the admixture fractions and which drastically increases with increasing CO admixture. The degree of modulation of the energy distribution in different parts of the electron energy space and its population on the time average at higher energies are determined by the relation between the rf field frequency and the mentioned lumped energy dissipation frequency.     

Resonant interaction of the Langmuir wave with quasi-stationary plasma electrons

Evolution of the Langmuir wave in quasi-stationary plasma is considered. A consistent solution to the closed system of the Vlasov–Poisson equations is obtained in the adiabatic approximation. Dispersion of the wave evolving in the electron distribution tail with variable electron concentration or plasma temperature is described. It is established that the plasma oscillation energy increases with decreasing electron concentration or increasing temperature. After plasma regains its initial state, the wave parameters also restore their initial values. That is, the wave evolution in the quasi-stationary plasma is a completely reversible process.     

Time - Dependent Multi - Term Treatment of Plasma Electrons Acted upon by RF Electric Fields

Using a new method for solving the time-dependent electron Boltzmann equation in higher order accuracy, studies of the temporal behaviour of electrons in weakly ionized, collision-dominated plasmas under the action of rf fields have been performed. The method is based upon a multi-term approximation of the Legendre polynomial expansion of electron velocity distribution function and is applied to investigate the established periodic behaviour of the electron velocity distribution in helium, argon and CO plasmas. The results obtained in various approximation orders are discussed. The analysis has shown that the simplified treatment using only two terms of the velocity distribution expansion can fail in several conditions. In general, the four-term approximation gives already a good representation of the convergent solution of the electron Boltzmann equation at each instant of the rf period. The discrepancies between two-term and convergent results are found to depend sensitively on the specific atomic data, in particular on the magnitude of the various electron collision cross sections involved. Furthermore, the results obtained in the multi-term approximation are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between convergent eight-term Boltzmann and Monte Carlo calculations is found.     

On nonlinear dynamics of a sheet electron beam

The nonstationary model is considered allowed to describe the sheet electron beam dynamics with nonuniform current density profile in collisionless approximation. The kinetic distribution function is used dependent on the particle motion integral, so the distribution function automatically satisfies to Vlasov equation. The results of numerical and analytical calculations are discussed.     

Temporal relaxation of plasma electrons acted upon by directcurrent electric and magnetic fields

On the basis of the time-dependent electron Boltzmann equation the temporal relaxation of the electrons in the presence of electric and magnetic fields in weakly ionized, collision dominated plasmas has been studied. The relaxation process is treated by using a strict time-dependent two-term approximation of the velocity distribution function expansion in spherical harmonics. A new technique for solving the time-dependent electron kinetic equation in this two-term approximation for arbitrary angles between the electric and magnetic fields has been developed and the main aspects of the efficient solution method are presented. Using this new approach and starting from steady-state plasmas under the action of time-independent electric fields only, the impact of superimposed DC magnetic fields on the electron relaxation is analyzed with regard to the control of a neon plasma. The investigations reveal an important effect of the magnetic field on the temporal relaxation process. In particular, it has been found that the relaxation time of the electron component with respect to the establishment of steady-state can be enlarged by some orders of magnitude when increasing the magnetic field strength     

激光烧蚀脉冲放电激发的土壤等离子体电子数密度和温度的研究

以激光烧蚀快脉冲放电激发土壤为例,研究了激光烧蚀快脉冲放电等离子体技术产生的土壤等离子体的电子数密度和温度。根据实验测得的Si原子和离子谱线的强度和萨哈玻尔兹曼方程,计算了等离子体的电子温度,并从分析Si I 250.69nm谱线的斯塔克展宽中导出了等离子体的电子数密度。与使用同样激光能量激发的激光等离子体相比,激光烧蚀快脉冲放电激发等离子体的电子数密度和温度都明显增加,与观察到的光谱信号强度是一致的。     

低真空下紫外激光烧蚀铜诱导发光的机理

采用时间与空间分辨的光谱测量技术,测量了在低真空下XeCl紫外激光烧蚀金属Cu诱导产生等离子体发光羽的发射光谱随时间和空间的强度分布,利用快速同步照相的方法获得了发光羽的相片,结果发现发光羽的不同区域有不同的颜色特征。根据实验结果建立了非常可能的激光烧蚀诱导发光的理论模型,认为不同区域的主要发光机理不同,连续辐射背景光来自近靶处高能电子的运动而产生的轫致辐射;原子线的产生来自电子碰撞传能以及电子与离子的复合激发;离子线的产生来自电子与离子碰撞传能激发。此模型不仅能解释单一激发模型所能解释的实验现象,而且还能够很好地解释单一模型所不能解释的实验现象,低真空下紫外激光烧蚀铜诱导发光的机理与常压下相似,在此实验条件下可以更准确地揭示诱导发光的机理。     

The homogeneity of a stabilized discharge-pumped XeCl* laser

* laser arrangement. The special pumping technique of this laser discharge is based on the additional use of a stabilizing low-current preliminary discharge. The model takes into account the time-dependent electron Boltzmann equation including electron–electron interaction for the determination of the electron kinetics, an extensive reaction kinetics involving various heavy particles and photons, and the relevant electrical circuit equations. The study has shown that density perturbations of preionization electrons lead to the inhomogeneity of the discharge plasma and the laser output. Furthermore, the impact of the spatial distribution of preionization electrons, of the HCl portion of the gas mixture, and of a low-current preliminary discharge for the discharge operation is discussed. Received: 10 September 1996/Revised version: 21 July 1997     

The Nonstationary Behaviour of the Electron Current Density in the Weakly Inonized Plasma at High Field Frequencies

Based upon former studies concerning the nonstationary electron kinetics in collision dominated, weakly ionized plasmas the phase delay between the ac electric field component and the resultant ac electron current density has been analysed, theoretically and experimentally, under the specific conditions of a microwave field superimposed to a dc discharge plasma column. The complex plasma conductivity and thus the phase delay has been calculated by solving an appropriate electron kinetic equation. The same quantities have been experimentally determined by using the microwave cavity which operates with different resonator modes. A comprehensive comparison between calculated and measured quantities for different neon discharge plasmas leads to a complete confirmation of the theoretical expectations.     

Self-consistent hybrid model for a stratified positive column of a low pressure glow discharge

The stratification of a positive column of a low-pressure glow discharge in inert gases has been studied with the help of a self-consistent hybrid model. The model is based on the solution of a nonlocal kinetic Boltzmann equation for the electron distribution function, a nonstationary drift-diffusion equation for the ions, and the Poisson equation for the electric field. Spatial electron and ion density distributions and the electric field distribution in the positive column were obtained. The converged solution of the model gives a self-consistent resonant strata length L and the value and the form of the modulated plasma parameters. An unexpected surprising result was obtained: for a given potential drop in the positive column of a low-pressure glow discharge, a self-consistent spatially modulated striation-like electric field does not lead to the resonant increasing of the ionization frequencies in the discharge as compared with a constant electric field with the same potential drop. Usually, it was assumed that, in spatially modulated field distributions, all the parameters in a striated plasma will be more pronounced and have a resonant form. The text was submitted by the authors in English.     

On the Question of Increasing Maxwellization of the Electron Energy Distribution Function due to Electron — Electron Interaction with Growing Ionization Degree in the Beam Discharge Plasma

The question of the establishment of an almost complete Maxwellian energy distribution of the electrons in a given discharge plasma is of importance, especially under the aspect of a more convenient determination of transport and rate coefficients. In [5] an energy space averaged criterion for the establishment of such a structure of the electron energy distribution function in the stationary beam discharge plasma of molecular gases was formulated from a heuristic point of view. This paper investigates this question in detail starting from the adequate Boltzmann equation of such plasmas. Energy resolved conditions for the establishment of an almost complete Maxwellian distribution are derived from the kinetic equation. Using one of these conditions, the formal derivation of the mentioned averaged condition is performed and its limitations are shown. The fulfilment of the energy resolved and of the averaged conditions are illustrated and discussed using solutions of the kinetic equation in purely molecular hydrogen for two parameter sets yielding larger and smaller deviations of the real distribution function from the Maxwellian form.     

Temporal Characteristic of M--M Transition Lasers in Strontium Atom Vapour

The kinetic process of Sr atom metastable-metastable transition lasers in He-St longitudinal pulsed discharge is analysed and a concise self-consistent physical model is developed. The temporal evolutions of discharge parameters, main paxticle densities, the electron temperature, and the lasing pulses are numerically calculated. The results provided by the model agree well with the experiment, and the temporal behaviour of each laser pulse is explained successfully by the simulation results.