Spatiotemporal evolution of the distribution function of electrons in sign-changing electric field

A numerical model for solving the Boltzmann unsteady non-local kinetic equation for the distribution function of electrons over energy is constructed. The Boltzmann equation for isotropic part of the distribution function written in natural variables the kinetic energy — the coordinate was solved by the pseudo-unsteady method. The model was applied for describing the spatiotemporal evolution of the distribution function of electrons in a uniform electric field. For a model distribution of the electric field with the “negative” value in the Faraday dark space and the “positive” value in the positive column of the glow discharge, the main macroscopic parameters of electrons are obtained, the diffusion mechanism of the electron current transfer in the negative electric field region is confirmed. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 07-02-00781-a) and by State Contract No. 02.513.11.3242.     

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.     

Local electron mean energy profile of positive primary streamer discharge with pin-plate electrodes in oxygen nitrogen mixtures

Local electron mean energy (LEME) has a direct effect on the rates of collisional ionization of molecules and atoms by electrons. Electron-impact ionization plays an important role and is the main process for the production of charged particles in a primary streamer discharge. Detailed research on the LEME profile in a primary streamer discharge is extremely important for a comprehensive understanding of the local physical mechanism of a streamer. In this study, the LEME profile of the primary streamer discharge in oxygen-nitrogen mixtures with a pin-plate gap of 0.5 cm under an impulse voltage is investigated using a fluid model. The fluid model includes the electron mean energy density equation, as well as continuity equations for electrons and ions and Poisson’s electric field equation. The study finds that, except in the initial stage of the primary streamer, the LEME in the primary streamer tip tends to increase as the oxygen-nitrogen mole ratio increases and the pressure decreases. When the primary streamer bridges the gap, the LEME in the primary streamer channel is smaller than the first ionization energies of oxygen and nitrogen. The LEME in the primary streamer channel then decreases as the oxygen-nitrogen mole ratio increases and the pressure increases. The LEME in the primary streamer tip is primarily dependent on the reduced electric field with mole ratios of oxygen-nitrogen given in the oxygen-nitrogen mixtures.     

The influence of dielectric surface charge distribution upon thepartial discharge behavior in short air gaps

A two-dimensional breakdown model based upon the continuity equations for electrons and ions and the Poisson equation is employed to examine the influence of surface charges upon the partial discharge behavior of a short metallic-dielectric plane-parallel electrode gap of 0.05 cm in an air-like mixture at atmospheric pressure. The form of charge distribution at the dielectric electrode surface is found to significantly affect a number of important discharge parameters, such as the uniformity of the electric field, the charge density and its radial distribution within the gap, as well as the discharge propagation time     

A simple model of processes in the drift region of negative corona discharge in a mixture of air with halocarbons

A model for negative glow corona discharge in a coaxial electrode configuration is presented. The main goal of this model is to describe the influence of a more efficiently electron-attaching gas on the distribution of free electron density in the drift region. The calculated distributions of electrons and other ionic components are shown. The model was applied in experiments realized in air + freon mixtures. A qualitative agreement between theoretical and experimental results was achieved.     

具有空心阴极放电特征的射频放电的两电子组模型

 运用两电子组模型，考虑了射频放电中的α过程和γ过程两种电离机制，并结合流体模型，研究了中等气压下窄电极间隙容性耦合射频放电在运行模式转变区的等离子体密度以及电离速率分布等特性。理论研究表明，γ电离过程在高电流模式运行中起主要作用，并证实了此类放电中存在显著的电子摆钟效应，具有类似于空心阴极放电的特征。     

Optimum conditions for pumping laser transitions of cadmium ions by various processes in a hollow-cathode discharge

The interaction of electrons of various energies with helium and cadmium atoms in a hollow-cathode discharge is analyzed. On the basis of the results of this analysis the conclusion is made that helium is ionized predominantly by electrons moving from the cathode wall to the cavity axis and having energies 70<ε<300 eV, whereas helium and cadmium are ionized predominantly by electrons with energies 9<ε<70 eV which move chaotically. For each of these energy ranges, the kinetic equation is solved and the electron energy distribution function (EDF) is determined, which is used for calculating pumping rates for laser transitions of cadmium ions. The conclusion is made that the rate of population of laser transitions through charge transfer is determined by electrons having a predominant direction of motion and an anisotropic EDF. The population rate associated with electron impact and the Penning ionization is determined by electrons moving chaotically and having an isotropic EDF. The analysis of the EDF made it possible to explain differences in discharge conditions (helium and cadmium pressures) providing optimum lasing for lines pumped by different processes. Radial profiles of pump rates obtained from the analysis made it possible to calculate and explain the dependence of the laser output power on the cathode diameter.     

Modelling of the Positive Column in an Argon-Hexamethyl-disiloxane dc Glow Discharge

A model is presented of the positive column of a dc glow discharge in argon with small admixtures of hexamethyldisiloxane (HMDS). The axial electric field, the ion production rates for direct-, stepwise-, pair-, and Penning ionization, the densities of metastable Ar atoms and of electrons, and the wall current of HMDS ions are calculated in dependence on HMDS admixture and discharge current density. For the calculations particle balance equations were used for a diffusion determined plasma in a mixture of two gaseous components. The reaction rates for the electron collision processes were determined applying the electron distribution function calculated for pure argon. Taking into account PENNING ionization of HMDS molecules by metastable argon atoms the decrease of electric field for increasing HMDS admixtures is according to the experimen-tally measured values. Also ion wall currents and electron densities are compared with experimen-tal values for thin film formation rate and results of probe measurements.     

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     

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     

Space-charge effects on multipactor on a dielectric

Analyzes the effects of space charge shielding on the steady state of a multipactor discharge on a dielectric. Analytic methods are used to obtain an exact function for the potential in the discharge, assuming a Maxwellian distribution of emitted electrons. An equation for the amount of power deposited on the dielectric by the multipactoring electrons, for a given saturation level, is given. A simple method for obtaining the saturation level, for a given material, is obtained     

Study of magnetically enhanced corona pre-charger

In this paper, experimental investigations of the discharge characteristics of magnetically enhanced corona discharges, for the purpose of capturing fine aerosol particles, are presented. The discharge mechanism during such a process is analyzed as well. The effects of magnetic enhancement under different magnet flux densities, and in positive- or negative-corona discharges, were experimentally compared. The magnetically enhanced effects in different inter-electrode regions were studied. Experimental results demonstrated that the magnetic field could efficiently increase the concentrations of both the negative ions and the free electrons during negative-corona discharge. The dominant mechanism of magnetic enhancement in a corona discharge involves the Larmor precessions of free electrons which enhance ionization of the gas molecules near the discharge electrode. A convenient configuration for enhancing corona discharge was formed by placing permanent magnets with a local strong magnetic field near the discharge electrode. A magnetically enhanced negative-corona (MNC) pre-charger was assembled in front of an electrostatic enhancement filter. The influence of the MNC pre-charger on the efficiencies of an electrostatic enhancement filter was measured and compared with that of a conventional corona pre-charger. The free-electron-charging mechanism of the MNC pre-charger was preliminarily analyzed. Our results show that the new pre-charging technique is promising for capturing fine aerosol particles in electrostatic enhancement filters or electrostatic precipitators.     

Effect of the experimental parameters on the number of free electrons in the drift region of a wire-cylinder electrostatic precipitator

The aim of this paper is to highlight the number evolution of free electrons in the drift region of a wire-cylinder electrostatic precipitator in negative voltage depends on the experimental parameters, more particularly of gas composition. A numerical model of the negative DC corona discharge developed by Chen et al. was used and modified to investigate the negative discharge corona for different gases. A parametric study was conducted to examine the effect on the electron distribution of operating conditions. The results showed the electron concentration increases with temperature, decreases when the pressure increases, and is closely related to gas composition.     

Mechanisms for formation of the electron distribution function in the positive column of discharges under Langmuir-paradox conditions

The form of the electron distribution function in the positive column of low-pressure discharges is examined under conditions such that the electron mean free path exceeds the vessel radius. Its formation is analyzed taking all major factors into account, including elastic and inelastic collisions, radial and axial electric fields, and the loss of fast electrons to the wall. It is shown that the main mechanism controlling the fast part of the distribution function is the loss of electrons to the wall, which is determined by the scattering of electrons into a comparatively small loss cone that depends on the relationship between the axial and radial components of the velocity. Since the elastic collision rate for all elements has a weak dependence on the energy beyond the ionization threshold, ultimately the high-energy part of the electron energy distribution function in the positive column of low-pressure discharges is nearly Maxwellian. The subthreshold portion of the distribution function, in turn, is determined by the energy diffusion, in a comparatively strong field, of Maxwellian electrons which arrive after inelastic collisions. The final electron distribution function is well approximated by an exponential with a single slope over the entire energy range. Only within a narrow range of scattering angles is the electron distribution function strongly depleted by the loss of electrons to the vessel walls. In the end, it is concluded that this phenomenon, like the Langmuir paradox, may be related to aspects of the physics of the formation of the electron distribution function owing to a combination of already known mechanisms, rather than to a hypothetical mechanism for thermalization of the electrons, as assumed up to now in the literature. A comparison of solutions of the model kinetic equation given here with published Monte Carlo calculations and experimental data shows that they are in good agreement. Zh. Tekh. Fiz. 69, 34–41 (November 1999)     

Mechanism of Striation in Dielectric Barrier Discharge

The mechanism of striations in dielectric barrier discharge in pure neon is studied by a two-dimensional particle- in-cell/Monte Carlo collision （PIC-MCC） model. It is shown that the striations appear in the plasma background, and non-uniform electrical field resulting from ionization and the negative wall charge appear on the dielectric layer above the anode. The sustainment of striations is a non-local kinetic effect of electrons in a stratified field controlled by non-elastic impact with neutral gases. The striations in the transient dielectric barrier discharge are similar to those in dc positive column discharge.     

Unconventional Approach to Orbital-Free Density Functional Theory Derived from a Model of Extended Electrons

An equation proposed by Levy, Perdew and Sahni (Phys. Rev. A 30:2745, 1984) is an orbital-free formulation of density functional theory. However, this equation describes a bosonic system. Here, we analyze on a very fundamental level, how this equation could be extended to yield a formulation for a general fermionic distribution of charge and spin. This analysis starts at the level of single electrons and with the question, how spin actually comes into a charge distribution in a non-relativistic model. To this end we present a space-time model of extended electrons, which is formulated in terms of geometric algebra. Wave properties of the electron are referred to mass density oscillations. We provide a comprehensive and non-statistical interpretation of wavefunctions, referring them to mass density components and internal field components. It is shown that these wavefunctions comply with the Schrödinger equation, for the free electron as well as for the electron in electrostatic and vector potentials. Spin-properties of the electron are referred to intrinsic field components and it is established that a measurement of spin in an external field yields exactly two possible results. However, it is also established that the spin of free electrons is isotropic, and that spin-dynamics of single electrons can be described by a modified Landau-Lifshitz equation. The model agrees with the results of standard theory concerning the hydrogen atom. Finally, we analyze many-electron systems and derive a set of coupled equations suitable to characterize the system without any reference to single electron states. The model is expected to have the greatest impact in condensed matter theory, where it allows to describe an N-electron system by a many-electron wavefunction Ψ of four, instead of 3N variables. The many-body aspect of a system is in this case encoded in a bivector potential.     

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