Theoretical Description of the Radial Distributions of the Ions and of the Electrons in the Subnormal Positive Column

A relatively simple set of differential equations describing the radial profiles of the number densities and of the radial drift velocities of the ions and the electrons and of the radial electric field intensity in the subnormal positive column is derived. The inertia of the ions is taken into consideration, but the ion temperature is supposed to be zero. Corresponding boundary conditions are used. For discharges in argon under diffusion and under free-fall conditions numerical solutions are given.     

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.     

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.     

Ladungsträgerdichte,Neutralgasdichte, elektrisches Potential und Elektronentemperatur in der zylindrischen Diffusionssäule unter Berücksichtigung des Elektronendruckes

The profiles of charged particle density, neutral gas density, charged particle generation and the electron temperature itself are calculated in the cylindrical positive column under diffusion conditions. The electron pressure is taken into account. The nonlinear differential equations for the charged particle density and the neutral gas density are solved by means of relatively well konverging power series. Inside the column the neutral gas partial pressure decreases with increasing electron partial pressure. Thereby, the profiles for charged particle density and electrical potential are flattened near the axis and fall more rapidly near the wall, and the electron temperature increases. The electron pressure increases with rising electric power input into the column. The necessary condition for the existence of a steady-state low pressure discharge with high current densities is investigated shortly.     

Lokale Diagnostik einer Argon-Niederdruckentladung mit Hilfe der resonanten Laserstreuung

We report on the experimental investigations on a laser-like low pressure argon gas discharge. The discharge parameters varied in the range from 0,05 to 1 Torr for the gas pressure and from 10 to 30 A for the discharge current. Local electron densities and temperatures have been measured with an adjustable spherical probe. Spatially resolved measurements of the temperatures and drift velocities of the Ar⁺-ions in the radial and axial direction of the positive column have been carried out by the resonant laser light scattering (fluorescence technique). The radial density profiles of the excited Ar⁺-ions have been determined in two different ways and have been compared with the calculations based on a simple collisional radiative model.     

Detailed comparison between probe density measurements of glow discharge in argon and in helium

In this article we shall look a bit more closely at some of the fundamental plasma parameters obtained by a cylindrical Langmuir probe within low-pressure electrical gas discharge plasma. The presented measurements were made in argon and in helium glow discharge plasmas. We are mainly concerned with the densities of the charged particles (electrons and ions) within the plasma and the effect of the discharge conditions upon them. The electron density is calculated from the electron current at the space potential and from the integration over the EEDF. The ion density is calculated by using the OML collisionless theory. The parameterization of Laframboise's numerical results is also used for the ion density calculation. In the range of our experimental conditions the results of plasma density, for both gases, tend to show that the ion densities measured with the OML and Laframboise theories exceeds the measured electron densities. The results also show that the plasma electron and ion densities increased with both discharge power and gas pressure.     

The Theory of the Low Pressure Discharge in the Strong Ionization Regime

A system of integro-differential equations describing the velocity distribution functions of the neutral atoms and of the ions and the radial profiles of the electric potential and the particle densities in the positive column at low pressures and high degrees of ionization is derived. This system is solved for a simplified, but self-consistent, plane model. Both the initial velocity of the ions and the neutral gas depletion caused by the ionization processes are taken into account. For a cylindrical model a solution is obtained for the region near the axis. With rising neutral gas temperature the radial ion flux density is slightly increasing. The pressure tensor, the heat flux tensor, and several components of the corresponding tensor of the fourth order for the ion gas are calculated. It is shown that on the axis the radial and the azimuthal ion temperatures are smaller than the neutral gas temperature because the ions generated out of neutral atoms are retarded during the flight to the axis.     

Geschwindigkeitsverteilungsfunktionen von Atomen und Ionen in verschiedenen Anregungs- und Ionisationsstufen in Niederdruck-Entladungen bei hohem Ionisationsgrad

Supposing free-fall conditions the velocity distribution functions of atoms and ions in various levels in gas discharges at low pressures are calculated. In particular, plasmas at high degrees of ionization are considered. Solving the Boltzmann equation for the motions transverse to the wall of the discharge tube it is shown that the velocity distribution functions can considerably deviate from the Maxwellian and become non-isotropic. Inelastic collisions with electrons and the ionization by electron impacts considerably determine the velocity distribution function of the neutral atoms. The velocity distribution function of the ions is also essentially determined by the electric field within the plasma. For the motions transverse to the wall the half widths of the velocity distribution functions do not only depend on the temperature of the wall, but on the electron density and on the electron temperature as well. At small electron densities the half widths for excited atoms and for ions can be narrower than the one for the ground state atoms. The charge exchange between atoms and ions is shortly taken into consideration.     

The influence of the radial ion drift in the population densities in cw argon ion lasers

By solving the equations of continuity and of momentum transfer it has been found that in some cases the population densities in cw argon ion lasers are noticeably reduced by the ion drift towards the wall. This effect is investigated in dependence on various parameters.     

Effects of Applied DC Radial Electric Fields on Particle Transport in a Bumpy Torus Plasma

The toroidal ring of plasma contained in the NASA Lewis Bumpy Torus may be biased to positive or negative potentials approaching 50 kilovolts by applying DC voltage to twelve or fewer midplane electrode rings. The electric fields, which are responsible for raising the ions to high energies by ExB/B2 drift, then point radially outward or inward. The profiles of plasma number density are observed to be flat or triangular across the plasma diameter. The absence of a second derivative in the density profile, combined with the flat electron temperature profiles which are observed, implies that the radial transport processes are not diffusional in nature and are dominated by the strong radial electric fields which are applied to the plasma. Evidence from a paired comparison test shows that the plasma number density and confinement time can increase more than an order of magnitude if the electric field acting along the minor radius of the toroidal plasma points inward, relative to the values observed when the electric field points radially outward. Some characteristic data taken under nonoptimized conditions yielded the highest plasma number density (2.7 × 1011/cc on axis) and the longest particle containment times (1.9 milliseconds) observed so far in this experiment.     

Radial Distributions of Dusty Plasma Parameters in a DC Glow Discharge

A non‐stationary non‐local kinetic model for radial distributions of dusty plasma parameters based on the solution of Boltzmann equation for electron energy distribution function is presented. Electrons and ions production in ionizing collisions and their recombination on dust particle surface were taken into account. The drift‐diffusion approximation for ions was used. To obtain the self‐consistent radial distribution of electric potential the Poisson equation was used. It is shown that at high dust particle density the recombination of electrons and ions can exceed their production in ionization collisions in the region of dusty cloud. In this case the non‐monotonous radial distribution of the electric field is formed, the radial electric field becomes reversed and the radial electron and ion fluxes change their direction toward the center of the tube (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nichtgleichgewichtsdichten inhomogener Plasmen mit Photoabsorption

The electron and population densities in nonequilibrium plasmas are computed. For these computations rate equations dependent on geometrical dimensions were used. Such rate equations result if the unknown radiation intensity is eliminated. This is achived by using the radiative transport equation. Our density computations are valid for a quasi neutral plasma. The total pressure or the density of the heavy particles and the distribution of the electron energy have to be assumed. For homogeneous plasmas the inelastic collision processes and the radiation processes are considered. For inhomogeneous plasmas the diffusion processes of the excited atoms are considered in addition to the collision and radiation processes. Using this method of calculation the electron and population densities of a cesium plasma are computed. We assumed maxwellian distributions and a total pressure of 1 Torr.     

Spatial and temporal electron and ion density variations within the focal region of an intense laser beam in a tenuous plasma

The recent availability of focussed laser beams with flux densities well in excess of 10¹⁵ watts/cm² at 1.06 μm has led to experimental investigations of direct interaction between intense electromagnetic fields and charged particles. In this paper the relevant hydrodynamic two-fluid mode equations for a singly ionized tenuous plasma eveloped by an intense spatially varying electromagnetic field at the focus of a pulsed laser beam is solved by computer simulations for a cylindrically symmetric geometry. Radial, axial and temporal variations of electron and ion densities are given for different laser intensities and particle number densities. Fluctuations in electron density are found due to the bulk oscillation of electrons relative to what is essentially a static array of massive ions. The possibility of generating intense electromagnetic fields devoid of charged particles is discussed.     

Influence of Negative Ions on Drift Waves in a Low‐Density Ar/O2‐Plasma

The effect of negative ions on the drift wave instability has been studied in detail in a linear device by means of Langmuir probes and cross‐correlation analysis. Drift waves are excited in low‐density (5 × 10¹⁴ m^–3) and strongly magnetized (0.5 T) pure argon plasmas and in the presence of an oxygen admixture. The radial density profile of negative ions is hollow. For increasing concentration of negative ions the wave frequency decreases by about 25%. Despite of an axial density gradient, a global wave frequency is established for the entire column length. While for the noble gas case the drift wave frequency is given by the equilibrium plasma parameters in the mid‐plane, there is no such relationship for the argon plasma with oxygen admixture. This different finding is attributed to the inhomogeneous distribution of the negative ions (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical analysis of chemical reaction processes in different anode attachments of a high-intensity argon arc

The attachment mode of arc on anode is closely related to the non-equilibrium chemical kinetics process of the anode region of arc. In this paper, the detailed chemical reaction mechanisms in the flow-affected region for both diffuse and constricted argon arc attachments are investigated by means of one-dimensional discharge coupled with a single-fluid, two-temperature model. The collisional-radiative model is used to examine the chemical reaction processes occurring in the anode region, including the arc centreline and fringe region. The numerical results are validated by comparison with available experimental data. The obtained radial distributions of electron temperature, electron density, excited states densities, ionization, and recombination processes reveal that different mechanisms dominate the diffuse and constricted arc-anode attachments.