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.     

Längsfeldstärke,Elektronentemperatur, mittlere Neutralgasdichte,Ionenstromdichte auf die Wand und mittlere Entladungsstromdichte in der Freifallsäule bei hohem Ionisationsgrad

On the basis of a foregoing paper new theoretical results for the positive column at low pressure and strong ionization, especially for discharges in noble gas ion lasers, are given. The mean velocity v_n0 of the neutral atoms reemitted from the wall is taken into account. The electric conductivity is calculated for an argon plasma. The formulas connecting the electron temperature, the mean neutral gas density, and the electric field strength are derived. The electron temperature, the axial electric field intensity, the degree of ionization, the axial electron drift velocity, the ion flux to the wall, and the force density causing the main part of gas pumping along the column are calculated as functions of the product of the mean current density and the tube radius, and of v_n0 for argon. The axial drift velocity of the electrons is still smaller than the mean thermal electron velocity for high discharge currents, except at very low gas pressures. In general, the ion flux to the wall is not directly proportional to the discharge current. The factor for the determination of the charged particle density by means of probe measurements at the wall is discussed. The self-magnetic field affects the discharge only at high electron temperature, high degree of ionization, and relatively large tube radius, i.e. at high current density and low gas pressure in not too narrow discharge channels.     

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.     

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.     

Untersuchungen der kontrahierten Edelgassäule bei mittleren Drücken. I Verfahren zur Ermittlung der Plasmaparameter und ihrer Radialverteilungen

Presented is a method to determine iteratively electron density, electron temperature, and gas temperature in medium pressure rare gas discharges. This method bases on the linear relationship between emission coefficient of continuum radiation and electron density according to electron-atom-bremsstrahlung. The radial profile of gas temperature is determined by solving the energy balance equation. The electron temperature is calculated from the reduced electric field strength and the degree of ionization. The received profiles and the values at axis permit to examine present theoretical conceptions and to estimate the influence of various elementary processes on discharge mechanism.     

Das Neutralgasprofil und die Elektronentemperatur in der Freifallsäule bei hohem Ionisationsgrad

The neutral gas flux from the wall into the column - connected with the ion flux to the wall - and the anisotropy of the velocity distribution of the neutral gas are included into the theory of the steady-state positive column. d/l_n and v_n0/v₀ occur as characteristic parameters. d denotes the radius of the column, l_n the mean free path of the neutral atoms for ionization, v_n0 the mean velocity of the neutral atoms re-emitted from the wall, v₀ = (2kT_e/M)^1/2, M the ion mass, T_e the electron temperature. On the axis the neutral gas density N_n is decreasing, if d/l_n is rising. At the wall N_n is increasing for v_n0 ? v₀, but it is almost constant or decreasing for v_n0 ? v₀ at the same time. In the plasma the total number of the atoms and the ions is taken as constant. In the case of small v_n0 the degree of ionization is high only for d ? l_n. However, it is already high for d ≈ l_n in the case of high v_n0. Therefore, the radial profiles of the neutral gas densities of different gases in a column can differ from each other. Almost full ionization can be reached near the axis. These results hold, too, if the initial velocity of the ions and a magnetic field are taken into account. d/l_n, the degree of ionization, and the electron temperature are given as functions of the electric power input and of the total number of the neutrals and the ions. The velocities of the re-emitted atoms depend on the accomodation coefficient of the ions recombining at the wall. With rising d/l_n an increasing number of the neutral atoms is re-emitted with superthermal velocities and the total number of the neutrals and the ions can be decreased. The anisotropy of the velocity distribution of the neutral atoms and the ions must be taken into account for the interpretations of spectroscopical measurements.     

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.     

Particle‐in‐cell/Monte Carlo simulation of electron and ion currents to cylindrical Langmuir probe

Electron and ion currents to a cylindrical Langmuir (electrostatic) probe were calculated using the particle‐in‐cell/Monte Carlo (PIC/MC) self‐consistent simulation for a neutral gas in the pressure range 2–3,000 Pa. The simulation enables us to calculate the probe currents even at high neutral gas pressures when the collisions of collected charged particles with neutral gas particles near the probe are important. The main aim of this paper is the calculation of probe currents at such high gas pressures and the comparison of the results with experimentally measured probe currents. Simulations were performed for two cases: (a) probes with varying radii in a non‐thermal plasma with high electron temperature at low neutral gas pressure of 2 Pa (in order to verify the correctness of our simulations), and (b) probe with the radius of 10 μm in the afterglow plasma with low electron temperature and a higher neutral gas pressure (up to 3,000 Pa). The electron probe currents obtained in case (a) show good agreement with those predicted by the orbital motion limited current (OMLC) theory for probes with radii up to 100 μm for the given plasma conditions. At larger probe radii and/or at higher probe voltages, the OMLC theory incorrectly predicts too high an electron probe current for the plasma parameters studied. Additionally, a formula describing the spatial dependence of the electron density in the presheath in the collisionless case is derived. The simulation at higher neutral gas pressures, i.e. case (b), shows a decrease of the electron probe current with increasing gas pressure and the creation of a large presheath around the probe. The simulated electron probe currents are compared with those of measurements by other authors, and the differences are discussed.     

An analysis of ionization kinetics models in a hypersonic flow past a cylinder

A calculation-theoretical analysis of the possibility of using several chemical and ionization kinetics models accepted in aerophysics and models of the nonequilibrium dissociation of diatomic molecules in the interpretation of the results of experimental studies of transverse passage of molecular nitrogen past cylindrical models at a rate of 11.3 km/s was performed. The two-dimensional problem of transverse flow of a viscous heat-conducting chemically and physically nonequilibrium gas past a cylinder was solved. A comparison of experimental gas density and electron concentration distributions with calculation results was performed to discuss the sensitivity of calculations to various chemical and ionization kinetics models and nonequilibrium dissociation.     

Anfachung und Dämpfung von Ionisationswellen in MHD-Kanälen und ihr Einfluß auf die effektive elektrische Leitfähigkeit,den effektiven Hall-Parameter und die mittlere Elektronentemperatur

The phase velocity, the amplification rate and the critical Hall parameter are theoretically determined for ionization waves in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both the magnetic field and the stream velocity. The investigations hold for seeded rare gases at any degree of seed ionization. The critical Hall parameter β_c depends on the degree of ionization, the ionization energy and the temperatures of electron gas T₀ and neutral gas T_g · β_c is always greater than one, if 0 < T₀ — T_g ? T₀ holds. The three-dimensional treatment indicates the existence of waves with a nonvanishing wave vector component in the direction of the magnetic field. The influence of ionization waves on mean current density, mean Hall field intensity and mean electron temperature is determined up to second order terms in the relative fluctuations of the electron temperature. The amplification of ionization waves reduces the effective electric conductivity, the effective Hall parameter and the mean electron temperature compared to the undisturbed state. Similar results are also obtained for steady state homogeneous isotropic turbulence and a special case of axially symmetric turbulence. Furthermore, a component of the electric field in direction or in opposite direction to the magnetic field vector may be generated by non isotropic and non homogeneous turbulence.     

闪电放电通道等离子体成分及相关特性的研究

以无狭缝摄谱仪获得了青海和西藏地区的云对地闪电回击过程的光谱,依据谱线波长和相对强度等信息,结合等离子体相关理论,得到了放电通道温度和电子密度;在此基础上,根据Saha方程、电荷守恒方程和粒子数守恒方程计算了闪电通道主要元素各级电离的离子数密度,进而得到通道质量密度、压强及平均电离度, 并分析了不同强度闪电放电通道的电离度、粒子数密度及其分布特征。结果表明：回击通道接近于完全电离,一次电离离子占主要地位,且NⅡ离子数密度最高;不同强度的闪电放电通道中,NⅡ和OⅡ离子的相对浓度值变化不大;计算过程中考虑带电离子间库仑相互作用以后,原子电离能的计算值降低,中性原子以及一次电离离子数密度的计算值变小,高次电离离子数密度的计算值变大。     

MHD cylindrical shock wave in self-gravitating gas

Summary Similarity solutions of the propagation of cylindrical blast waves through a self-gravitating polytropic gas caused by an instantaneous release of finite energy are investigated theoretically including the influence of transverse magnetic field. A comparative study of the distributions of velocity, density, mass, pressure, temperature and magnetic field has been illustrated through figures. The authors of this paper have agreed to not receive the proofs for correction.     

Fluid model of the positive column in argon‐oxygen direct current glow discharge

The positive column of argon‐oxygen direct current (DC) glow discharge was investigated using a fluid model at pressures of around 410 Pa and discharge currents from 10 to 40 mA. The model was used to study the influence of an oxygen admixture on the properties of argon discharge. The simulated intensity of the electric field strength was compared with measured values at 5% and 100% of oxygen concentration. The one‐dimensional model in a cylindrical tube is based on the drift‐diffusion approximation of particle flux and the mean‐electron‐energy approximation is used to describe the electron interaction. The model takes into account the radial profile of particle concentration, the neutral gas kinetic temperature profile, and interactions with the wall in the cylindrical glass discharge tube. It was shown that 2% of the oxygen admixture causes a significant increase in longitudinal electric field strength and gas heating.     

Probe Measurements of Wave Fluctuations Excited in Glow Discharges

Fluctuations of the electric field, the charged particle density, the electron temperature and the plasma potential are simultaneously measured by a probe in the positive column of helium glow discharge at a few torr gas pressure by exciting a small amplitude ionization wave. It is proposed that these values can be determined by analyzing the probe current.     

Probe Measurements of Wave Fluctuations Excited in Glow Discharges

Fluctuations of the electric field, the charged particle density; the electron temperature and the plasma potential are simultaneously measured by a probe in the positive column of helium glow discharge at a few torr gas pressure by exciting a small amplitude ionization wave. It is proposed that these values can be determined by analyzing the probe current.