Showing papers in "Contributions To Plasma Physics in 1980"

Motion of Electrons and Ions in a Weakly Ionized Gas in a Field. 1. Foundations of the Integral Theory

Abstract: A detailed analysis of an integral transport theory of electrons and ions in a gas in a field is presented. Different procedures allowing, in principle, the rigorous calculation of velocity distribution, drift velocity and diffusion coefficients are discussed. A derivation of a general expression for the transition probability, from a given velocity to another, which holds for any kind of collision, is given. Some questions linked to the convergence of iterative procedures of solution of some basic integral equations are also treated.

Reaktionskinetik der Ozonbildung in der Sauerstoffglimmentladung

Abstract: Hg-light absorption at λ = 2537 Ǎ by O3 has been used to measure the concentration of O3 in the positive column of an oxygen glow discharge under the nonstationary conditions of the Q-form (tube diameter 3:4 cm). For all gas pressures investigated (p = 7 — 12 torr) the O3 density (n3) as a function of the current reaches a remarkable maximum at i ≈ 15 mA. n3max was found to increase almost linearly with the gas pressure. At i = 80 mA, on the other hand, n3 increases according to a quadratic relation. In order to understand the dependence of n3 on the pressure and on the current density (or equivalently on the electron density ne) a kinetic model previously developed has been used involving the following particles . For example, it can be shown that in the region of the maximum of n3 one main production process of ozone is the associative detachment reaction . The calculated maximum of the ozone density is higher than the measured one and appears at higher electron density.

The Erosion Rates of Arc Cathode Spots by Crater Formation

Abstract: The erosion of arc cathodes is caused by evaporation and by forced fluid motion of the molten metal layer at the spot surface. The gross erosion rates (X1X2) of both components are derived from the equations of stationary and non-stationary cathode spot models in a first approximation. These rates depend mainly on thermal properties of the metal, the atomic mass and the ionization state of the cathodic plasma. The calculated total gross rates Xt are between 67 μg/As (Be) and 3300 μg/As (Bi); the measured net rates (X) amount to about 10% 30% of these gross rates. The range of the ratio X2/X1 = v is 0,56 (Cd) ≦ v ≦ 2,64 (Mo). The various gross rates X1.2t are strongly correlated with the net rates X the relative rms deviations σrel from a power law fit are between about 15% and 30%. Resistive heating results in a worse correlation of the rates than ion impact heating. Probable causes of the deviations from exact functional dependencies are discussed.

The Calculations of the Concentrations, of the Radial Distributions, and of the Radial Particle Currents of Excited and of Doubly Charged Ions in Low Pressure Discharges

Abstract: A system of differential equations describing the radial profiles of the number densities and of the radial drift velocities of the ions and of the electrons in positive columns at low pressure containing several species of ions is derived. Excited ions and doubly charged ions, generated in two-step processes by electron impacts, the inertia of the ions and space charge effects are taken into account. For the excited ions de-excitation processes by electron collisions and by spontaneous emission are regarded. A set of nonlinear equations to determine the population densities and the initial values of the differential equations and corresponding boundary conditions are put up. Numerical solutions are given for discharges in argon under free-fall conditions similiar to argon ion lasers. One notices that without stepwise processes via excited ion levels the concentration of double charged ions remains small. In some cases the radial drift of the ions considerably reduces the population of the metastable ion levels. The radial density profiles of the double charged ions and of long-living excited ions considerably deviate from the squared radial profile of the electron density. In addition, for low degrees of ionization the theory of the free-fall column given by Tonks and Langmuir is extended to plasmas containing two species of ions.

Selfconsistent electron energy distribution functions in non equilibrium oxygen - Effects on the dissociation rate

Abstract: Electron energy distribution functions (edf) in non equilibrium oxygen have been calculated by solving the Boltzmann equation coupled to a system of vibrational master equations. The results show the importance of both superelastic vibrational collisions and of the presence of oxygen atoms in affecting edf. The coupling between the Boltzmann equation and the system of vibrational master equations brings to a temporal evolution of edf, which progressively changes from a cold molecular gas situation (all molecules in the ground vibrational level) to a vibrationally excited molecular gas and finally to a gas composed by oxygen molecules and oxygen atoms. All electronic rate coefficients follow a temporal evolution. due to the corresponding evolution of edf. Finally the present results are used for discussing the dissociation rate of molecular oxygen in electrical discharges.

Das diffusionsbestimmte Plasma der positiven Säule von Niederduckentladungen in Neon bei mittleren Ionisierungsgraden von 10−8—10−3

Abstract: Ausgehend von den in den letzten Jahren entwickelten Naherungsmethoden zur mikrophysikalischen Beschreibung des axial homogenen Plasmas der diffusionsbestimmten positiven Saule sowohl im Bereich hinreichend schwacher (Schwachstromsaule) als auch starker Strome (Starkstromsaule) wird in der vorgelegten Arbeit eine quantitative Behandlung des Saulenplasmas in Neon fur den gesamten Strombereich von ≈ 1 mA bis ≈ 10 A vorgenommen. Diese Untersuchungen basieren auf der simultanen Losung der Konzentrationsbilanzen der Elektronen und der in den 18-und 2p-Niveaus angeregten Neon-Atome, der Strombilanz des Saulenplasmas und der Elektronen-Boltzmann-Gleichung unter zusatzlicher Berucksichtigung von Stufenprozessen und der Coulomb-Wechselwirkung zwischen den Elektronen. Dabei wird die radiale Variation insbesondere der Stosraten fur Elektronenstose uber die Berechnung der quasihomogenen Anderung der Geschwindigkeitsverteilung der Elektronen infolge der radial variierenden Intensitat der Stufenprozesse und der Coulomb-Wechselwirkung beschrieben. Die numerisch erhaltenen Ergebnisse uber die Stromabhangigkeit der axialen Feldstarke, der Elektronen- und Angeregtenkonzentration, der verschiedenen Erzeugungsprozesse von Ladungstragern und der Geschwindigkeitsverteilung der Elektronen werden diskutiert und teilweise experimentell gewonnenen Resultaten gegenubergestellt. In recent years approximate methods were developed for the microphysical description of the axial homogeneous plasma of the diffusion determined positive column in the range of sufficient low as well as high electric currents. Using these methods in this paper a quantitative treatment was performed of the neon column plasma for the broad current region from ≈ 1 mA to ≈ 10 A. These investigations are based upon the simultaneous solution of the concentration balances for the electrons and for the neon atoms excited in the 18- und 2p-levels, of the current balance for the column plasma and of the electron Boltzmann-equation taking additionally into account the step by step processes and the Coulomb interaction between the electrons. In this treatment the radial dependence especially of the different electron collision rates are described via the quasi-homogeneous alteration of the electron energy distribution function due to the radial variations of the intensity of the step by step processes and of the Coulomb interaction. The numerical results concerning the current dependence of the axial electric field strength, of the electron and excited atom concentrations, of the different generation processes of charge carriers and of the electron energy distribution function are discussed and compared to some experimental results.

Kinetics of the Electron Component in the Turbulent Electron‐Beam Discharge Plasma in Diatomic Gases and Comparison of some Macroscopic Properties between the Plasmas of the Beam and the Glow Discharge

Abstract: The present paper is devoted to the investigation of the kinetics of the electron component in the stationary beam discharge plasma in molecular nitrogen. Using the Boltzmann equation with the inclusion of the elastic and the main inelastic binary collisions and also the Coulomb interaction between the charged particles we have calculated the energy distribution function and some macroscopic quantities of the electrons within a large range of parameters. Using our earlier results for the beam discharge plasma in hydrogen, also the dependence of the macroscopic quantities on the kind of molecular gas is discussed. Finally, the comparison of some macroscopic properties of the beam and the glow discharge plasma was performed under the condition of equal power input per volume unit in both types of plasmas in nitrogen.

Diffusionstheoretische Beschreibung der Dissoziation und des Ionenhaushaltes im schwachionisierten Säulenplasma der Wasserstoffentladung. II. Makroskopische Kenngrößen der Elektronen im H/H2-Mischplasma

Abstract: Fur das stationare und homogene H/H2-Mischplasma werden die Ergebnisse der Berechnung des Isotropteils der Geschwindigkeitsverteilungsfunktion f(U), der Transportgrosen Ū, be, De. der Stosfrequenzen fur Dissoziation und Direktionisation sowie aller wesentlichen Energieverluste durch elastische und unelastische Stose an die Komponenten des Mischplasmas mitgeteilt. Diese Berechnungen erfolgten mittels der Boltzmanngleichung der Elektronen in Abhangigkeit von der normierten elektrischen Feldstarke E/p0 und der Gemischzusammensetzung xD und wurden fur E/p0-Werte von 7,5–100 V/cm Torr und fur beliebige Gemischzusammensetzung durchgefuhrt. The results of the calculation of the energy distribution function f(U), of the transport coefficients Ū, be, De, of the collision frequencies for dissociation and direct ionization and of the main energy loss rates due to elastic and inelastic collisions of the electrons with the components of the mixture are presented for a stationary and homogeneous hydrogen plasma. These calculations, based upon the Boltzmann equation for the electrons, are performed in dependence of the normalized electric field strength E/p0 and the mixture ratio xD in the range of 7.5 to 100 V/cm Torr for E/p0 and for any mixture ratio.

Unified System of Differential Equations for Plasmas and Boundary Layers

Abstract: Starting from the Boltzmann equation the moment equations up to the third order for a non-quasineutral plasma are derived. It is shown that for a non-quasineutral plasma, in the distinction from the second order set of moment equations, the systems of the first order and of the third order can be closed in a physically reasonable manner by a relatively simple method when near the walls the ion gas has a high drift velocity caused by an electric field. From this follows that in non-quasineutral plasmas the ion pressure must be neglected in the first order set of equations consisting of the equations of continuity and of momentum transfer. Terms of the first order in the ion pressure related to the electron pressure are taken into consideration for the third order system. In this way one obtains a unified set of differential equations to treat both the quasineutral plasma core and the space charge sheath at the walls jointly taking into account a non-vanishing ion temperature. This set of equations is applied to the positive column in the free-fall regime.

Methods of Wall Charge Determination in External Electrode Gas Discharges. I. Experimental Arrangement

Abstract: For direct and absolute determination of wall charges an electrostatic probe method, the field mill and the Faraday cup technique are used. The first scans the charge density distribution, while the two latter methods measure total charge magnitudes. Indirect methods, estimating the wall charges by integration of discharge current pulses are also used in the arrangement. The discharges are generated in a cylindrical quartz insulated Ne + N2-filled discharge gap by individual voltage pulses having small risetimes and long duration. Preliminary tests, comparison of the methods and first results concerning charge density distributions will be given in part II of this paper.

On Nonlinear Resonant Absorption of Surface Waves

Abstract: We consider the resonant absorption of surface waves in a cold electron plasma by taking into account the nonlinear change in the electron density profile which is caused by the wave pressure in the transition layer. Equations, which describe the time evolution of the amplitudes of the electric fields of the surface waves, are obtained and solved. It is shown that the time-behaviour of the surface waves can be significantly different from that obtained from linear theory, and nonlinear effects can thus change the rate of absorption of the surface wave energy and can also stabilize linear surface wave instabilities.

Nonideal Plasma Generation by Mechanical Compression

Abstract: Nonideal plasmas have been generated by mechanical compression with a so-called ballistic compressor. The Debye numbers reached were 0.4 in argon and 0.2 in xenon. The experimentally determined pressure, specific volume, and temperature are compared with calculations of the compression using different models of the charged particle interaction. This comparison shows that heat losses may take an essential part in the interpretation of the experimental results.

Nonlinear resonant interaction of three extra-ordinary waves in a hot electron plasma

Abstract: The coupled mode equations and coupling coefficients for the resonant nonlinear interaction of three extra-ordinary waves in a hot magnetized plasma are derived by Whitham's method of averaged Lagrangian. The wave vectors of the three waves are taken as noncollinear and perpendicular to the external uniform magnetic field. Of the three waves one is of high frequency mode and the other two are of low frequency mode.

On the Interaction of an Alternating Electrical Field with a Magnetized Fully Ionized Plasma

Abstract: The electron distribution function for a plasma interacting with an alternating electric field is studied, without using the Fourier expansion in terms of time. For this distribution function a more complete expression was deduced. Also the expressions for the current density are computed. Recurrently, we find the general form of the solution for our problem. A dependence of the current density of the form E and EEE was obtained. This dependence being characteristic to the nonlinear interaction of the waves in a plasma with the collision frequency depending on the velocity.

Methods of Wall Charge Determination in External Electrode Gas Discharges. II. Preliminary Tests, Comparison of Methods, Distributions

Abstract: First experiments with the arrangement described in part I of this paper resulted in three spurious effects: shifting of characteristic values due to ageing effects, dissymmetric behaviour of wall charges and currents with respect to the voltage pulse sign, and backfiring. The comparison between the direct and the indirect methods demonstrated the sensitivity of the indirect ones to uncertainties and variations in effective cell capacities. The wall charge density distributions are axially symmetric and can be described in the electrode range by ƒ (x) = ae.

Drifting Electron Effects on Strongly Non-Linear Ion-Acoustic Solitons

Abstract: The influence of drifting electrons on the properties of ion acoustic solitons is discussed. The range of Mach numbers within which solitary waves are possible and the dependence of soliton velocity on amplitude are given. It is shown that solitary waves exist for Mach numbers M < 1 in the presence of drifting electrons.

Verallgemeinerung der Methode der singulären Normallösungen für isotherme irreversible Vlasov‐Systeme

Abstract: Irreversible Vlasov-Systeme, d. h. Systeme, die durch eine kinetische Gleichung vom Vlasov-Typ mit zusatzlichen entropieproduzierenden Stostermen zu beschreiben sind, werden mit der Technik der singularen Normalmoden und singularen Integralgleichungen untersucht. Dazu wird eine neue indirekte Methode entwickelt, die eine einfache Verallgemeinerung des ursprunglich fur stosfreie Vlasov-Plasmen entwickelten Formalismus von Case gestattet, im Gegensatz zu einer komplizierteren Methode, die von den Autoren fur eine erstmalige Anwendung des Formalismus der singularen Normalmoden auf irreversible Vlasov-Systeme angegeben wurde (1970). Der linearisierte Vlasov-Operator, der durch vollstandige Bhatnagar-Gross-Krook-Stosintegrale als die wichtigsten Modellstosterme vervollstandigt ist, wird fur ein nichtrelativistisches, nichtentartetes, stationares Elektronengas mit neutralisierenden positiven Ionen und neutralen Teilchen ohne Magnetfeld und bei konstanter Temperatur im Detail untersucht, Verallgemeinerungen auf kompliziertere irreversible Vlasov-Systeme sind moglich. Der wesentliche Punkt der entwickelten indirekten Methode ist die Einfuhrung einer transformierten Elektronen-Verteilungsfunktion, die als additives Glied ein Integral uber die gewohnliche Verteilungsfunktion enthalt. Die neue kinetische Gleichung und ihre adjungierte Gleichung werden wieder lineare Integralgleichungen und liefern einen Satz von regularen und singularen Normalmoden, fur die der Beweis der Orthogonalitat und der Vollstandigkeit angegeben wird. Das Anfangswertproblem wird exakt gelost. Ein Vergleich der Ergebnisse mit denen der Laplace-Transformationstheorie nach Landau, die fur die volle Vlasov-BGK-Gleichung formuliert wird, ergibt Ubereinstimmung der Losungen. Das Zeitverhalten der Losungen wird diskutiert.

Relaxation of Plasma Electrons towards Stationary States as Related to Different Initial Energy Distributions and for a Wide Range of the Final Electric Field Strength

Abstract: Starting from former investigations concerning the collision dominated relaxation of the electron component in weakly ionized inert gas plasma we generalize the results obtained. Also in the present paper we use the same adaquate kinetic equation for the electron energy distribution function. On one side the influence of non-stationary, analytically given initial energy distributions on the relaxation behaviour and on the resulting adjustment time of stationary states was investigated. On the other side the calculation, especially of the adjustment time, was extended to a whole variety of final stationary states ranging from those determined only by energy loss due to elastic collisions to those determined only by exciting collisions. The adjustment time obtained varies by about four orders of magnitude within this wide range of final stationary states.

Mikrowellendiagnostik der Rauschtemperatur im Stickstoffplasma der Schwachstromsäule

Abstract: Diese Arbeit behandelt die Berechnung und Messung der Rauschtemperatur fur ein stationares und axial homogenes Saulenplasma einer Stickstoff-Entladung. Die Berechnungen basieren auf einer Energieverteilungsfunktion der Elektronen, welche durch Losung der Boltzmann-Gleichung fur ein Stickstoffplasma erhalten wurde. Die Rauschtemperatur in der Schwachstromsaule dieses Plasmas wurde mit einem Dicke-Radiometer gemessen. Der Vergleich der berechneten und gemessenen Werte der Rauschtemperatur zeigt eine gute Ubereinstimmung im betrachteten Parameter-bereich. Zusatzlich wurde die Rauschtemperatur theoretisch naherungsweise unter Verwendung einer uber die Energiebilanz der Elektronen angepasten Maxwell-Verteilung bestimmt und der kinetisch begrundeten Rauschtemperatur gegenubergestellt. This paper covers the calculation and measurement of the noise temperature for a stationary and axial homogeneous column plasma of a nitrogen discharge. The calculations are based on an electron energy distribution function which was obtained by the solution of the Boltzmann equation for a nitrogen plasma. In the low current column of this plasma the noise temperature was measured, using a Dicke-radiometer. The comparison between the calculated and measured values of the noise temperature shows a good agreement in the considered parameter region. Using a Maxwellian distribution, which was fitted to the real nitrogen plasma by the aid of the formulation of an energy balance for the electrons, the noise temperature was additionally determined in a approximate way and compared to the first calculations.

Nichtstationäre Reflexion und Reemission von Wellen bei Herausbildung elektromagnetischer Strukturresonanzen im Plasma

Abstract: The nonstationary resonant reflectivity of a density profile is studied which consists of two homogeneous overcritical layers, separated by a vacuum region whose width increases linearly in time. Analytical expressions are derived for the time dependence of both the reflexion coefficient and the cavity field in the case of normal incidence. If the configuration passes through a structure resonance, where the eigenfrequency of the density cavity coincides with the frequency of the external wave, the cavity field is strongly enhanced. The temporary formation and the subsequent decay of this resonant field leads to oscillations of the reflexion coefficient. In the case of a loss-less plasma it may reach the extreme values |R| = 0 |R| ≈ 3 and the moving plasma configuration temporarily acts as an energy storage (|R|2 1).

Diffusionstheoretische Beschreibung der Dissoziation und des Ionenhaushaltes im schwachionisierten Säulenplasma der Wasserstoffentladung. III. Kenngrößen der positiven Säule bei verschiedenen Drücken (0,3 … 10 Torr) und Strömen (10−4 … 1 A)†

Abstract: Auf der Grundlage der Losung der Boltzmann-Gleichung fur das Elektronengas werden die Teilchenbilanzen verschiedener Ionen (H+, H2+, H3+, H3+, H5+) und der neutralen Komponenten im H/H2-Saulenplasma unter Berucksichtigung zahlreicher Elementprozesse (Volumen- und Wand-prozesse) diskutiert. Dies liefert ein detailliertes Verstandnis der elektrischen Charakteristik des Plasmas in Verbindung mit der chemischen Zusammensetzung des Gases. Im Bereich kleiner Drucke und hoherer Strome treten grose Dissoziationsgrade auf. Experimentelle Untersuchungen bestatigen diese theoretischen Ergebnisse. Auf noch bestehende Unterschiede zwischen der gemessenen und berechneten elektrischen Charakteristik wird hingewiesen. Based on the solution of the electron Boltzmann equation the particle balances of different ions (H+, H2+, H3+, H5+) and of the neutral components are discussed in the H/H2, column plasma taking into account a large number of elementary processes (volume and wall processes). This results in a detailed understanding of the electric characteristic in relation to the chemical composition of the gas. In the region of low pressures and larger currents considerable high degrees of dissociation occur. Experimental investigations confirm these theoretical results. Remaining differences between the measured and calculated electric characteristic are mentioned.