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.     

Anfachung und Dämpfung magneto-akustischer Wellen in MHD-Kanälen und ihr Einfluß auf die mittlere Stromdichte und die mittlere Hall-Feldstärke

Magneto-acoustic waves generated by fluctuations in the Hall parameter, the electric conductivity and the stream velocity are theoretically investigated in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both magnetic field and stream velocity. The investigations hold for seeded rare gas plasmas at any degree of seed ionization but are resticted to waves propagating in parallel or antiparallel direction to the current density vector and in parallel or antiparallel direction to the stream velocity vector and to wave lengths which are small in comparsion to the interaction length which occurs as a characteristic wave length. The influence of these waves on the mean current density and the mean Hall field intensity is calculated in case of small amplitudes and low degree of seed ionization up to second order terms. Omitting Ohmic heating the dispersion equation can be solved exactly. A phase shift exists between the fluctuations in gas density and gas velocity. The phase velocity and the amplification rate depend on the wave length. Typical results are represented in a diagram. For both types of waves the phase velocity slightly rises with increasing wave length, while the amplification rate decreases. Waves propagating in opposite direction to the current density vector are amplified, if the electron velocity exceeds a critical value. They reduce the mean current density and the mean Hall field intensity. Waves propagating in opposite direction to the stream velocity vector are also amplified except for very high degrees of seed ionization. The threshold current density is greater than that for the waves of the first type approximately by the Hall parameter as factor. At extremely high degree of seed ionization the phase velocity is directed opposite to the direction occuring at weakly ionized seed. Waves of the second type decrease the mean current density, but increase the mean Hall field intensity.     

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.     

Geschwindigkeitsverteilung,Teilchendichte, transversale Driftgeschwindigkeit und Energiedichte des Neutralgases in der Freifallsäule unter Berücksichtigung der „Neutralgasaufzehrung”︁ durch die Ionisationsvorgänge

A neutral gas rarefaction caused by ionization processes occurs in the plasma of the low pressure gas discharges. The velocity distributions, the particle density, the transversal drift velocity and the energy density of the neutral gas are calculated both for the plane and for the cylindrical positive column under free fall conditions. The neutral gas rarefaction is taken into account. It is shown, that the velocity distributions is non-Maxwellian and anisotropic. The pressure tensor is anisotropic, too. Particle density and energy density of neutral gas decrease with increasing electron density and electron temperature relatively homogeneously over the cross section of the column. Only, if the degree of ionization is high, these densities are much smaller near the axis than at the wall. Decreasing neutral gas temperature causes a similar change in the particle density profile as increasing electron density and electron temperature do. The transverse neutral gas pressure decreases from the axis to the wall in all cases. In the steady-state column an upper limit exists for the transverse particle current density of the neutral gas and of the ion gas. This limit depends on the gas temperature, the filling pressure and the atomic mass of the filling gas. In the appendix the Boltzmann equation is given in a form, which is suitable to investigate cylindrical problems not only for simple examples.     

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.     

Lokale Messung von Driftgeschwindigkeit und Temperatur der Ionen einer Argon-Niederdruckentladung mit resonanter Laserstreuung

The radial ion drift velocity and temperature in an argon low-pressure discharge have been measured by a resonant laser scattering method with high spatial resolution. The detection limit for the drift velocities was 2 · 10⁴ cm · s^?1. In the vicinity of the discharge axis the drift velocity grows linear with the distance from the axis. The measurements have shown the existence of a radial dependence of the ion temperature T¹(r). Comparisons of axial ion temperature T_? with T_‖(r = 0) are an experimental demonstration of the anisotropy of the ion velocity distribution in this kind of discharges.     

Effect of small admixtures of N<Subscript>2</Subscript>, H<Subscript>2</Subscript> or O<Subscript>2</Subscript> on the electron drift velocity in argon: experimental measurements and calculations

The electron drift velocity in argon with admixtures of up to 2% of nitrogen, hydrogen or oxygen is measured in a pulsed Townsend system for reduced electric fields ranging from 0.1 Td to 2.5 Td. The results are compared with those obtained by Monte Carlo simulations and from the solution of the electron Boltzmann equation using two different solution techniques: a multiterm method based on Legendre polynomial expansion of the angular dependence of the velocity distribution function and the S _n method applied to a density gradient expansion representation of the distribution function. An almost perfect agreement between the results of the three numerical methods and, in general, very good agreement between the experimental and the calculated results is obtained. Measurements in Ar-O₂ mixtures were limited by electron attachment to oxygen molecules, which contributes to the measured drift velocity. As a result of this attachment contribution, the bulk drift velocity becomes larger than the flux drift velocity if attachment is more probable for electrons with energy below the mean value and smaller in the opposite case. Attachment also contributes to the negative differential conductivity observed in Ar-O₂ mixtures.     

New approach to surface ionization and drift-tube spectroscopy of organic molecules

A new physical model of ionization of organic molecules from the class of amines on the oxidized surface of transition metals is suggested. According to this model, the process involves the capture of protons or hydroxyl groups forming on the oxide surface upon water molecule adsorption. The adequacy of the model is demonstrated experimentally with test amines, such as Novocaine (procaine), bencaine, Dimedrol (diphenylhydramine), etc. A theory of drift motion of ion beams that includes the space charge effect is proposed. It is shown that the quantity P _i=μj/ε₀ v _g ² (where μ is the ion mobility, j is the ion current density, ɛ₀ is the permittivity, and v _g is the longitudinal velocity of an ionized gas) plays the role of perveance for intense drift ion beams. A new type of drift-tube spectrometer that uses an ion source due to surface ionization is developed.     

Investigations on the Electron Component in an Argon-Hexamethyldisiloxane (HMDS) Low Pressure Glow Discharge by Probe Diagnostics

Probe measurements were carried out in the positive column of an argon glow discharge in a flow system with different admixtures of hexamethyldisiloxane (HMDS). From this the mean electron energy n_e, number density n_e and gradient E were determined. Some results concerning the predominant ionization mechanism and the ion distribution in the gas phase could be obtained. By means of probes it is also possible to get some information about the deposition mechanism in polymerizing plasmas.     

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.     

Propagation and Diagnostic of Ion Acoustic Waves in a Low Pressure Argon Discharge

In a dc argon discharge column of pressure 5 × 10^?4 torr, ion acoustic waves are studied experimentally. Plasma parameters obtained from the phase velocity of waves are compared with the Langmuir probe measurements. The wave diagnostic method yields the electron temperature lower than the probe method by a factor of 3…?5, if the atomic argon ion is assumed as a dominant ion species. The axial profiles of ion drift velocity show the presence of ions flowing toward the anode along the potential drop in flont of it. Also it is found that the surface condition of the cathode sensitively affects the propagation of ion acoustic waves through the changes in discharge parameters.     

Power Consideration for Pulsed Discharges in Potassium Seeded Argon

Minimization of energy consumed in plasma generation is critical for applications, in which a large volume of plasmas is needed. We suggest that a high electron density atmospheric pressure plasmas can be generated by pulsed discharges in potassium seeded argon at an elevated temperature with a very small power input. The ionization efficiency and power budget of pulsed discharges in such plasmas are analytically studied. The results show that ionization efficiency of argon, especially at small reduced electric field E/N （the ratio of the electric field to the gas number density）, is improved effectively in the presence of small amount of potassium additives. Power input of pulsed discharge to sustain a prescribed average level of ionization in potassium seeded argon is three orders of magnitude lower than that in pure argon. Further, unlike in pure argon, it is found that very short high-voltage pulses with very high repetition rates are unnecessary in potassium seeded argon. A pulse with lOOns of pulse duration, 5kHz of repetition rate, and 2Td （1 Td = 1 × 10^-21 Vm^2） of E/N is enough to sustain an electron density of 10^19 m^-3 in 1 arm 1500K Ar＋0.1% K mixture, with a very small power input of about 0.08 × 10^4 W/m^3.     

Influence of SF6 on HF laser plasma parameters

Summary This paper presents the results of calculations of electron drift velocity, mean energy and ionization, and attachment coefficients in SF₆: C₃H₈: He mixtures performed according to the multiterm Boltzmann-equation analysis. The parameters for wide variation of gas mixture composition andE/N values are obtained. The results presented may be useful in studying the HF laser action, analysis of the gas discharge, and research, development and modelling of this type of lasers. The authors of this paper have agreed to not receive the proofs for correction.     

Ionization of hydrogen and helium atoms by highly charged fast ions in collisions with small momentum transfer

Ionization of hydrogen and helium atoms is studied for the case of “soft” collisions with highly charged fast ions with v≲Z≪v² and v≫v ₀, where Z is the ion charge, v is the collision velocity, and v ₀∼1 is the characteristic velocity of the electron in the ground state of the atom. Analytical expressions are derived for the singly and doubly differential cross section for ionization of a hydrogen atom accompanied by the ejection of a slow electron v _e≲v ₀, where v _e is the velocity of the ejected electron with respect to the recoil ion). The results are generalized to the case of single ionization of helium. It is shown that soft collisions provide the main contribution to the hydrogen ionization cross section and for all practical purposes determine the cross section for single ionization of helium. The asymmetry in the angular distribution of the ejected slow electrons and the properties of momentum exchange in such collisions are discussed. Finally, a formula for the cross section for single ionization of helium is proposed. Zh. éksp. Teor. Fiz. 112, 1966–1977 (December 1997)     

Effect of E × B electron drift and plasma discharge in dc magnetron sputtering plasma

Study of electron drift velocity caused by Etimes B motion is done with the help of a Mach probe in a dc cylindrical magnetron sputtering system at different plasma discharge parameters like discharge voltage, gas pressure and applied magnetic field strength. The interplay of the electron drift with the different discharge parameters has been investigated. Strong radial variation of the electron drift velocity is observed and is found to be maximum near the cathode and it decreases slowly with the increase of radial distance from the cathode. The sheath electric field, E measured experimentally from potential profile curve using an emissive probe is contributed to the observed radial variation of the electron drift velocity. The measured values of the drift velocities are also compared with the values from the conventional theory using the experimental values of electric and magnetic fields. This study of the drift velocity variation is helpful in providing a useful insight for determining the discharge conditions and parameters for sputter deposition of thin film.     

Feldstärke,Stromdichten und mittlere Energien im Katodenfallraum von Glimmentladungen

By integration of energy distribution functions for the cathode fall of H₂ glow discharges we may show:

• 1) Space charge is almost constant within a large part of the dark space, therefore the field strength is a nearly linearly decreasing function of distance from cathode. Deviations from linearity are quantitatively discussed.
• 2) Composition of space charge: The contribution of atomic ions to the space charge may range from 5 to 10%. and the contribution of electrons from 0,1 to 10%, increasing with growing voltage.
• 3) Relative ion and neutral current densities at the cathode (ion current from the glow edge = 1) are decreasing with growing voltage. Molecular neutral current density equals 3 to 10 times molecular ion current density, in case of atomic particles the relation is from 1 to 5.
• 4) Total current density is increasing from 2.0 · 10^?4 A/cm² torr² at the voltage U₀ = 0,19 kV to 3,7 A/cm² torr² at U₀ = 10 kV; cathode field strength is increasing from 0,53 kV/cm torr to 97 kV/cm torr.
• 5) The mean energy of neutrals is smaller than the mean ion energy by a factor of about 0.45…0.85, and the mean energy of molecules is smaller than the energy of atoms by a about 0.2…0.8. The dependence of the mean energies from voltage is discussed.
• 6) The energy gain of electrons is growing from 15% of total dark space energy at 0.19 kV to 70% at 10 kV; the energy gain of neutrals is decreasing at the same time.

     

The space-time-averaging procedure and modeling of the RF discharge

An approach to modeling RF discharges and the ensuing analysis of fast electron and ion motions for the case of electrode sheaths in the high-pressure RF discharge is discussed. Time-averaging over fast electron motions with the applied voltage frequency gives analytic expressions for the average electric field and average ionization density. The resulting relatively simple equations for the ion density profile describe drift, diffusion, ionization, and recombination processes. The simple scaling rules, the approximate expressions for the density profile in various regions, the sheath length, the ion density at the plasma-sheath boundary, and the dimensionless criteria for various discharge regimes can be deduced. For the non-self-sustained discharge, it is demonstrated that the ion drag towards the electrode and the diffusion results in significant lowering of the ion density in the sheath compared with the positive column at not too high a pressure. The analytic transition criterion from α to γ forms of the self-sustained discharge is obtained. The numerical solution of the averaged ion equations yields the results which nearly coincide with the results of full-scale modeling     

Gas dynamics and thermal-ionization instability of the cathode region of a glow discharge. Part I

A model of the cathode sheath of a glow discharge is developed. The model includes the equations for calculating the non-steady-state nonequilibrium physicochemical gas dynamics, cathode temperature, and electric field. The model applies to describing the flow of a viscous, heat-conducting, moderately rarefied gas at Knudsen numbers of about Kn ∼0.03. The electric field and gas density distributions are determined consistently by renormalizing the values obtained by the Engel-Steenbeck theory. A formula for calculating the time during which a homogeneous volume discharge phase exists is proposed. The formula is based on the relation between the rates of electron production via associative ionization (A+B → AB ⁺+e) and impact ionization (A2+e → A ₂ ⁺ +e+e). Calculations are carried out for nitrogen and air. It is shown that, at high current densities, due to the dissociation and strong heating of the gas, the rate of thermal ionization becomes as high as that of electrical ionization. The calculated ionization time is in reasonable agreement with the measured duration of a uniform anomalous cathode sheath.