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.     

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.     

Einfluß von Drehungen auf die piezoelektrische und photoelastische Wechselwirkung im kristallinen Medium

Influence of Electric Polarization on the Piezoelectric and Photoelastic Interaction in Crystalline Medium Because of the moments of force induced by electric polarization in solids the stresstensor is no longer symmetric, so that the antisymmetric parts of the distortion tensor is a thermodynamic state function too. The corresponding antisymmetric parts of the piezoelectric and photoelastic tensors are expressed by the spontaneous electric polarization and the linear electric susceptibility. Some consequences, also with regard to numerical values, are discussed.     

Die Zurückführung der Gleichungen eines rotationssymetrischen,statischen, inkompressiblen Plasmas von unendlicher Leitfähigkeit auf ein Randwertproblem

The equations of a rotationally symmetric, static, incompressible plasma with infinite conductivity are equivalent to an elliptic differential equation for the function where p means the pressure, ? the density, and Φ the potential of the external forces. Moreover this differential equality contains two arbitrary functions of ξ. When ξ_?² + ξ_?² < 0, both arbitrary functions can be computed from the boundary values of Hφ und H⊥ (the component of H , which is perpendicular to the boundary).     

Totale effektive Streuquerschnitte für die Streuung von He,HD und D2 an verschiedenen Molekülen

The measured velocity dependence of the total scattering cross section for the scattering of He, HD, and D₂ by the molecules CH₄, N₂, O₂, NO, CO, HD, and D₂ can be described relatively well by a Lennard-Jones-(12.6)-potential. Only for the systems with a CO₂ target are large deviations from the L. J.(12,6) predictions found: the measured glory amplitudes are considerably smaller. The deformation of the spherically symmetric potential which must be made in order to fit the CO₂ glory pattern is given. Furthermore, the CO₂ systems were calculated using an angle-dependent L.J.(12.6)-potential, taking into account only elastic processes. The agreement with the measurements is good.     

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.     

Das Neutralgasprofil und die Elektronentemperatur in der Freifallsäule bei hohem Ionisationsgrad

The formula for the ion density is corrected. Furthermore, for different accommodation coefficients at the wall numerical values of the neutral atom velocities in argon ion lasers are estimated. The neutral gas heating by electron collisions is relatively small in argon ion lasers.     

Stoßionisierungskoeffizient α, mittlere Elektronenenergien und die Beweglichkeit von Elektronen in Gasen

From the analysis of oscillograms of electron avalanches values of the ionization coefficient α for electrons were determined for oxygen, methane, carbon dioxide, and some organic vapors atE/p-values between some 100 and several 1000 volts/cm Torr. Over a certainE/p-region the values satisfy the relation α/p=A exp(-Bp/E)for which the constants are given. — Values of the mean diffusion energyD/b of the electrons were determined for oxygen, nitrogen, hydrogen, and some other gases and vapors ranging from 4 evolts atE/p?50–100 to some 20 evolts atE/p of several 1000 volts/cm Torr. These values of the diffusion energy are in agreement with those obtained from values of the ionization coefficient α. — The mobility of the electrons is calculated in dependence on the energyD/b and compared with experimental values. It is shown that satisfactory agreement is obtained only when the first two terms of the expansion of the velocity distribution are taken into account.     

Theorie der parametrischen Vier-Photonen-Wechselwirkung. VI Einfluß von Phasenverstimmung und Doppelbrechung auf die Schwellenleistung des doppeltresonanten Vier- Photonen-Oszillators

Theory of Parametric Four-Photon - Interaction. VI. Influence of Phase-Mismatching and Double Refraction on Threshold Pump Power of a Doubly Resonant Four-Photon -Oscillator It is shown, that the threshold pump power of a doubly resonant four-photon oscillator strongly increases with increasing phasemismatching and double refraction.     

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.     

Die Hyperfeinstruktur in den 4f7 6s 6p-Termen des Eu I und die elektrischen Kernquadrupolmomente von Eu151 und Eu153

The hyperfine structure of the statesz ¹⁰ P _11/2,z ¹⁰ P _9/2,z ¹⁰ P _7/2,z ⁸ P _9/2,y ⁸ P _9/2,y ⁸ P _7/2,y ⁸ P _5/2,z ⁶ P _7/2,z ⁶ 6s P _5/2 of the 4f ⁷ 6p configuration of EuI was investigated with a photoelectric recording Fabry Perot spectrometer using enriched isotopes of Eu¹⁵¹ and Eu¹⁵³, which have been excited in liquid air cooled hollow cathodes. From the measurements the values for the nuclear quadrupole moments

$$Q(Eu^{151} ) = (1.16 \pm 0.08) \cdot 10^{ - 24} cm^2 $$     

Untersuchung der unelastischen Wechselwirkung langsamer monoenergetischer Elektronen mit einfachen Kohlenwasserstoff-Molekülen I.Elektronenanlagerungs-Wirkungsquerschnitte in Abhängikeit von der Elektronenenergie und vom Molekülaufbau

Investigation of the Inelastic Interaction of Slow Monoenergetic Electrons with Simple Hydrocarbon Molecules. I. Dependence of the Electron Attachment Cross Sections on Electron Energy and on Molecular Structure The formation of negative ions from a series of simple hydrocarbons was studied experimentally via an interaction of hydrocarbon molecules with monoenergetic electrons in the range of 0–15 eV. The ion formation is characterized by means of the attachment cross section in dependence on electron energy. Negative ions were formed as well by dissociative electron attachment as by direct electron attachment. The electron attachment is depending on electron energy, molecular seize, and on the number of unsaturated C-C-bonds in the molecule. The formation processes are discussed and the role of negative hydrocarbon ions in the plasma is estimated.