Zur theoretischen Beschreibung zylindersymmetrischer modulierter Lichtbögen

In this paper properties and dependence upon parameters of electric d.c. arcs with a.c. components are investigated. Expanding older theories analytical solutions of the basic equations of the one fluid modell are given for this problem using an extended Bessel modell and numerical calculations are made. Thereby the exact equations determine dependences upon parameters in limiting cases. The obtained results are compared with experimental data given in literature. The good agreement shows the validity of the applied methods.     

Zur nichtlinearen Theorie der Strahl-Plasma-Wechselwirkung III. Vorbereitung der numerischen Rechnungen

In order to prepare the system of ordinary differential equations, describing approximately the non-linear behaviour of a beam-plasma system, for numerical solution, at first the dispersion relation is analized. In particular it is shown, that in the case of a three component plasma the complex wave number k = k_r + i_γ can be found without difficulties as a function of frequency ω and the plasma parameters, if the electron densities n_b and n_p are treated as the two dependent quantities. The expressions on the right hand sides of the differential equations are transformed in such a way, that all complex integrals can be found as functions of one basic integral, tabulated in the literature, not only for negative values of γ (amplification) but also for positive values of γ (evanescence). In this way it will be possible, to describe the behavior of the wave amplitude not only for short distances from the input, where amplification of the wave takes place, but also for larger distances, where nonlinear Landau-damping may occur.     

Relativistisch invariante Beschreibung strukturierter Elementarteilchen

Within a dynamic theory of fusion the three-particle-system is examined. Under suitable boundary conditions a method of integra ion is developed, which yields the exact solution of the relativistic three-particle-equation. This solution describes an elementary particle with internal structure. A thorough discussion of the collective motion supplies the massM and spin 1/2 for the new particle and the proper Diracequation, so that an identification of the three-particle-system with the electron is possible.     

Zur mikrophysikalischen Beschreibung des schwachionisierten Säulenplasmas von Glimmentladungen in Stickstoff-Neon-Gemischen. I. Vergleich zwischen gemessenen und berechneten Geschwindigkeitsverteilungsfunktionen der Elektronen

The isotropic part of the velocity distribution function of electrons is determined experimentally and theoretically for the plasma of the positive column of glow discharges in N₂-Ne mixtures. The distribution functions are measured with electrical probes using the Druyvesteyn method. The calculation of the isotropic part of the distribution functions for homogeneous and stationary conditions from the Boltzmann equation takes into consideration the essential elastical and unelastical collision processes. The character of the obtained distribution functions is fixed by the reduced field strength E/p₀ and the mixture ratio x = N₂/N₂ + Ne), which is varied in this paper in the range between pure nitrogen and pure neon. The distribution functions are found to be influenced by elastic and unelastic collisions of electrons with nitrogen molecules even at smal admixtures of N₂. Comparing the experimental results for the distribution functions with those received by the calculations a good agreement is observed.     

Zur mikrophysikalischen Beschreibung des schwachionisierten Säulenplasmas von Glimmentladungen in Stickstoff-Neon-Gemischen III. Bilanzierung des Säulenplasmas und Berechnung seiner inneren Parameter

For the plasma of the low current positive column in the N,-Ne-mixture the equations for the concentration of different kinds of ions and excited particles are set up. The axial electric field strength, the degree of ionization and the concentration of excited Ne-atoms and of the different kinds of ions are calculated by simultaneous solution of these balances together with the electron Boltzmann equation for this mixture and the balances for the electric current and quasineutrality of the column plasma. All these macroscopic properties of the discharge column are investigated for electric currents of 0.5 mA to 13,5 mA, for total pressures of 0,37 torr to 3,7 torr and for any mixture ratio. A comparision between measured and calculated electric field strengths shows a good agree-ment. The ionization of the N,-molecules by collisions with the metastable Ne-atoms (Penning-ionization) is of great significance for the generation of new charge carriers in such a mixture. In these investigations the collision rate zp of the Penning-ionization was obtained to 3 · 10^?11 cm³ s^?1 by the aid of a comparision between measured and calculated electric axialgradients of the column.     

Beschreibung von Verweilzeitverteilungen bei Anwendung stabiler Isotope als Indikatoren

Eine Gleichung zur Berechung von Verweilzeitspektren in einem System hintereinandergeschalteter idealer Rührkessel bei Eingabe des Indikators in Form eines Rechteckimpulses wird hergeleitel. Die Anwendung dieser Gleichung für den Fall einer Markierung mittels stabiler Isotope als Indikatoren in chemischen Reakton und Apparaten wird diskutiert.     

Modellmäßige und numerische Beschreibung eines toroidalen Lichtbogens

This paper deals with a wallstabilized, toroidal electric arc at atmospheric pressure. Contrary to cylindrical arcs there appear asymmetrical thermal, electrical and magnetical values. The displacement of the maximum of temperature out of the centre of cross-section to the centre of curvature may be a criterion for this asymmetry. The effects of curvature are realized analytically in this paper by a model theory. Further-more, a theory of conform mapping of the numerical results of a cylindrically-symmetric arc to a torus geometry yields to values, which are in good correspondence with numerical solutions of the energy balance of the toroidal geometry. In addition convection — caused by the asymmetry of the Lorentz forces — are pointed out.     

Über die Anwendung von Greenfunktionen zur Beschreibung von Paarungseffekten bei deformierten Atomkernen

The theory of nuclear pairing correlations, recently developed byMigdal, introduces only one constant, which should be nearly the same for all nuclei. This Green's function method is compared with the well known BCS-theory. The constant is fitted and the problem has been solved by numerical methods. We found that the constant varies likeA ^?1/2. The individual magnitude of the pairing energy depends strongly on the single particle level density which determines the value of the renormalized coupling constant of the pairinteraction. This enables us to reproduce the deviations of the pairing energy from the curveδ _n =11,2A ^?1/2. The results are independent from the choice of the cut-off level.     

Modellunabhängige Beschreibung kugelsymmetrischer Ladungsverteilungen bei der Streuung schneller Elektronen an Atomkernen

A method is given to evaluate in a model independent way cross sections for scattering of fast electrons by nuclei. For this purpose the charge distribution in the nucleus will not, as usual, be described by means of the charge densityρ(r), but by the first moment functionT(Q): $$T(Q) = \int\limits_0^Q {r(Q')dQ'} .$$ The integration has to be performed over this part of the charge distribution in which the charge will increase from the value 0 to the valueQ. ThusT(Q) gives the first moment of this part. It will be shown that this function can be fixed by elastic scattering within certain limits.