Kinetic Description of the Stationary Band-Like Weakly Turbulent Beam Discharge Plasma in Hydrogen II. Budget of Ions and Metastables — Analysis of the Balance Equation System

In the first part [1] of our paper a kinetic model for the band-like beam discharge plasma in hydrogen was derived, numerically obtained results on the ionization and dissociation degree were presented and a detailed explanation of the influence of the electron kinetic properties on the macroscopic plasma behaviour was given. Continuing these investigations, we now report and discuss the results on the ion- and metastable atom-budget. On this basis an analysis is made of the resulting balance equation system with a view to finding the most important physical processes, and a simplified equation system is derived which allows to interpret the essential features of the macroscopic plasma properties.     

On the Solution of the Electron Boltzmann Equation in Higher Order Legendre Polynomial Expansion

The paper deals with the mathematical structure of the general solution and the selection of the physical relevant solution of the hierarchy resulting from the electron Boltzmann equation by the Legendre polynomial expansion for a weakly ionized plasma with elastic and exciting collisions and under the action of an electric field. At first the properties of the general solution for the two and four term approximation of the distribution function are analyzed and then the study is extended to arbitrarily even order of the hierarchy using the theory of weakly and strongly singular differential equation systems for the investigation of the solution behaviour of the truncated hierarchy at small and at large energies, respectively. In this way, especially the free parameters of the non-singular part of each general solution, which is obtained for small and large energies and is of interest for the construction of the desired solution, could be found, and the procedure for their final determination is explained. A first illustrative example is given of the application of these studies for the determination of the velocity distribution function of the electrons in four term approximation for a model plasma.     

On connectivity of triangulations of manifolds

An edge of a k-graph is “separating” if there is a k-coloring of the vertices assigning all colors to that edge only. We prove that no edge of any triangulation of any manifold of any dimension is separating.     

Die colorimetrische Zuckerbestimmung

Ohne Zusammenfassung     

Operator-Ungleichungen und ihre numerische Anwendung bei Randwertaufgaben

Ohne Zusammenfassung