In the kinetic theory a great variety of physical systems is investigated by means of Boltzmannlike equations. This approach is used for neutral gases, neutron as well as radiation transport, plasmas etc. For msny problems the knowledge of the properties of the collision operators is of great importance, especially if eigenvaiue problems occur.The paper presents an investigation of the properties of the collision operators of the Boltzmann equation covering elastic, exciting and deexciting processes in a weakly ionized plasma. First, a short survey of the importance of eigenfunctions and eigenvalues in the kinetic theory of various systems is given. Then, properties of the outscattering operator as dependent on the course of the differential cross section are considered. Finally, for the inscattering operator such properties as selfadjointness and rotational invariance are investigated in detail. These considerations provide the basis for the proof of compactness and for first conclusions on the spectral properties of the collision operators in the second part of this paper.
Based on the semigroup approach a newproof.is presented of the existence of o unique solution of the non-stationary Boltzmann-equation for the electron component of a collision dominated plasma. All interactions can be included which yield bounded collision operators. The electric and magnetic fields were permitted to be inhomogeneous in space, and the investigations were performed for a bounded plasma. It has been shown that the Boltzmann-operator is the infiitesimal generator of a strongly continuous operator-semigroup which uniquely determines the nonnegative solution from a given initial function taking into account the given boundary conditions. Existenz und Eindeutigkeit der LSsung der nichtstationLen Boltzmann-Gleichung fur die Elektronen in einem sto Bbestimmten Plasma mit Hilfe von Operator-Halbgmppon Inhaltsubersicht. Im Folgenden wird ein neuer Beweis fur die Existenz einer eindeutigen Lijsung der nichtstationiiren Boltzmann-Gleichung fur die Elektronenkomponente eines stoI3bestimmten Plasmas auf der Grundlage der Halbgruppen-Theorie erbracht. Dabei lassen sich solche Wechselwirkungen mitberiicksichtigen, deren zugehorige StoDoperatoren beachriinkt sind. Elektrisches und magnetisches Feld werden als orteabhiingige Funktionen angeaehen und den Untersuchungen ein begrenztes Plasma zugrunde gelegt. Es wird gezeigt, d a B der Boltzmann-Operator infinitesimal eneugender Operator einer stark stetigen Operator-Halbgruppe ist, welche die nichtnegative Liisung unter vorgegebenen Randbedingungen aus der Anfangsverteilung eindeutig angibt.
In a preceding part of the paper, based on experimentid methods and on a corresponding kinetic model, especially the impact of the effective life times of the 63P1 and 61P1 Hg resonance levels on the main properties of the low pressure Hg-Ar positive column has been studied. In the presented second part these investigations, which have been performed under the aspect of their applicnt.ion in fluorescent lamps, will be continued. They are related to the effects of tube radius and discharge current density. New fluorescent lamps have reduced tube radii from R = 18 t o 13 mm and compact lamps down to R = 5 mm. Thus it is of interest to study the electron distribution function and main macroscopic properties of such low pressure discharge plasmas, where the latter properties nre obtained by adequate energy space averaging. At first, results are reported and discussed which are related to the dependence of main plasma parameters on the Hg partizrl pressure when reducing the discharge tube radius for constant discharge current i and argon pressure P,,~. Starting from the electron distribution function thc particle and energy budget will be studied in detail, especially of course the change of the ultraviolet radiation output from both Hg resonmce levels 63P, and 61P1 and, in addition, of visible radiation. Then, to understand the effect of the discharge current density, as a reprcsentntive example two cases with different v i h e s of R, i and pAr but with equal current density have been investigated and discussed.Altogether the investigations made will shed light upon the complex relntions in the mentioned mixture plasma and give hints to select suitable pnrnmetcr values which can be usefill to irnprovc light soiirccs.
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