Die Relaxation der Geschwindigkeitsverteilungsfunktion der Elektronen im homogenen Feld mit elastischen und anregenden Stößen. III. Die Einstellung des periodischen Verhaltens der Elektronen-komponente im elektrischen Feld großen Modulationsgrades

To continue the kinetic investigations concerning the periodic behaviour of the electron component of a low ionized Ne-plasma of a glow discharge column in a periodic electric field [4] with high degree of modulation in this paper the adjustment of the isotropic distribution function of the electrons and by the latter determined macroscopic quantities are calculated and discussed. Starting with the non-stationary Boltzmann equation the adjustment process is considered using different direct components of the field but nearly constant degree of modulation. In the whole range from a nearly momentary adjustment to an adjustment in the high frequency limit of only small modulated distribution function we obtained results concerning the adjustment behaviour and its characteristic times by variation of the cycle time of the electric field starting from the different stationary states. At the other hand the influence of the different degrees of modulation on the adjustment process and its characteristic times was investigated and interpreted. For this interpretation the spectrum of adjustment times of stationary states corresponding to all momentary values of the periodic electric field strength in one cycle plays a dominant role. From the investigations follows that the adjustment times of periodic states can alter their values by some orders of magnitudes in dependence on the parameters of the electric field.     

Zur Theorie der stationären Bewegung von Ionen im elektrischen Feld

In a static electric field a one-dimensional model of the motion of ions, controlled solely by charge exchange (electron capture from gas moleculs) is considered. Solutions of the kinetic equastions for ions and fast neutrals are derived in several special cases. If the charge exchange cross section is constant, the kinetic equation is easily solvable in a closed form; if the cross section is a function of ion energy, however, the problem is reducible to a simple integral equation for the energy distribution function.     

Stoßbestimmte Relaxation des Elektronenensembles im Plasma bei zusätzlicher Aufheizung durch ein elektrisches Feld. III. Das periodische Verhalten der Elektronenkomponente im elektrischen Feld großen Modulationsgrades

Collision Dominated Relaxation of the Electron Ensemble in a Plasma with Additional Heating by an Electric Field. III. The Periodic Behaviour of the Electron Component in an Electric Field with a Large Modulation Amplitude With the aid of the non-stationary Boltzmann-equation the periodic behaviour of the isotropic part of the velocity distribution of electrons and thereby determined macroscopic quantities is calculated for periodic electric fields with large modulation amplitude. The investigations concern a weakly ionized column plasma in neon under typical low and medium pressure conditions. Based on the numerical results for typical ranges of field strength and cycle times of the electric field a qualitative physical interpretation for the periodic behaviour of the electron component is obtained. The introduction of special field-dependent adjustment times allows the formalution of conditions which characterize the case of quasi-stationary behaviour and also the case of small amplitudes of modulation in the macroscopic quantities determined by the isotropic distribution function. The periodic states between these two limiting cases can be interpreted as due to two competing processes. The first one is the energy input controlled by the electric field and the second one is the energy loss in binary collisions of the electrons with the atoms.     

Die Relaxation der Isotropverteilung und makroskopischer Kenngrößen der Elektronen im abklingenden feldfreien Neon-Plasma

Relaxation of Distribution Function and Macroscopic Parameters of Electrons in Temporal Decaying Neon Plasma without Field Heating We investigate the field-free collision-dominated relaxation in the afterglow of a weak ionized plasma in the first period of temporal decay which is determined especially by the quick alterations in the electron component because of the small inertia of electrons. Therefore the evolution in time of the electron distribution and hence the macroscopic coefficients determined thereby are calculated in dependence on the action of elastic and exciting collisions between electrons and neutral atoms. On the basis of these results we have found characteristic times controlling the relaxation process which depend especially on the action of the different kinds of collisions. Thus it is possible to get a good microscopic understanding of the field free collision dominated relaxation of the electron component.     

Stoßbestimmte Relaxation des Elektronenensembles im Plasma bei zusätzlicher Aufheizung durch ein elektrisches Feld I. Die charakteristischen Zeiten für den Übergang in stationäre Zustände

Collision Dominated Relaxation of the Electron Ensemble in a Plasma with Additional Heating by an Electric Field. I. Characteristic Times for the Transition to Stationary States Starting from time dependent Boltzmann equation for electrons the time development of the isotropic part of the distribution function and of macroscopic quantities as mean energy, mobility, excitation frequency and energy transfer quotients during transition between two stationary states are determined. The computation is referred to weak ionized neon plasmas which are typical for low pressure and for medium pressure discharges. As a result of this investigations we get informations about the characteristic relaxation times which are different in order of magnitude, and about their dependence of the processes of energy transfer. The energy transfer quotients which determine the energy loss by different collision processes in consideration are found to be suitable quantities to characterize the relaxation times.     

Die kinetischen Eigenschaften der Elektronen des anisothermen homogenen stationären Neon-Plasmas im Ionisierungsgradbereich von 10−9 bis 10−2

The time dependence of the spectral and spatial energy density of the fluorescence radiation of an atomic system generated by the resonance scattering of an intense laser pulse was calculated. Particularly the influence of the duration and the intensity of the incident laser pulse and of the atomic relaxation constants upon the fluorescence radiation has been studied.     

Mikrophysikalische Bestimmung elektronenkinetischer Kenngrößen im binären Molekül-Mischplasma von Stickstoff und Wasserstoff I. Geschwindigkeitsverteilungsfunktion,Transportgrößen und Stoß-frequenzen für Dissoziation und Direktionisation im Mischplasma

For the low ionized anisothermal plasma in a mixture of moleculare nitrogen and molecular hydrogen the isotropic part of the velocity distribution function of the electrons is calculated and compared with the experimentally determined velocity distribution. the calculation of this distribution is performed by the help of the homogeneous and stationary electron Boltzmann-equation and takes into consideration all essential collision processes between the electrons and the N₂ and H₂ molecules. Furthermore, the calculated results of the mean energy, of the transport coefficients, of the collision frequencies for dissociation and direct ionization of the molecules, of the first Townsend coefficient of the molecules and of the collision rates for the direct ionization of the N- and H-atoms in the mixture are represented for the range 6–100 V/(cm Torr) of the reduced electric field strength and for any composition of the N₂-H₂ mixture.     

Diffusionstheoretische Beschreibung der Dissoziation und des Ionenhaushaltes im schwachionisierten Säulenplasma der Wasserstoffentladung. II. Makroskopische Kenngrößen der Elektronen im H/H2-Mischplasma

The results of the calculation of the energy distribution function f(U), of the transport coefficients ū, b_e, D_e, of the collision frequencies for dissociation and direct ionization and of the main energy loss rates due to elastic and inelastic collisions of the electrons with the components of the mixture are presented for a stationary and homogeneous hydrogen plasma. These calculations, based upon the Boltzmann equation for the electrons, are performed in dependence of the normalized electric field strength E/p₀ and the mixture ratio x_D in the range of 7.5 to 100 V/cm Torr for E/p₀ and for any mixture ratio.     

Mikrophysikalische Bestimmung elektronenkinetischer Kenngrößen im binären Molekül-Mischplasma von Stickstoff und Wasserstoff. II. Elektronenstoßfrequenzen für die Anregung und Ionisierung langlebiger elektronischer Molekülzustände und die Energieverlustraten der Elektronenkomponente des Mischplasmas

In this second part of the in [l] started paper the results of microphysical determined collision frequencies of the electrons for the excitation and ionization of metastable molecules, excited in electronic states, and of the energy loss rates of the electrons due to elastic collisions, vibrational excitation, electronic excitation, dissociation and ionization of the molecules in a N₂ - H₂ -plasma are represented and discussed. These investigations are related to a low ionized, homogeneous and stationary plasma in a mixture and are performed for the range 6- 100 V/(cm Torr) of the reduced electric field strength and for any composition of the N₂ - H₂-mixture.