On the Nonlocal Electron Kinetics in s- and p-Striations of DC Glow Discharge Plasmas: I. Electron Establishment in Striation-like Fields

The nonlocal behavior of the electrons in strongly modulated and period-averaged electric fields typical of s- and p-striations in neon glow discharge plasmas is investigated by numerically solving the axially inhomogeneous electron Boltzmann equation. A good agreement between the period lengths measured in the striations and those obtained from the spatially periodic electron relaxation in the period-averaged field of the striations is found confirming the close relation of both phenomena. The s- and p-striations represent the fundamental and first harmonics of the inherent periodic electron relaxation. Furthermore, starting from different boundary conditions the establishment of the velocity distribution function and of selected macroscopic quantities of the electrons into unique periodic states under the action of strongly modulated striation-like fields is investigated. It is shown that the same damping processes that cause in homogeneous fields a relaxation into homogeneous states lead to unique periodic states in strongly modulated fields.     

Spatial relaxation of electrons in nonisothermal plasmas

The spatial relaxation of electrons to homogeneous states under the action of space-independent electric fields is investigated in helium, krypton, and N₂ plasmas for various electric field strengths. These investigations are based on a new method recently developed for solving the one-dimensional inhomogeneous electron Boltzmann equation in weakly ionized, collision-dominated plasmas. Elastic as well as conservative inelastic collisions of electrons with gas atoms have been included in the kinetic treatment. The spatial relaxation is caused by an imposed direct disturbance in the velocity distribution of the electrons on a spatial boundary. A pronounced dependence of the relaxation structure and the resultant relaxation length on the atomic data of the electron collision processes in different gases has been found. Furthermore the relaxation process sensitively depends on the electric field strength in the region of medium field values.     

Spatial Transition of the Electron Gas from the Active to the Remote Plasma State

Starting from the active region of a weakly ionized plasma the spatial transition of the electron gas through an adjacent field decay region into the field-free remote plasma is studied in neon on a rigorous basis by using two independent kinetic approaches. The main objective of the analysis concerns the complex features of the electron gas in its transition process from a field-driven active plasma to a purely diffusion-driven remote plasma. In addition to the energy resolved characterization of the velocity distribution, in particular, the spatial decay behavior of important, energy space averaged transport and dissipation properties of the electrons, as the density, the particle and energy fluxes and the power transfer rates to the gas particles in electron collisions, is elaborated and interpreted. Moreover, the influence of a variation of the active plasma conditions and of the spread of the field decay region on the resultant transition behavior of the electron gas is evaluated. A particular finding is that the spatial field decay is generally accompanied by a large density increase in order to allow the continuation of the electron flux by a pure diffusion process in the adjacent remote plasma. This finding could be completely confirmed by the almost perfect coincidence of corresponding results obtained by two independent kinetic approaches.     

Spatial Electron Relaxation: Comparison of Monte Carlo and Boltzmann Equation Results

In former investigations on the spatial relaxation of the electron component of weakly ionized plasmas a considerable spectrum of distinct spatial structures has been found in the velocity distribution function as well as in various macroscopic quantities of the electrons. These results have been mainly obtained by solving the spatially inhomogeneous electron Boltzmann equation considering the action of uniform electric fields and the impact of elastic and inelastic collisions of the electrons with the gas atoms. To verify these partly unexpected results on the complex structure formation, analogous Monte Carlo simulations were performed now for a helium plasma at various reduced electric field strengths. Detailed comparisons were made between the results of the two independent kinetic approaches with respect to the spatial evolution of the velocity distribution function as well as of associated macroscopic quantities. Good agreement was generally found, thus confirming the earlier results on the complex spatial relaxation structures.     

On the mechanisms of spatial electron relaxation in nonisothermal plasmas

The impact of different collision processes of the electrons with the gas atoms on their spatial relaxation under the action of space-independent electric fields is analyzed in a weakly ionized, collision-dominated helium plasma. Based on the numerical solution of the one-dimensional inhomogeneous electron Boltzmann equation, the spatial evolution of the electron velocity distribution function and of the related macroscopic quantities is investigated for different models concerning the treatment of the elastic, exciting, and ionizing collision processes. The spatial relaxation into homogeneous states is initiated by a disturbance which is directly imposed on the electron velocity distribution as a boundary condition. At moderate and higher electric fields this disturbance excites spatially periodic structures in the distribution function which are damped out by special mechanisms inherent in the exciting and ionizing collision processes. With decreasing field strength the damping due to the energy loss in elastic collisions becomes more effective and causes at lower fields an aperiodic establishment into homogeneous states.     

Study of the Anode Region of a DC Glow Discharge by a Spatially One-Dimensional Hybrid Method

The anode region of a dc glow discharge at low pressure and current is studied by a new self-consistent, spatially one-dimensional hybrid method. The method consists of the coupled solution of the steady-state fluid equations of electrons, ions, and excited atoms and the Poisson equation using the electron transport properties as well as the excitation and ionization frequencies from a strict solution of the non-uniform kinetic equation of the electrons. Results such as the electric potential, the electron velocity distribution function, and the densities of the charge carriers and excited atoms are reported for the anode region of neon glow discharges. Physical properties of the plasma in the anode region known from experiments have been confirmed by the model such as the occurrence of the anode fall, a formation of plateau-like areas of the potential profile in front of the anode, the anode dark space, and the anode glow.     

On plasma parameters of a self-organized plasma jet at atmospheric pressure

Electron temperature and electron concentration in the active zone of a miniaturized radio frequency (RF) non-thermal atmospheric pressure plasma jet in argon have been determined using two independent approaches: the spectroscopic measurement of the broadening of Balmer H_b_\beta and H_g_\gamma lines and a time-dependent, spatially two-dimensional fluid model of a single discharge filament. The plasma source has been configured as a capacitively coupled RF jet (27.12 MHz, 8 W generator output power) with two outer ring electrodes around a quartz capillary with diameter of 4.0 mm between which Ar flows at typical rates of 0.3 slm. The discharge has been operated in a self-organized mode, where equidistant, stationary filaments rotate regularly with a constant frequency at the inner wall of the outer capillary. For the purpose of calculating the spectral line broadening different models applicable at higher electron concentration have been evaluated. Resulting electron concentrations are between 2.2 and 3.3 × 1014 cm^-3. The calculation according to the line broadening model provides electron temperatures between 20 000 and 30 000 K which is in agreement with the results of the fluid model calculations. Here, a broad radial profile with a maximal value of about 22 000 K in the centre of the column and an electron concentration of about 7 × 10¹³ cm^-3 have been obtained. Moreover, the results of the model calculations reveal a structural change of the filament from the dielectric surface through the sheath to the column. The axially inhomogeneous region has an extension of about 0.5 mm. In the column a concentration of about 10¹³ cm^-3 has been found for the excited argon atoms, whose collisions with electrons represent the most important ionization channel there.