V. O. Nekuchaev

Diffusion-path approximation in nonlocal electron kinetics

For the positive column of a discharge, nonlocal distribution functions obtained by averaging over radial diffusion paths are compared with the exact solution to the kinetic elliptic equation. For a discharge in argon, as an example, the limits of applicability of the approximate solution for various macroscopic characteristics of the plasma were identified. It was previously believed that the approximation based on averaging has the limits of applicability determined by the condition that the plasma inhomogeneity size be smaller than the energy relaxation length. This condition restricts the applicability of the approximation to low pressures. In the present work, it is shown that, for determining a number of macroscopic parameters, such as the concentration, mean energy, mobility, diffusion coefficient, and thermal conductivity of electrons, the pathaveraging approximation works well over a pressure range of up to a few Torr. A number of subtle characteristics, such as the excitation rate, ionization rate, and others, largely influenced by fast electrons, cannot be calculated from the averaged distribution functions at pressures above a few tenths of a Torr.

Role of resonance radiation transfer in the ionization balance of positive column discharge

A method is proposed for the joint solution of the balance equation of charged particles, which is described by a differential equation of ambipolar diffusion, and the balance equation of resonant atoms, which is described by the integral equation of radiative transfer. The method is associated with the replacement of the differential and integral operators by a system of linear algebraic equations. The difference between the results of the exact solution of the problem and the conventional solutions in the approximation of an effective probability of the resonance transition is demonstrated. The effect of the higher diffusion and radiation modes in the transition to the contracted discharge regime is noted.

Stratification of discharge in noble gases from the viewpoint of the discrete dynamics

Based on the analysis of electron phase trajectories in sinusoidal electric fields, a new point of view on discharge stratification is proposed. It is shown that the positive column can be considered as a spatial resonator in which electric fields with a fundamental period length LS or higher mode length qpLS establish, where p and q are integers and p > q. The fundamental mode length LS is equivalent to the distance on which electrons gain energy equal to the lowest excitation threshold. This distance determines a length of the S-striation. Unlike kinetic theory, in the presented model resonance properties of the discharge column are not connected with elastic collision energy losses. A point map is used to obtain the resonance trajectories of electrons in the phase plane. Stable points for the positions of inelastic collisions in the resonance trajectories have been found at the positions of field maxima in the case of integer ratios pq. For non-integer ratios pq, multiple resonance trajectories arise a...

Advances in the study of striations in inert gases

We present a review of studies of striations in a dc discharge in inert gases over recent decades. Physical mechanisms of stratification are described for various discharge conditions. Main attention is paid to striations at low pressures and small currents (S, P, and R striations). The origin of these striations is associated with electron bunching in spatially periodic resonant fields. The idea of this mechanism and qualitative interpretation of the S and P striations based on the analytic theory are described in the pioneering work by L.D. Tsendin (1982). We describe the evolution of these ideas on quantitative level. New ideas concerning nonintegral resonances responsible for the formation of R striations are considered. The theory is compared with experiment.

On relaxation of the electron distribution function in resonant striation-like fields

Relaxation of an approximately δ-shaped distribution function of electrons injected into P and R striation-like fields on one of the resonant trajectories is analyzed. It is shown that as a result of energy diffusion, electrons appear on other resonant trajectories after several periods. Ultimately, a steady state corresponding to the distribution function in the P and R strata is formed as a result of compression to resonant trajectories and energy diffusion.

Effect of Elastic Collisions on the Ion Distribution Function in Parent Gas Discharge Plasma

An analytical solution is obtained for the Boltzmann kinetic equation for ions in the plasma of its gas with allowance for the processes of resonant charge exchange and elastic ion scattering on the atom. The cross section of differential elastic scattering was assumed to be isotropic in the system of the mass center, and the resonant charge exchange process is independent of the elastic scattering. It is shown that the ion velocity distribution function is determined by two parameters and differs significantly from the Maxwellian one. The allowance for elastic scattering with these assumptions leads to a change in the ion angular distribution and also to a decrease in the average ion energy due to the transfer of part of the ion energy to atoms upon elastic collisions. The calculated values of the drift velocity, the average energy, and the coefficient of transverse diffusion of He+ ions in He, Ar+ ions in Ar are compared with the known experimental data and the results of Monte Carlo calculations; they show good agreement.

Ion velocity distribution function in intrinsic gas at cryogenic gas temperatures

The influence of elastic scattering on the ion distribution function in the plasma of an intrinsic gas in weak fields has been considered. An analytical expression valid for cryogenic temperatures of atoms has been obtained. The reduced He+–He, Ar+–Ar mobilities as functions of the temperature of atoms in a range of 4–1000 K have been calculated in the approximation of the zero field taking into account elastic collisions; the calculated dependences well agree with the available experimental data. It has been demonstrated that elastic collisions play an important role in the formation of the ion distribution function at low temperatures. The results of measurement of the ion mobility in the limit of the zero field at low temperatures can be used to obtain data on the ratio of elastic scattering and resonance charge exchange cross sections.

Is the Collecting Surface of a Flat One-Sided Probe Constant when Measuring the Ion Distribution Function?

The correctness of the known plane single-ended probe method for measuring the anisotropic ion distribution functions in a gas-discharge plasma has been considered. Analysis has been performed for positive probe potentials relative to the plasma with magnitudes on the order of the mean ion energy, which as a rule is much lower than the mean electron energy. We have analyzed the dependence of the collection surface area of a plane probe on its potential in this range. The structure of the near-probe layer has been determined for an isotropic electron distribution function of the Maxwellian or Druvestein type and an anisotropic ion distribution function. These results are used to derive analytic relations for the correction to the second derivative of the probe current with respect to the plane probe potential. It has been shown that, when the ion distribution function is measured in a wide range of conditions in the gas-discharge plasma, when the approximation of a collisionless probe layer is applicable, and the probe does not perturb the plasma, the dependence of the collection surface area of the probe on the potential can be disregarded in this range.

Contraction of the positive column of a glow discharge in inert gases with account of resonance radiation transport

A previously proposed method for accurate description of resonance radiation transport in solving self-consistent problems is applied to a model of the contraction of the positive column of a glow discharge in argon. The exact solution to the problem and the solution obtained within the framework of the traditional approximation of local effective transition probability according to Biberman are compared. The influence of radiation transport on various plasma parameters is demonstrated

Mutual influence of higher diffusion and radiation modes on the contraction of the positive column discharge

Fourier analysis of various plasma components in contracted discharge is made by an expansion over diffusion and radiation modes. Resonance atoms transport is traditionally described by an approximation of the effective lifetime by Holstein which considers only a fundamental radiation mode. Proposed method makes it possible to estimate the role of resonance radiation transport quantitatively by comparing the mode spectra. Behavior of resonance atoms successively considered on simple three-level energy models in a linear Shottky theory and in a semi-analytical non-linear diffusion-recombination theory, describing a discharge contraction. Suggested Fourier analysis method has been applied to a detailed model of the DC column contraction in Argon glow discharge. An expansion of different plasma components (electron density, metastable and resonance atoms densities) over the corresponding orthonormal set of diffusion or radiation modes is performed. The comparison of spectra obtained using the traditional Holstein approximation and in case of accurate treatment of resonance radiation transport shows an increase of fundamental diffusion and radiation modes and an effect of higher harmonics suppression in the modes spectra when the resonance radiation transport is described precisely. The role of higher radiation modes in formation of radial profiles of the electron density, metastable and resonance atoms densities as well as current–voltage characteristics is demonstrated by specific examples.