Elastic Electron-atom Collisions Research Articles

Kinetic Theory of Instability of the Electron Beam-Plasma System Taking into Account the Elastic Electron-Atomic Collisions for an Arbitrary Scattering Indicatrix

A kinetic theory of stability of a fast electron beam-gas-discharge plasma system under conditions when the electron mean free path relative to elastic collisions with atoms is of the order of the plasma dimension along the direction of the beam propagation is developed. It is assumed that the cross section of elastic electron-atom collisions is considerably higher than the cross section of inelastic processes with electrons. The dispersion equations for an arbitrary indicatrix of elastic electron-atom scattering are obtained. Despite the smallness of the cross section for inelastic scattering in comparison with elastic one, it is also necessary to consider inelastic processes when the plasma Knudsen numbers are less than 0.3. As the Knudsen number decreases beneath 0.3 the growth rate considerably decreases in the range of instability, because the role of elastic scattering of electrons by atoms increases.

Comparison of electron heating and energy loss mechanisms in an RF plasma jet operated in argon and helium

The μ-APPJ is a well-investigated atmospheric pressure RF plasma jet. Up to now, it has mainly been operated using helium as feed gas due to stability restrictions. However, the COST-Jet design including precise electrical probes now offers the stability and reproducibility to create equi-operational plasmas in helium as well as in argon. In this publication, we compare fundamental plasma parameters and physical processes inside the COST reference microplasma jet, a capacitively coupled RF atmospheric pressure plasma jet, under operation in argon and in helium. Differences already observable by the naked eye are reflected in differences in the power-voltage characteristic for both gases. Using an electrical model and a power balance, we calculated the electron density and temperature at 0.6 W to be , 1.2 eV and , 1.7 eV for argon and helium, respectively. In case of helium, a considerable part of the discharge power is dissipated in elastic electron-atom collisions, while for argon most of the input power is used for ionization. Phase-resolved optical emission spectroscopy reveals differently pronounced heating mechanisms. Whereas bulk heating is more prominent in argon compared to helium, the opposite trend is observed for sheath heating. This also explains the different behavior observed in the power-voltage characteristics.

Role of thermal effects in neon and argon constricted discharges

The paper is aimed at investigating the role of inhomogeneous heating of the neutral gas in a constricted glow discharge in neon and argon. It is shown that inhomogeneous heating is not the primary cause of constriction in specified gases at pressures of tens and hundreds Torr cm and reduced currents not exceeding 100–200 mA cm−1. Constriction of the positive column occurs even with an insignificant gas heating in a pulsed regime. An abrupt constriction is caused by the nonlinear dependence of the ionization number on the electron density. In mentioned discharge conditions the frequency of electron–electron collisions is comparable to the electron energy relaxation frequency due to elastic electron-atom collisions. Thermal effects play a secondary role in the formation of a constricted discharge. At the same time, inhomogeneous gas heating in argon is more notable than in neon. Unlike neon, stationary argon discharge loses spatial stability in a vertically oriented tube as the pressure and current increase and a buoyancy effect takes place in a horizontal orientation. Such difference in the behavior of constricted neon and argon discharges is mainly caused by the difference in shape of elastic electron-atom collision cross sections. Interferometric methods allowed to study the temperature field of neutral atoms, dynamics of both gas heating and ascent of constricted cord. Observed effects are interpreted on the basis of the heat equation and the Navier–Stokes equation. Comparison of experimental and theoretical results shows good agreement.

Nonthermal effects on the elastic electron–atom collision in generalized Lorentzian semiclassical plasmas: Lorentzian renormalization shielding

The Lorentzian renormalization plasma shielding effects on the elastic electron–atom collision are investigated in generalized Lorentzian semiclassical plasmas. The eikonal analysis and the effective interaction potential are employed to obtain the eikonal scattering phase shift, differential eikonal collision cross section, and total eikonal collision cross section as functions of the collision energy, impact parameter, nonthermal renormalization parameter, and spectral index of the Lorentzian plasma. It is found that the influence of Lorentzian renormalization shielding suppresses the eikonal scattering phase shift and, however, enhances the eikonal collision cross section in Lorentzian semiclassical plasmas. Additionally, the energy dependence on the total collision cross section in nonthermal plasmas is found to be more significant than that in thermal plasmas.

Non-thermal renormalization shielding on the electron–atom collision in partially ionized generalized Lorentzian non-thermal plasmas

AbstractThe non-thermal renormalization shielding effects on the elastic electron–atom collision process are investigated in partially ionized generalized Lorentzian non-thermal plasmas. The eikonal analysis for the Hamilton–Jacobi solution and impact parameter method are employed to obtain the eikonal scattering phase shift and eikonal cross section as functions of the collision energy, Debye length, impact parameter, and spectral index of the Lorentzian plasma. It is found that the non-thermal renormalization shielding effect enhances the eikonal scattering phase shift as well as the eikonal collision cross section, especially for small impact parameter domains. It is also found that the non-thermal renormalization shielding effect on the eikonal scattering phase shift decreases with an increase of the impact parameter. In addition, it is found that the maximum position of the eikonal collision cross section has receded from the collision center with an increase of the non-thermal character of the plasma.

Influence of the renormalization plasma screening on the electron-atom collision in partially ionized plasmas

The renormalization plasma screening effects on the elastic electron-atom collision are investigated in partially ionized dense hydrogen plasmas using the eikonal method. It is found that the renormalization plasma screening suppresses the eikonal phase shift and cross section for the elastic electron-atom collision in partially ionized plasmas. It is also found that the renormalization plasma screening effect on the elastic electron-atom collision process increases with an increasing impact parameter. In addition, it is found that the maximum position of the differential cross section is receded from the center of the atom with an increase of the Debye length.

Quantum-mechanical effects on polarization elastic electron–atom collisions in partially ionized dense hydrogen plasmas

The quantum-mechanical effects on the polarization elastic electron–ion collisions are investigated in partially ionized dense hydrogen plasmas. The second-order eikonal method with the impact parameter analysis is applied to obtain the total eikonal phase and the differential eikonal cross-section as functions of the impact parameter, de Broglie wavelength, Debye length and collision energy. The results show that the quantum effects strongly suppress the eikonal phase as well as the eikonal cross-section, especially, for small impact parameters. In addition, the quantum effects are found to be decreased with increasing the collision energy.

Screening effects on elastic electron–atom collisions in partially ionized hydrogen plasmas

The non-ideal collective and plasma screening effects on elastic electron–atom collisions are investigated in partially ionized hydrogen plasmas using the first-order eikonal method. The effective pseudopotential model, taking into account the screening and collective effects, is applied to describe the interaction potential in non-ideal plasmas. Semiclassical trajectory analysis is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase and cross section as functions of the impact parameter, the non-ideality plasma parameter, the Debye length, and the collision energy. The results show that the collective and screening effects enhance the differential eikonal cross section for small impact parameters, but suppress the cross section for large impact parameters. It is also found that the non-ideal collective effects enhance the total eikonal cross section.

Acoustic Instability in Inhomogeneous Gas-Discharge Plasma

The possibility of amplification of acoustic waves in inhomogeneous atomic dc gas-discharge plasma (positive column of glow discharge) is investigated theoretically. This amplification is caused by the transfer of thermal energy from electrons to colder electron gas under conditions of elastic electron-atom collisions. It is demonstrated that the inclusion of nonuniform distribution of equilibrium temperature, neutral gas concentration, and electron concentration over the plasma column cross section, similar to the case of uniform distribution, cannot result in acoustic instability and, consequently, in the interpretation of the experimental results in sound amplification in weakly ionized plasma. The dispersion equation for sound waves in inhomogeneous glow-discharge plasma is derived and numerically analyzed in detail. Comparison of the theoretical and experimental results enables one to identify the reasons for their discrepancy and to actually reveal the basic principles essential for constructing a theory which will make it possible to quantitatively and adequately describe the experimental data on the amplification of sound in weakly ionized atomic plasma.

Theory of the acoustic instability and behavior of the phase velocity of acoustic waves in a weakly ionized plasma

The amplification of acoustic waves due to the transfer of thermal energy from electrons to the neutral component of a glow discharge plasma is studied theoretically. It is shown that, in order for acoustic instability (sound amplification) to occur, the amount of energy transferred should exceed the threshold energy, which depends on the plasma parameters and the acoustic wave frequency. The energy balance equation for an electron gas in the positive column of a glow discharge is analyzed for conditions typical of experiments in which acoustic wave amplification has been observed. Based on this analysis, one can affirm that, first, the energy transferred to neutral gas in elastic electron-atom collisions is substantially lower than the threshold energy for acoustic wave amplification and, second, that the energy transferred from electrons to neutral gas in inelastic collisions is much higher than that transferred in elastic collisions and thus may exceed the threshold energy. It is also shown that, for amplification to occur, there should exist some heat dissipation mechanism more efficient than gas heat conduction. It is suggested that this may be convective radial mixing within a positive column due to acoustic streaming in the field of an acoustic wave. The features of the phase velocity of sound waves in the presence of acoustic instability are investigated.

Conductivity of a photoplasma of sodium vapor-inert gas mixtures

Parametric computations of electron energy distribution function (EEDF) and of electron mobility in photoplasma of sodium mixture with different inert gases are presented. The conditions of a weak external electric field are considered when electron heating is provided by super-elastic impacts (second kind collisions) with excited sodium atoms. It is demonstrated that nonequilibrium EEDF arising in heavy inert gases due to Ramsauer minimum on the cross section of elastic electron-atom collisions can considerably affect electron mobility. It results in complex nonmonotonous dependence of electron mobility from partial pressure of mixture components, plasma ionization degree, and from resonant-excited sodium atoms density. In Na+Kr, Na+Xe mixtures by low plasma ionization degree, the electron mobility can differ by more than two times from the one calculated with Maxwellian EEDF. In Na+Ar mixture, in certain conditions, the mobility may take on negative values. The critical plasma parameters (sodium excited atoms density, plasma ionization degree, electric field strength) determining this effect are revealed. The influence of nonequilibrium EEDF on electron mobility helps to explain abnormally low conductivity of photoplasma in Na+Ar mixture observed earlier in the experiment.

Laser-assisted elastic electron-atom collisions: low electron energy and small scattering angle

The authors report experimental measurements of electron spectra resulting from the scattering of low energy (6.2-32 eV) electrons by helium atoms through an angle of 9 degrees in the presence of a high intensity ( approximately 108 W cm-2)CO2 laser. The intensities of the additional peaks caused by the presence of the laser which occur separated from the elastic scattering peak by multiples of the photon energy are much greater than expected on the basis of calculations, using the Kroll-Watson approximation (1973). The intensity of these free-free transitions also increases with decreasing electron energy, again in disagreement with the calculations. The authors propose that the disagreement between the experimental results and those calculated is due to the electrons scattering from a helium target polarized by the laser field.

Evaluation of the viscosity cross sections for elastic electron-atom collisions in krypton and xenon at low electron energies

The results of viscosity cross sections evaluations for elastic electron-atom scattering from rare gases krypton and xenon, carried out in the energy interval from 0.1 to 54.4 eV are presented and discussed. The evaluations are based on four independent sets of partialwave phaseshifts, one theoretical and three experimental, taken from literature. An analytical estimate for the contribution of all the terms not included in the summation, for truncation at any chosen value of the electron angular momentum, is derived. The validity of assumption of isotropic angular scattering is investigated in the energy range considered. The present results invariably show significant deviations from the values calculated with this assumption.

Modeling the Hg-Ar low-pressure-discharge positive column: A comparative study.

For the description of the low-pressure Hg-Ar positive column a self-consistent collisional-radiative model has been used. Calculations of the population densities for the fundamental and the first five excited Hg levels, electron and rare-gas temperature, and densities have been carried out. All these quantities, except electron temperature, have been evaluated as functions of the radial position in the axially uniform positive column; no assumptions on the radial profiles have been made. Macroscopic quantities such as electric-field strength and radiative power output have been also calculated. A diffusion-controlled positive column has been assumed. The most important collisional processes in the plasma have been taken into account (elastic collisions, electron-atom and atom-atom inelastic collisions including excitation, direct and stepwise ionizations, and also superlastic collisions). Argon excitation and stepwise ionization have been included. Radiation trapping has been taken into account, including pressure broadening of resonance lines due to Ar. In our calculations a non-Maxwellian electron-energy distribution function has been used. Diffusion of the charged particles in the presence of ${\mathrm{Hg}}^{+}$ and ${\mathrm{Ar}}^{+}$ has been considered. Diffusion of the metastable Hg levels has been taken into account. The results obtained in this paper have been compared to corresponding values given in the literature and detailed discussion of the validity of several models has been carried out.

Evaluation of the viscosity cross sections for elastic electron-atom collisions in argon and neon at low electron energies above 0.13 eV

The importance of the viscosity cross section for elastic electron-atom collisions in various domains of electron kinetic and transport theories is pointed out. Results of numerical evaluations of the velocity-dependent viscosity cross sections for elastic electron-atom collisions in argon and neon are presented and discussed. Two series of results are given. They are based on theoretical and experimental sets of partial-wave phaseshifts for the two atomic species, taken from the literature. Special consideration is given to deviations, sometimes very significant, of the results obtained in the present calculations from those which would have followed if the scattering were assumed isotropic.

Probe measurements of the electron collision integrals in plasmas

The probe method for the measurement of the electron-atom collision integral in a plasma is described. The method is applied to the plasma of the positive column of an electrical discharge in helium. The collision integrals S0, S1 and the transport cross section of the elastic electron-atom collision are measured.

Energy Spectrum of an Abnormal Glow Discharge Created Electron Beam

Abnormal glow discharge created electron beams, applied to microelectronic film processing, have been studied theoretically and experimentally. The beam mode of operation occurs in the discharge region adjacent to the glow to arc transition regime. A numerical model simulates the energy distribution I(E) of transmitted beam electrons both inside and outside the cathode sheath. Changes in the I(E) spectrum are calculated as a function of distance in the field-free region outside the sheath. In the theoretical model of beam generation and propagation we include secondary electrons created at the cathode following ion bombardment, the electron energy gain that occurs in the field of the cathode sheath, elastic electron-atom collisions, electron-atom ionization collisions, electron-atom excitation collisions, super-elastic electron-atom collisions, and electron-electron collisions. The calculated I(E) spectrum agrees with experimentally measured data at a total ambient pressure of 0.2-0.9 torr in a helium-oxygen mixture with a cathode current density in the range of 10-100 mA/cm2.

Hot-electron zero-field mobility and diffusion in rare-gas moderators.

An efficient discrete-ordinate method of solution of the time-dependent Boltzmann equation is employed in the calculation of the zero-field electron mobility and diffusion coefficients for hot-electron thermalization in rare-gas moderators. The discrete-ordinate method is modified to permit a rescaling of the quadrature points. This procedure is somewhat analogous to the two-temperature-moment methods employed in the theoretical analysis of electron swarms. The time-dependent transport coefficients are given as a sum of exponential decay terms characterized by the discrete eigenvalues of the Lorentz-Fokker-Planck operator for elastic electron-atom collisions. For argon, krypton, and xenon, the time dependence is strongly influenced by the Ramsauer-Townsend minimum and leads to maxima in the transient mobility and diffusion coefficient. Helium and neon with hard-sphere-like cross sections exhibit transient mobilities which initially are below the thermal zero-field mobility and then increase to the thermal mobilities as the electron distribution approaches equilibrium. The transient mobility for cross sections with Ramsauer minima are sufficiently sensitive to the details of the cross sections such that it may be feasible to distinguish between different cross sections experimentally. The calculations also indicate that the transient mobility is insensitive to the initial distribution function. A nonequilibrium phenomenon not previously recognized is the possibility of a negative transient mobility which occurs provided that the momentum-transfer cross section increases sufficiently rapidly with energy.

Kinetic theory of transport processes in weakly ionized gases

A consistent method for the treatment of a plasma of arbitrary degree of ionization is presented. This method consists of a perturbation expansion in the framework of the multiple time scales formalism. Here the results are presented for a weakly ionized gas where elastic electron-atom collisions dominate. It appears that an isotropic correction to the zeroth order Maxwellian electron distribution function is necessary. Calculated electron transport coefficients are compared with the Frost mixture rule and with other calculations.

A program for calculating relativistic elastic electron-atom collision data

A program for calculating relativistic elastic electron-atom collision data