Fluid models of gas discharges require the input of transport coefficients and rate coefficients that depend on the electron energy distribution function. Such coefficients are usually calculated from collision cross-section data by solving the electron Boltzmann equation (BE). In this paper we present a new user-friendly BE solver developed especially for this purpose, freely available under the name BOLSIG+, which is more general and easier to use than most other BE solvers available. The solver provides steady-state solutions of the BE for electrons in a uniform electric field, using the classical two-term expansion, and is able to account for different growth models, quasi-stationary and oscillating fields, electron–neutral collisions and electron–electron collisions. We show that for the approximations we use, the BE takes the form of a convection-diffusion continuity-equation with a non-local source term in energy space. To solve this equation we use an exponential scheme commonly used for convection-diffusion problems. The calculated electron transport coefficients and rate coefficients are defined so as to ensure maximum consistency with the fluid equations. We discuss how these coefficients are best used in fluid models and illustrate the influence of some essential parameters and approximations.

https://www3.nd.edu/~sst/teaching/AME60637/reading/2005_PSST_Hagelaar_Pitchford_bolsig.pdf

Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models

Many-particle charged-particle plasma simulations using spatial meshes for the electromagnetic field solutions, particle-in-cell (PIC) merged with Monte Carlo collision (MCC) calculations, are coming into wide use for application to partially ionized gases. The author emphasizes the development of PIC computer experiments since the 1950s starting with one-dimensional (1-D) charged-sheet models, the addition of the mesh, and fast direct Poisson equation solvers for 2-D and 3-D. Details are provided for adding the collisions between the charged particles and neutral atoms. The result is many-particle simulations with many of the features met in low-temperature collision plasmas; for example, with applications to plasma-assisted materials processing, but also related to warmer plasmas at the edges of magnetized fusion plasmas. >

Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC

Plasma–liquid interactions represent a growing interdisciplinary area of research involving plasma science, fluid dynamics, heat and mass transfer, photolysis, multiphase chemistry and aerosol science. This review provides an assessment of the state-of-the-art of this multidisciplinary area and identifies the key research challenges. The developments in diagnostics, modeling and further extensions of cross section and reaction rate databases that are necessary to address these challenges are discussed. The review focusses on non-equilibrium plasmas.

/pdf/plasma-liquid-interactions-a-review-and-roadmap-4kfoerpjnh.pdf

Plasma-liquid interactions: A review and roadmap

Particle-in-Cell Charged Particle Simulations, plus Monte Carlo Collisions with Neutral Atoms, PIC-MCC

Cold Target Recoil Ion Momentum Spectroscopy: a &momentum microscope' to view atomic collision dynamics

The energy distribution and angular dependence of secondary electrons generated by the impact of 100–2000‐eV electrons on He, N2, and O2 and by the impact of 500‐eV electrons on Ne, Ar, Kr, Xe, H2, NO, CO, H2O, NH3, CH4, C2H2, and CO2 have been measured over the 4–200‐eV range. The measurements were made in a crossed‐beam apparatus with the use of a fixed hemispherical electrostatic analyzer and a rotatable electron gun. The observed spectra were integrated over angle to obtain relative cross sections for secondary‐electron production. It was found that the shapes of the spectra of all the gases (except Ar, Kr, and Xe, which contain intense electron emission features in this energy range) were smooth and qualitatively similar, approaching a constant cross section at low secondary energies, and falling off at high secondary energies slightly faster than Es−2, where E8 was the energy of the secondary. The shape of the spectrum was found to be nearly independent of primary energy in He, O2, and N2.

Measurements of Secondary‐Electron Spectra Produced by Electron Impact Ionization of a Number of Simple Gases

Tables of secondary-electron-production cross sections

Available data on the electron transport properties and electron swarm coefficients are discussed for the following electronegative gases: SF6, CF4, C2F6, C3F8, C4F10, CCl2F2, O2, air, H2O, CO2, F2, NF3, Cl2, Br2, I2, N2O, NO, HCl, NH3. Graphical presentations comparing measured and calculated data are given for the electron drift velocity, the ratio of diffusion to mobility, the electron attachment and ionization coefficients, and the electron growth constant as functions of E/N, the reduced field strength, for each gas. Graphs of the detachment and excitation coefficients are presented where these data are available. Data originally reported in terms of rate coefficients as functions of mean electron energy are graphically presented in that form. Recommendations concerning reliability are made.

An Annotated Compilation and Appraisal of Electron Swarm Data in Electronegative Gases

The mobility of ${\mathrm{He}}^{+}$ ions in helium gas was measured, the result being 10.40\ifmmode\pm\else\textpm\fi{}0.10 (${\mathrm{cm}}^{2}$/V-sec). The ${\mathrm{He}}^{+}$ ions were observed to react with the helium gas, the attachment frequency being [1.08\ifmmode\pm\else\textpm\fi{}0.05]\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}31}$ ${n}^{2}(invsec)$, where $n$ is the gas density in atoms/${\mathrm{cm}}^{3}$. This value of the attachment frequency is roughly compatible with the theoretical estimate of Bates and with the mass-spectrometric measurement of Phelps and Brown for the rate of the three-body attachment reaction producing ${\mathrm{He}}_{2}^{+}$. The mobility of the production, ${\mathrm{He}}_{2}^{+}$, was found to be 16.70\ifmmode\pm\else\textpm\fi{}0.17. This mobility is compatible with recent ambipolar diffusion coefficient measurements on cold afterglows, where the identification of the ion is confirmed by the spectroscopic observations of Kerr. This mobility is inconsistent with the widely quoted value of Biondi and Chanin and with the theoretical analyses of Geltman and Dalgarno. Mobility determinations were also made on another ion, which is possibly what Biondi and Chanin called ${\mathrm{He}}_{2}^{+}$. The actual identity is unknown, the ion possibly being ${\mathrm{He}}^{2+}$, possibly a contaminant.

Mobilities and Reaction Rates of Ions in Helium

Optical detection of the ground state hyperfine transition has been reported for sodium vapor and for cesium vapor. The collisional narrowing technique suggested by Dicke was used to reduce the Doppler width, Results are reported for Rb/sup 87/ vapor using a different optical pumping method. Absorption lines narrower, by a factor 300, than the normal Doppler width were achieved. The experimental arrangement is described. (W.D.M.)

E. C. Beaty

Papers

Measurements of Secondary‐Electron Spectra Produced by Electron Impact Ionization of a Number of Simple Gases

Tables of secondary-electron-production cross sections

An Annotated Compilation and Appraisal of Electron Swarm Data in Electronegative Gases

Mobilities and Reaction Rates of Ions in Helium

Optical Detection of Narrow Rb 87 Hyperfine Absorption Lines