Dielectric-barrier discharges (silent discharges) are used on a large industrial scale. They combine the advantages of non-equilibrium plasma properties with the ease of atmospheric-pressure operation. A prominent feature is the simple scalability from small laboratory reactors to large industrial installations with megawatt input powers. Efficient and cost-effective all-solid-state power supplies are available. The preferred frequency range lies between 1 kHz and 10 MHz, the preferred pressure range between 10 kPa and 500 kPa. Industrial applications include ozone generation, pollution control, surface treatment, high power CO2 lasers, ultraviolet excimer lamps, excimer based mercury-free fluorescent lamps, and flat large-area plasma displays. Depending on the application and the operating conditions the discharge can have pronounced filamentary structure or fairly diffuse appearance. History, discharge physics, and plasma chemistry of dielectric-barrier discharges and their applications are discussed in detail.

https://www3.nd.edu/~sst/teaching/AME60637/reading/2003_PCPP_Kogelschatz_dbd_review.pdf

Dielectric-barrier Discharges: Their History, Discharge Physics, and Industrial Applications

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

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

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

https://zenodo.org/record/1253854/files/article.pdf

A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges

We review the data and models describing the production of the electrons, termed secondary electrons, that initiate the secondary and subsequent feedback avalanches required for the growth of current during breakdown and for the maintenance of low-current, cold-cathode discharges in argon First we correlate measurements of the production of secondary electrons at metallic cathodes, ie the yields of electrons induced by Ar+ ions, fast Ar atoms, metastable atoms and vuv photons The yields of electrons per ion, fast atom and photon vary greatly with particle energy and surface condition Then models of electron, ion, fast atom, excited atom and photon transport and kinetics are fitted to electrical-breakdown and low-current, discharge-maintenance data to determine the contributions of various cathode-directed species to the secondary electron production Our model explains measured breakdown and low-current discharge voltages for Ar over a very wide range of electric field to gas density ratios E/n, ie 15 Td to 100 kTd We review corrections for nonequilibrium electron motion near the cathode that apply to our local-field model of these discharges Analytic expressions for the cross sections and reaction coefficients used by this and related models are summarized

https://iopscience.iop.org/article/10.1088/0963-0252/8/3/201/pdf

Cold-cathode discharges and breakdown in argon: surface and gas phase production of secondary electrons

As part of a systematic study of approximations commonly made in solutions of the Boltzmann equation for electrons in molecular gases, we have investigated the effects of anisotropic scattering on electron transport coefficients in ${\mathrm{N}}_{2}$ and have extended our study of the multiterm expansion technique to higher E/n. A critical survey of published data yields a set of differential and integral cross sections for electron energies from 0.003 to ${10}^{4}$ eV. For electric-field--to--gas-density ratios E/n between 10 and 500 Td (1 Td${=10}^{\mathrm{\ensuremath{-}}21}$ V ${\mathrm{m}}^{2}$), the changes in the commonly measured transport and reaction coefficients resulting from the introduction of anisotropic elastic and inelastic scattering, while keeping the elastic momentum-transfer cross section constant, are less than 1%.These calculations were made with use of the multiterm spherical-harmonic expansion solution of the Boltzmann equation. For 500lE/nl1500 Td the changes in scattering anisotropy cause changes in transport and reaction coefficients which increase with E/n to about 10%. The errors in drift velocity, mean energy, and the reaction coefficients resulting from the use of the two-term spherical-harmonic expansion rather than a six-term expansion are less than 3% at 1500 Td.However, the errors in the diffusion coefficients become large (g25%) at our highest E/n. The calculated transport coefficients are in generally good agreement with experiment for E/n less than 300 Td, but the differences increase at higher E/n. The importance of proper interpretation of ionization and excitation experiments at high E/n is illustrated by calculations which model either an exponential growth of density in time or an exponential growth with position. The calculated ionization coefficients are low compared to most experiments for E/n less than 200 Td. At E/ng600 Td the agreement is good for the spatial growth experiments, but the calculated values are below experiment from the temporal growth experiments. The calculated excitation coefficients are generally higher than experiment at low and high E/n but in agreement with experiment at E/n near 150 Td.

Anisotropic scattering of electrons by N2 and its effect on electron transport.

Graphical and tabulated data and the associated bibliography are presented for cross sections for elastic, excitation, and ionization collisions of N+, N+2, N, and N2 with N2 and for Ar+ and Ar with Ar for laboratory energies from 0.1 eV to 10 keV. Where appropriate, drift velocities and reaction or excitation coefficients are calculated from the cross sections and recommended for use in analyses of swarm experiments and electrical discharges. In the case of N+ in N2, cross sections for momentum transfer, charge transfer, electronic excitation, and electron production are recommended. Drift velocity calculations predict runaway for N+ in N2 for electric field to gas density ratios E/n greater than 4.3×103 Td, where 1 Td (townsend)=10−21 V m2. For N+2 in N2, the cross sections include those for N+ and N+3 formation, electronic excitation, and electron production. Drift velocities and average cross sections are calculated for E/n≥500 Td. In the case of N in N2, only cross sections for momentum transfer are ...

Cross Sections and Swarm Coefficients for Nitrogen Ions and Neutrals in N2 and Argon Ions and Neutrals in Ar for Energies from 0.1 eV to 10 keV

We suggest consistent sets of Ar++Ar and Ar+++Ar differential and integral cross sections for modeling ion scattering that take into account differential scattering data and the fact that symmetric charge transfer collisions are one aspect of elastic scattering collisions. These suggestions make possible a considerable improvement in the accuracy of future Monte Carlo calculations of the angular, energy, and temporal distributions of Ar+ and Ar++ ions passing through the electrode sheaths of low‐pressure, rf, and dc discharges in Ar. The cross sections necessary for a proper modeling of the energy dissipation in the gas and at the electrodes by fast neutral Ar atoms formed in symmetric‐charge‐transfer collisions of Ar+ and Ar++ with Ar are also reviewed.

The application of scattering cross sections to ion flux models in discharge sheaths

Calculations have been made of transport coefficients of electrons in gas mixtures for ratios CO2:N2:He of 1:1:8, 1:2:3, 1:7:30, and 1:0.25:3. New cross sections for CO2 derived from swarm experiments are used together with previously published cross sections for N2 and He. Curves are presented of the predicted electron drift velocity, transverse and longitudinal diffusion coefficients, and ionization and attachment coefficients for E/N values ranging from 10−18 to 1 × 10−15 V cm2; E is the electric field strength and N the gas number density. Examples are given of derived distribution functions and comparisons are made with a Maxwellian distribution function. The percentage of the input electrical power which excites vibrational processes coupled to the 001 upper laser level of CO2 is given as a function of E/N. The maximum efficiency from these calculations increases for increasing ratios of N2:CO2, because the proportion of energy used to excite the bending and stretching modes of CO2 is then reduced. ...

A. V. Phelps

Papers

Cold-cathode discharges and breakdown in argon: surface and gas phase production of secondary electrons

Anisotropic scattering of electrons by N2 and its effect on electron transport.

Cross Sections and Swarm Coefficients for Nitrogen Ions and Neutrals in N2 and Argon Ions and Neutrals in Ar for Energies from 0.1 eV to 10 keV

The application of scattering cross sections to ion flux models in discharge sheaths

Predicted electron transport coefficients and operating characteristics of CO2–N2–He laser mixtures