A theory is presented for the development of the first streamer when a positive voltage is abruptly applied to a point in air at atmospheric pressure. The continuity equations for electrons, positive ions and negative ions, including the effects of ionization, attachment, recombination, electron diffusion, and photoionization, are solved simultaneously with Poisson's equation. With an applied voltage of 20 kV across a 50 mm gap, the streamer does not reach the cathode. An intense electric field front propagates away from the point into the gap to a distance of 35 mm in 200 ns. During the next 7.5 µs the streamer only moves a further 2 mm into the gap, and the electric field at the head of the streamer collapses. Finally, only positive space charge remains which moves away from the point, allowing the field near the point to recover after ∼10 µs; free electrons can thus give rise to a secondary discharge near the anode. The electric field distribution is shown to be quite different from that found previously for SF 6 in that the electric field in the column of the streamer is generally only a fraction of the critical field for which ionization equals attachment. Streamers for a given applied voltage have a far greater range in air than in SF 6. The results presented for air also apply to flue gas mixtures, since the important material properties of both gases are very similar.

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Abstract. For arcs at atmospheric pressure which have cathodes that are thermionic emitters, it is possible to calculate the major properties of the arc and the electrodes as a function of current, by accounting for electrode shape and the heat transfer processes occurring at the surface of the electrodes. Such processes occur due to eleclron and ion emission and absorption and also from radiation emission and absorption. Electrical resistance of the plasma near the electrodes is calculated either by laking account of ambipolar diffusion or simply using the local plasma value, with mesh sizes sufficiently large to account for ambipolar diffusion. Derived temperature profiles are in fair agreement with experiment. Results of electrode temperatures and arc melting effects, including such phenomena as the transition from globular to spray modes in arc welding, are also in good agreement with experiment. Prediction of properties for non-thermionic cathodes still constitute a major problem. Approximate calculations indicate that electrons at the surface of the non-thermionic cathodes may be produced by photo ionisation of neutral atoms rather than by field emission.

In this paper, we give a detailed review of recent work carried out on the numerical characterization of non-thermal gas discharge plasmas in air at atmospheric pressure. First, we briefly describe the theory of discharge development for dielectric barrier discharges, which is central to the production of non-equilibrium plasma, and we present a hydrodynamic model to approximate the evolution of charge densities. The model consists of the continuity equations for electrons, positive and negative ions coupled to Poisson's equation for the electric field. We then describe features of the finite element flux corrected transport algorithm, which has been developed to specifically aim for accuracy (no spurious diffusion or oscillations), efficiency (through the use of unstructured grids) and ease of extension to complex 3D geometries in the framework of the hydrodynamic model in gas discharges. We summarize the numerical work done by other authors who have applied different methods to various models and then we present highlights of our own work, which includes code validation, comparisons with existing results and modelling of radio frequency systems, dc discharges, secondary effects such as photoionization and plasma production in the presence of dielectrics. The extension of the code to 3D for more realistic simulations is demonstrated together with the adaptive meshing technique, which serves to achieve higher efficiency. Finally, we illustrate the versatility of our scheme by using it to simulate the transition from non-thermal to thermal discharges.We conclude that numerical modelling and, in particular, the extension to 3D can be used to shed new light on the processes involved with the production and control of atmospheric plasma, which plays an important role in a host of emerging technologies.

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A theoretical method of predicting properties of free burning arcs and their cathodes is presented in a unified treatment. The method combines a one-dimensional model of the non-equilibrium plasma sheath adjacent to the cathode and a two-dimensional model for the arc column and the solid cathode. Two internal boundaries divide the arc-cathode domain into an arc region, a sheath region and a cathode region. The internal boundary conditions are adjusted during the iteration procedure to satisfy the energy conservation and current continuity equations. The effective resistance of the cathode sheath region is obtained from the sheath calculation assuming charge transport using an ambipolar diffusion approximation. No assumptions are made as to the distributions of, current density and temperature at the cathode surface. The model accounts for cathode surface effects and assumes that the cathode is a thermionic emitter. Material functions such as the thermal and electrical conductivities of the arc plasma and cathode are required as input parameters. Predictions are made, for any given arc current and cathode configuration, of the temperature and current density distributions in the arc and the cathode. Information is also provided about sheath properties. The results from a calculation for 200 A arc burning in argon with a thoriated tungsten cathode are in good agreement with the experimental measurements of the arc column and cathode surface temperatures and the arc voltage.

A theory for the current and light pulses of positive glow corona from a point in air is presented; this phenomenon was first observed as an apparently continuous glow by Michael Faraday. Results are obtained, in concentric sphere geometry, for air at atmospheric pressure, by solving the continuity equations for electrons, positive ions, negative ions and metastable oxygen molecules, coupled with Poisson's equation. A series of `saw-toothed' current pulses of period about is predicted with a DC current level. Accompanying the current peaks are discrete pulses of light 30 ns wide. Successive `shells' of positive ions, from successive current pulses, carry 96% of the mean current. The mean current - voltage relationship has the classic square-law form. The seed electrons required for successive pulses are detached from negative ions by metastable oxygen molecules. Photo-ionization is crucial for the discharge at the anode and for the formation of negative ions throughout the gap. The pulse frequency varies with applied voltage and is found to be approximately proportional to the positive-ion mobility. The surface electric field at the central electrode remains close to Peek's onset field. The origin of onset streamers is explained and sub-microsecond voltage pulses are found to produce streamers. The results for concentric-cylinder electrodes are described briefly.