R Morrow

Streamer propagation in air

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 Poissons 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 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 ; 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 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 . The results presented for air also apply to flue gas mixtures, since the important material properties of both gases are very similar.

Theoretical analysis of removal of oxides of sulphur and nitrogen in pulsed operation of electrostatic precipitators

An investigation has been made of the various plasma chemistry reactions that occur in the corona discharge of an electrostatic precipitator operating in a typical flue gas. Calculations have been made of the rate coefficients for electron dissociation of the principal gaseous components, namely, nitrogen, oxygen and water vapor as functions of electric field. In addition, calculations have been made of the rates of ionisation and attachment and also the rates of excitation of the principal excited states. The calculations indicate that sulphur dioxide is removed principally by reactions with OH radicals to produce sulphuric acid, while nitrogen oxides are removed principally by reduction via the N radical to molecular nitrogen. However, for these reactions to occur, values of E/N of 70 Td or more are necessary, which is higher than the E/N of 30 Td at which electrical breakdown normally occurs; E is electric field strength and N is the gas number density. Approximate calculations indicate that, for an E/N of 100 Td, voltage pulses of width less than 1 /spl mu/s need to be applied to avoid breakdown. It is also shown that small quantities of nitrous oxide are produced and that the presence of water vapor has a significant effect on the plasma chemistry and increases the breakdown voltage. >

A simplified unified theory of arcs and their electrodes

A recently developed unified theory of arcs and their electrodes, with cathodes which are thermionic emitters, has been simplified so that there is a reduction in computation times by approximately a factor of 100. Electrode and arc regions are treated together and points at the surface of the electrodes are treated in a special way to account for electrode effects; no assumptions are made concerning the current density at the cathode surface. The theory is used to make predictions of arc and electrode temperatures and arc voltages for arcs in argon as a function of current in the range 50 - 400 A. The maximum temperatures of the arc and the cathode and also the current - voltage characteristics are in reasonable agreement with experimental results for cathodes with a included angle. For a cathode with a included angle, we predict a maximum in the temperature several millimetres from the tip of the electrode, in approximate agreement with experiment. Temperatures of the cathode tip are predicted to be much higher for tungsten cathodes than for thoriated tungsten cathodes and are in reasonable agreement with experimental results. Tungsten electrodes are hotter than thoriated tungsten electrodes, partly due to increased ion heating, but largely due to greater heat conduction from the arc to the electrode due to the arc plasma covering a greater area of the electrode surface for tungsten.

The discharge current induced by the motion of charged particles in time-dependent electric fields; Sato's equation extended

The formula derived by Nobuyasu Sato (1980 J. Phys. D: Appl. Phys. 13 L3-L6), for the current flowing in an external circuit due to the motion of charged particles in a gap is extended to include a time-dependent applied voltage. The effects of negative ions, and electron, positive ion and negative ion diffusion are also included. It is found that Satos original equation still describes the contribution of charged particle motion to the external circuit current. The total circuit current is determined by adding the displacement current that effectively flows across the gap to the current determined by Satos equation. Some comments are also made about the interpretation of Satos equation in three dimensions.

A one-dimensional theory for the electrode sheaths of electric arcs

A non-equilibrium one-dimensional model is proposed for the plasma sheaths near the electrodes of electric arcs where the cathode is a thermionic emitter. Three coupled equations are solved: (a) the charge continuity equation, which accounts for ambipolar diffusion, recombination and ionization, (b) a form of Ohms law relating the effective electrical conductivity with a local electric field and (c) the energy balance equation, accounting for thermal conduction, Ohmic heating, plasma radiation and the effects which occur at the electrode surface, i.e. thermionic cooling, ion heating, radiative heating from the plasma and radiative cooling by thermal emission. The three equations give distributions of temperature, electric field and charge density within the sheath. Results are given for the sheath at the thoriated-tungsten cathode and anode for a 200 A arc in argon. Calculations have also been made of sheath properties for various electrode materials to determine the critical current density sustainable by a cathode without cathode melting. Critical current densities for anode melting are less than for cathode melting because of the cooling effect at the cathode of thermionic emission. The authors find that the effect of ion heating tends to keep the cathode temperature near to the temperature for which the current density from thermionic emission equals the imposed current density.

Theory of positive corona in SF/sub 6/ due to a voltage impulse

A theoretical examination is made of the mechanism of corona formation for a positive point-plane gap in SF/sub 6/ at 100 kPa. The impulse voltage applied has a rise time of 15 ns and peak value of 200 kV. Seed electrons are released 1 ns after the start of the voltage rise. For a 0.5-cm diameter positive sphere located 6.5 cm from a negative plane, the calculated circuit current initially consists of subnanosecond corona onset pulses, and then the current steadily rises to a maximum, as the voltage reaches a maximum, followed by a rapid fall in current. During the current rise a streamer moves out into the gap along a 100- mu m channel, with the electric field in the streamer trail E>E*, where E* is the critical field where ionization equals attachment. The light output during the discharge is predicted to be a maximum at the anode with only a minor pulse of light at the streamer head, making it hard to detect. After the current maximum, recombination rapidly reduces the numbers of positive ions, negative ions, and electrons, but the net charge density remains constant and thus so does the electric field. The electric field is E approximately E* in the streamer trail, but has a sharp maximum, E>>E* at the head of the streamer trail. The origin of mid-gap precursors, observed when the streamer channel reilluminates after some 100 ns, is attributed to this field maximum in the remnant electric field. The evolution of positive ions, negative ions, and electrons is described by one-dimensional continuity equations, with the space-charge electric fields determined by the disk method. The effects of ionization, attachment, recombination, electron diffusion, and photoionization are all included. New numerical methods allow resolution of the streamer head and the anode fall region to be obtained with a 1- mu m mesh, while following the streamer propagation for approximately 2 cm. >

Two-dimensional simulation of streamers using the FE-FCT algorithm

The improved finite-element flux-corrected transport method (FE-FCT), developed by the authors, has been applied in its full two-dimensional form to the numerical solution of streamer development and propagation in air at atmospheric pressure. The numerical algorithm used employs the FE-FCT method for the solution of transport equations of charged species under the action of space-charge electric field, with the field obtained from the solution of Poissons equation in cylindrical co-ordinates. Results of two-dimensional simulations of cylindrically symmetric streamers in air between parallel plate electrodes are presented. The breakdown voltages predicted by the model for different gap lengths are in agreement with the experimental measurements, which demonstrates the validity of the model. Furthermore, the avalanche-to-streamer transition - as described in Raether H 1964 Electron avalanches and breakdown in gases (London: Butterworths) - and the formation of anode and cathode directed streamers are numerically observed.

The theory of short-gap breakdown of needle point-plane gaps in air using finite-difference and finite-element methods

Numerical results are presented for the formation of breakdown streamers which bridge a 1 mm gap between a positive 50 µm radius hyperboloid point and a plane, when a dc voltage is applied. The results show that, for such gaps, no streamers form at voltages lower than or equal to 2.5 kV and that streamers bridge the gap at higher voltages. The streamer speed and radial dimensions of the streamer are found to linearly increase with the applied voltage and this agrees with what is predicted by existing two-dimensional models. The electric field in the streamer channel behind the streamer head is initially found to be much lower than that for longer gaps and becomes comparable only later in the development of the streamer. The results are obtained using a pre-existing finite-difference code and a new finite-element code developed using a new finite-element flux-corrected transport (FE-FCT) method. The finite-element results are shown to be almost identical to the finite-difference results. The finite-element method, however, through the use of unstructured grids, reduces significantly the number of unknowns and makes the modelling of streamers and arbitrarily shaped electrodes in two dimensions a feasible task.

Prediction of gas tungsten arc welding properties in mixtures of argon and hydrogen

A theory of gas tungsten arc welding (GTAW) arcs that treats the tungsten electrode, the arc, and the workpiece as a unified system has been applied to make predictions in two dimensions of the temperature distributions in the arc, the tungsten cathode, and the workpiece, for any given arc current and gas mixture. Predictions of arc temperatures, radii, and voltages are compared for argon and mixtures of argon and hydrogen. It is found that arcs in gas mixtures containing hydrogen are more constricted and have a higher maximum temperature and arc voltage than arcs in pure argon. The addition of hydrogen also significantly increases the volume of molten material in the weld pool due to the higher thermal conductivity of argon-hydrogen mixtures at temperatures at which molecules of hydrogen dissociate. Predictions are also compared for workpieces of steel and aluminum. The volume of molten material is very much less for aluminum, despite its lower melting point, because of the higher thermal conductivity of aluminum. Predicted arc voltages as a function of current for a mixture of 10% hydrogen in argon are in good agreement with experimental results.

Space-charge effects on drift dominated electron and plasma motion

The electron and ion continuity equations and Poissons equation are solved for the motion of pulses of (i) electrons and (ii) plasma in an applied electric field of approximately 6 kV cm-1. For the cases considered in nitrogen at a temperature of 293K and at pressures of 12 kPa, where E/N approximately 2*10-15 V cm-2, and drift distances are a few cm, electron drift dominates over diffusion. The relative motion of electrons and ions in a plasma pulse have characteristic features very different from ambipolar diffusion motion characteristic of low fields and pressures. An electron pulse of radius approximately 0.5 cm and density approximately 1011 cm-3 spreads rapidly due to space-charge fields, regardless of whether a uniform electric field is applied. Space-charge effects enhance the electric field at the leading edge of an electron pulse in a uniform electric field. For an initially neutral plasma of density 5*106 cm-3 in a uniform electric field, electrons move independently of the ions. When the density is increased, and space charge is significant, the electron distributions have a characteristic steep trailing edge and an almost flat leading edge. At the highest densities considered of approximately 1011 cm-3 the electric field is reduced almost to zero at the centre of the plasma by space-charge effects.