New Directions of Predictive Capability for Properties of Gas Discharges

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1 1 Doc New Directions of Predictive Capability for Properties of Gas Discharges John J Lowke CSIRO Materials Science and Engineering, PO Box 218, Lindfield, NSW 2070, Australia Study Group 212 July, Denver, USA

2 2 New Directions of Predictive Capability for Properties of Gas Discharges John J Lowke CSIRO Materials Science and Engineering, PO Box 218, Lindfield, NSW 2070, Australia Abstract In the past 50 years there have been enormous changes in the predictive capability for properties resulting from the use of gas discharges, e.g. properties from the use of electric arcs in arc welding. Fifty years ago heat transfer equations were solved using sophisticated and complex algebra to obtain solutions of arc profiles in terms of zero order Bessel functions assuming linear material functions. There were no real predictions, only the matching of experimental data using adjustable coefficients. Now it is possible, through the spectacular capabilities of computers, to make real predictions of actual weld profiles going from the basic atomic and molecular cross sections of the atoms of weld gases, through to calculate transport coefficients, and finally to solve conservation equations to predict weld profiles. Two quite new directions are now discussed. (1) Arc formation. Evidence will be presented that the theories giving the Townsend Breakdown Criterion and The Streamer Breakdown Criterion to form an arc do not fit at all with observations of the initiation of corona in air. Instead, evidence will be presented that breakdown in air results after the excitation of vibrational states of nitrogen which, due to their characteristic of being metastable, have a dominating influence on electron energy through their de-excitation on collisions with electrons, thus increasing electron energy. (2) Ion interaction with insulating surfaces. Ions accumulate on insulating surfaces, reducing the electric field on the side of the insulator subject to the incident ions, but increasing the electric field on the far side of the surface. Such effects can now be predicted, but are difficult to observe unless the increased fields produce ionization, possibly even Ball Lightning! 1. Introduction Old Achievements We don t really understand a scientific discipline unless we can make predictions as to future events within that discipline. An example of this top level of expertise is in astronomy, where predictions can be made of future eclipses of the sun to within a fraction of a second. There are two lesser levels of predictive capability. The second level is where predictions can be made, but not everyone believes them. Perhaps predictions of climate change! Methods of making theoretical predictions of weld shapes in Gas Metal Arc Welding are now being applied for metals other than steel and for weld gases for which there is little

3 3 experimental experience, indicating a shift from the second to the top stage of predictability. Then there is the most elementary stage of scientific predictability where comparisons are made of theoretical curves with experimental points but in reality no predictions are made at all. There is only curve fitting where theoretical parameters in an approximate theory are adjusted to give agreement with experimental results. In my professional life of 50 years I have seen two great changes in the science of the predictability of plasmas. The first is the change from the use of largely analytic and algebraic methods of making predictions to the use of numerical methods using computers. The arc energy balance equation (1) used to be solved in terms of Bessel functions. The energy balance equation for a cylindrical arc is 1 ( rk T) E 2 0, (1) r r r where Eq. (1) can be transformed into Bessel s equation, but only after making two transformations; k is the thermal conductivity and is the electrical conductivity, and r the radius and T the temperature [1]. Firstly the thermal conductivity k is eliminated by introducing a new function S, given by S = kdt, so that k T/ r became S/ r. Secondly, it must be assumed that is a linear function of S. Over the past two decades, with the spectacular development of computers, this whole approach has been completely transformed. Numerical solutions can now be obtained, in one, two, or three dimensions using a complete numerical representation of all material functions. The qualifications required of the scientists and engineers involved are completely different, the concerns now being the convergence of numerical methods of solution, numerical analysis and skills in computer programming. Examples of computer predictions are given in Figs 1 and 2. Fig. 1 shows a solution for a welding arc in 3 dimensions where the electrodes are of aluminum [2]. Fig. 1. Three dimensional prediction of properties of a welding arc and electrode melting with aluminum wire and electrodes [2].

4 Thermal Cond. kw/(cm K); Electrical Cond. S/cm; Specific Heat J/(gm K) Density gm/cc; Viscosity (dynes/cm 2 ) s 4 Fig. 2 Tungsten Inert Gas arcs in helium; theory and experiment. Fig. 2 shows a numerical solution for welding stainless steel, with a tungsten cathode, compared with a weld shape obtained from experiment. This case is for high sulfur stainless steel in which case surface tension effects reverse the normal convective flow in the weld pool so that such flow is downwards at the center of the weldpool, leading to a deeper than normal weld [3]. The second great change in the subject of Plasma Predictions of the last 50 years, is the utilization of an integrated hierarchy of three scientific disciplines. Top of this hierarchy is the ability to make useful predictions, for almost any application involving plasmas in Local Thermodynamic Equilibrium (LTE), examples being Figs 1 and 2. But at the basis Argon of Material this ability Functions; is a 1 bar second scientific discipline, namely the ability to calculate transport coefficients, as shown in Fig. 3 for argon Viscosity Electrical Conductivity Thermal Conductivity; Specific Heat Density Temperature; K 10-6 Fig. 3 Transport coefficients in argon at 1 bar.

5 Cross Section 5 In the last few years we have attained the capability of calculating such transport coefficients for any gas and any mixture of gases for any temperature range and any pressure, provided that the plasma is in local thermodynamic equilibrium [4]. All of these transport coefficients, for example of thermal conductivity and electrical conductivity, are necessary for the calculations of Figs 1 and 2. Finally, at the very basis of this tri-part hierarchy of disciplines are the atomic and molecular cross sections for the interaction of particles. Fig. 4 shows such cross sections for argon. 100 Argon Cross Sections 10 Elastic Inelastic Electron Energy Fig. 4 Electron atom cross sections for argon. The determination of basic data such as cross-sections for electron collisions of various types, as illustrated in Fig. 3 for argon, has proceeded both through experimental measurements and theoretical predictions [5]. The cross sections are determined at high energies usually by the analysis of the scattering of a mono-energetic beam of electrons with atoms or molecules, but different methods are needed for the different cross sections of ionization, electronic excitation or momentum transfer. The existence of such a hierarchy of an integrated treatment of predictability from basic atomic and physical properties, to transport coefficients and finally to detailed predictions has been developed rather more completely for plasmas than for solids or liquids. 2. New Directions (1) Detailed Molecular Processes Electrical Breakdown in Air Previous calculations, for example the predictions of properties of arc welding, usually assume that the plasma is in Local Thermodynamic Equilibrium. However, for the future, it is likely that more detail of the plasma chemistry will be required. I now discuss an old problem, that of the prediction of electrical breakdown in air. In my view both of the two existing criteria for electrical breakdown in air, namely the Townsend breakdown criterion [6], and also the Streamer breakdown criterion [7] are inadequate. Fig. 5 shows measured values for the onset electric field for corona, usually the precursor for breakdown, as a function of radius, for both wires and points. Also shown on the figures are calculated values of Q, which is the number of electrons in an avalanche resulting by ionization growth from a single electron in travelling away from the surface of such cylinders or points in the region where there is net ionization [8]. There are two aspects of these curves which are very significant for the two breakdown

6 Surface Field; kv/cm Surface Field; kv/cm 6 criteria. Firstly, the experimental results for the onset of corona for both negative voltages and positive voltages are the same, within a few percent. The Townsend criterion is based on the replacement of electrons at the cathode, which would be expected to be markedly different for positive and negative corona. Secondly, it is seen from Fig. 5 that all of the curves are approximately fitted by a value of Q of about 10,000. In other words there is an onset of corona when only 10,000 electrons have been developed from an initiating electron. The streamer criterion is based on space charge fields producing ionization to produce new plasma to bridge the breakdown gap, but the order of 10 8 electrons are required for there to be a significant increase in the electric field due to space charges. To explain these issues, it is proposed that the marked increase in ionization observed at corona onset occurs before the Townsend and streamer stages of breakdown development and is a separate but very significant stage of the breakdown process.. This increased ionization is due to the excitation of the vibrational states of nitrogen molecules. These states are metastable, have a lifetime of about 1 milli-second in air at atmospheric pressure [9], which is long compared with breakdown phenomena which occur in less than a micro second. Electrons excited by the electric field can excite these states successively into higher and higher levels; up to 60 quantum levels are possible extending to energy levels of 9.7 V [10]; see Fig. 6. These excited states of nitrogen are in approximate Boltzmann equilibrium, not with the thermal temperature of the air, which is ~ 300 K, but with the temperature of the electrons, which is at an average energy of about 1.8 V, or a temperature of about 20,000 K [11]. At equilibrium, not only are electrons losing energy in collisions which excite these vibrational states, but, according to the principle of detailed balance there are an equal number of collisions whereby vibrational states are de-excited with collisions of low energy electrons thus increasing the electron energy. Calculations have been made to account for such collisions using the code ELENDIF [12] and it is found that for vibrational states excited to 20,000 K, the number of electrons at ionization energies and also the ionization coefficients are increased by 4 orders of magnitude. Fig 6, shows calculations of the electron energy distribution function at E/N = 20 Td., which corresponds to an electric field of 5 kv/cm at 1 bar, and also calculations of ionization coefficients as a function of the electric field for air at 1 bar [13]. (a) (b) Spherical Geometry Numerical Q = 10 8 Q = 10 6 Q = 10 4 Q = 10 3 Experiment Peek Waters Schumann Experiment Numerical Q = 10 8 Peek Bandel - Q = 10 6 Bandel + Q = 10 4 Kip Q = 10 3 Nasser Radius; cm Radius; cm Fig. 5 Onset electric fields for corona for (a) wires and (b) points.

7 Distribution Function cm 2 7 Fig. 6 Energy levels of molecular nitrogen. (a) (b) No Metastable Excitation E/N = 20 Td. With Metastable Excitation; 20,000 K Energy; ev With Metastable Excitation; 20000K No Metastable Excitation E/N; Td Fig. 7 De-excitation of metastable states by electrons increases (a) the number of electrons at high energy and (b) the ionization coefficients for air at 1 bar. 2. New Directions: (2) Motion of Ions on Insulators Ball Lightning! A further new direction of computational physics as applied to plasmas is the prediction of properties of atmospheric ions interacting with insulators. Predictions of such interactions are difficult to confirm as they are difficult to see! However, occasionally such ion flow produces electrostatic charging which results in sparks or even ignition that can cause explosive damage, for example if it occurs at the fuel tank of aircraft flying through thunderstorms. There have been observations of Ball Lightning forming inside of the cockpits of aircraft, particularly during thunderstorms, when there is a likelihood of a high concentration of ions in the atmosphere. From calculations of effects of the accumulation of ions at an insulating window, for example at the cockpit of an aircraft or the window of a house, it is proposed [14] that the resultant high fields produced on the other side of the window can cause an electric discharge with properties similar to Ball Lightning [15]. Fig. 8 shows the calculated effect of a steady stream of negative ions of density ~ /cc on a thin glass window. The ions accumulate at the surface of the glass producing a field which opposes the further accumulation of ions on the surface. But on the other side of the glass, the accumulation of ions acts to intensify the electric field, approximately doubling the ambient field.

8 8 Fig. 8 Effects of a flow of ions on insulators. Electric fields of the order of 5 kv/cm are sufficient to sustain an electric discharge [16,17]. Calculations have been made to determine the character of any discharge which might form on the far side of the window of Fig. 8. Solutions have been obtained of the time dependent equations for the conservation of electrons, positive ions and negative ions, together with Poisson s equation to account for effects of space charge distortion of the electric field. Conventional values have been taken for the mobilities of charges as a function of the electric field, together with ionization and attachment coefficients [18]. However, the ionization coefficients have been increased to equal those of the attachment coefficients at ~ 5 kv/cm so that discharges can be sustained at these electric fields, as is known from experiment. Once a discharge is started it is found that charges of opposite sign to those on the outside of the window are attracted to the surface of the window, reducing the electric field near the window to be almost zero. The ball of plasma, now having a slight negative charge, then moves away from the glass window, pulsing on a microsecond time scale with properties similar to corona [19]. The calculated properties of this discharge is similar to that of Ball Lightning seen inside of aeroplanes and houses [14]. (a) (b) Fig. 9 Calculate (a) negative ion and (b) positive ion densities at an instant of the calculated pulsating discharge.

9 9 Fig. 10 Calculated electric fields corresponding to Fig. 9. It has not been possible to proceed in the calculations beyond the third plasma discharge pulse, due to effects such as numerical diffusion, as only an explicit numerical scheme was used. Figs. 9 and 10 gives the calculated densities of the positive and negative ions, and also the electric field at an instant near the end of the second pulse. These negative and positive ion densities are almost identical, except that there is a surface charge of negative ions on the outside of the window and a layer of approximately equal positive charge on the inside of the window. The electric field near the window is almost zero. Although there is also a very low field region within the ball, the electric fields at the edge of the ball are high, which would give, through enhanced ionization, an edge to the ball. The details of the shape and fields within the ball are continually changing there being no significance to the particular shape shown in the figure. 4. Summary. Over the past 50 years there has been a remarkable increase in the predictive power of properties of LTE plasmas, for example for the properties of welding arcs. Furthermore there has been a development unifying the sciences of (1) determining basic cross sections and atomic and molecular data (2) transport theory whereby transport coefficients, including diffusion coefficients are derived from this data to (3) the prediction of actual properties, such as weld profiles, that are becoming possible for any metal or weld gas mixture. Possible future developments are (1) the inclusion of detailed plasma chemistry of molecular states, for example to improve predictions of electrical breakdown and (2) the inclusion of properties of ion flow interacting with insulators, for example, to explain Ball Lightning. References [1] Maecker H 1959 On the characteristics of cylindrical arcs (in german) Zeitschrift fur Physik 157, 1-29, eq [2] Murphy A B 2012 submitted to 19 th Intern. Conf. Gas Discharges and their applications, Beijing. [3] Tanaka M and Lowke J J 2007 Predictions of weld pool shapes using plasma physics, J. Phys. D: Appl. Phys. 40, R1-R23.

10 [4] Murphy A B and Arundell C J 1994 Transport coefficients of argon, nitrogen, oxygen, argon-nitrogen and argon-oxygen plasmas Plasma Chem. Plasma Process. 14, [5] Phelps A V and Petrovic Z L 1999 Cold cathode discharges and breakdown in argon, Plasma Sources Sci. Technol. 8, R21-R44. [6] Llewellyn-Jones F 1966 Ionization and breakdown in gases, Methuen [7] Raether H 1964 Electron avalanches and breakdown in gases Butterworths [8] Lowke J J and D Alessandro F 2003 Onset corona fields and electrical breakdown criteria J. Phys. D:Appl. Phys. 36, [9] Millikan R C and White D R 1963 Systematics of vibrational relaxation, J. Chem. Phys. 39, [10] Lino da Silva M, Guerra V, Loureiro J and Sa P A 2008 Vibrational distributions in N 2 with an improved calculation of energy levels, Chemical Physics 348, [11] Capitelli M, Gorse C and Billing G D 1980 V-V pumping up in non-equilibrium nitrogen: effects on the dissociation rate Chem. Phys. 52, [12] Morgan W L and Penetrante B M 1990 ELENDIF a time dependent Boltzmann solver for partially ionized plasmas, Computer Physics Communications 58, [13] Lowke J J 2012 Toward a new theory of electrical breakdown in air, submitted to 19 th Intern. Conf. Gas Discharges and their applications, Beijing [14] Lowke J J, Smith D, Nelson K E, Crompton R W and Murphy A B 2012 The birth of Ball Lightning, submitted to J. Geophys. Res.; also 14 th Intern. Conf. Atmospheric Electricity, Aug 2011, Rio de Janiero, paper 117, pp [15] Stenhoff, M. (1999). Ball Lightning. An unsolved problem in atmospheric physics., Kluwer, London, U.K. [16] Phelps, C T and Griffiths R F (1976) Dependence of positive corona streamer propagation on air pressure and water vapor content, J. Appl. Phys. 47, 2929 [17] Feser, K. and R. C. Hughes (1988), Measurement of direct voltage by rod-rod gap, Electra 117, [18] Lowke J J 1992 Theory of electrical breakdown in air the role of metastable oxygen molecules J. Phys. D: Appl. Phys [19] Morrow, R. (1985), Theory of negative corona in oxygen, Phys. Rev. A 32, [20] Rakov V A and Uman M A 2003 Lightning Physics and Effects Cambridge UP, p111 10