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A collisional-radiative SF6 arc plasma model using Boltzmann analysis
Abstract
In order to investigate an SF<sub>6</sub> circuit breaker arc
under nonequilibrium conditions, a complete self-consistent kinetic
model has been set up. The number of chemical reactions equals 87,
involving 35 different species of the SF<sub>6</sub> dissociation
products and their ionized and excited states. The collisional-radiative
(CR) model determines the plasma composition and the temperature
simultaneously in one point. Additionally, the Boltzmann equation is
solved to determine the electron impact parameters. Results for a
free-recovering SF<sub>6</sub> arc as well as the SF<sub>6</sub> plasma
exposed to electric fields are presented
... the reaction rates of charged lower fluorine sulfides using collision cross-section parameters [42] or rate constant estimation equations [43]. ...
The compositions of SF6 arc plasma are contaminated by Cu vapor through electrode erosion and thus affect the performance of the high-voltage SF6 circuit breaker. But the essential data for chemical kinetic models to study the non-equilibrium compositions of SF6/Cu mixtures, namely the decomposition mechanism of SF6/Cu mixtures, is still not clear. Besides, SF6 decomposition products can be used to diagnose insulation faults of GIS and to evaluate the electric life of the SF6 circuit breaker, but the uncertainty of the decomposition mechanism of SF6/Cu mixtures hinders the application of the analysis method of SF6 decomposition products. Therefore, this work is devoted to investigating the decomposition mechanism of SF6/Cu mixtures by means of density functional theory in conjunction with 6-311G(d,p) basis set (for S and F atoms) and Lanl2DZ basis set (for the Cu atom). The optimized molecular structures, harmonic vibrational frequencies and energetic information of reactants, intermediate products (IM), transition states (TS) and products are thoroughly studied. And the complete decomposition pathways of SF6/Cu mixtures involving 15 reactions are derived. Detailed potential energy surfaces of SF6 + Cu decomposition reactions are also depicted as a result. Among all the decomposition pathways, the favorable decomposition reactions of SF6 + Cu mixtures are found: reaction R1 contributes more than reaction R2 in the decomposition of SF6 + Cu mixtures due to its lower energy released; reaction R3 is dominant in the decomposition of SF5 + Cu other than multi-step reactions; the chemical processes of SF4 + Cu → IMx → TSy (where x stands for 9, 10 and 13, and y denotes 7, 8 and 9) may play the same role in SF4 + Cu decomposition, but the reaction rate of R6 is higher than other reactions; reaction R9 and R11 are relative favorable among SF3 + Cu decomposition reactions; reaction R13 is dominant in the decomposition of SF2 + Cu because of its high potential well. This work hopes to outline a theoretical basis to investigate the non-equilibrium compositions of SF6/Cu arc plasma and the SF6 decomposition products analysis method.
This paper has for objectives to present the radiative and the transport
properties for people beginning in thermal plasmas. The first section will briefly recall the equations defined in numerical models applied to thermal plasmas; the second section will particularly deal with the estimation of radiative losses; the third part will quickly present the thermodynamics properties; and the last part will concern the transport coefficients (thermal conductivity, viscosity and electrical conductivity of the gas or mixtures of gases). We shall conclude the paper with a discussion about the validity of these results the lack of data for some specific applications, and some perspectives concerning these properties for non-equilibrium thermal plasmas.
In this paper, the solutions of three models of reaction kinetics in HV circuit breakers with SF6 after current zero are presented and compared. One model has been proposed by Bartlová, the co-author of this paper, the other two models under comparison have been taken over from the literature. In all the three models a constant pressure p(t) = 4 atm and the same dependence of temperature on time T(t) are assumed. For the description of the relation between equilibrium and kinetic composition in a system, the concept of asymptotic composition is introduced. A comparison of the composition and enthalpy of the products of SF6 dissociation and ionization for the given pressure and T(t) is made. General conclusions have been derived from the comparison.
Five necessary conditions for the so-called formal correctness of solutions of kinetic equations are formulated, which form a mathematical model of the reaction kinetics in HV circuit breakers after current zero for a given time-dependence of temperature and a given time-dependence of pressure or volume. The conditions are based on the mass action law, knowledge obtained from mathematical analysis of a system of ordinary differential equations, the principles of numerical analysis and the equilibrium-state principle of thermodynamics. Concrete solutions of kinetic equations are given and analysed for the products of SF6 dissociation and ionization. Two models are considered. In one model, the temperature drops from 10 000 to 2500 K, in the other it drops from 12 000 K to room temperature. A comparison of the time-dependent composition with the equilibrium composition is offered for both models.
An analysis of six different definitions of the rate of reaction is made and it is shown that some of the definitions are not consistent with the mass action law. Kinetic equations are derived whose solution is the time dependence of the composition of an arbitrary closed gaseous system in an ideal state for a given time dependence of temperature on the assumption that either the time dependence of pressure in or the time dependence of the volume of is given. Results are given of the computation of composition of a system of SF6 dissociation and ionization products at a temperature drop from 12 000 K to room temperature and a comparison is made of the time-dependent composition with equilibrium composition for pressures of 0.1, 0.5, 1 and 2 MPa.
A sustained current conduction in the breaking chamber after a current interruption has been observed. This current, which we named 'Post-recovery (PR) current', is in phase with the applied voltage and its value ranges from several milliamps up to several amps. The present study shows that the probable origin of the PR current is an ionic conduction of SF6 between the contacts. The estimated temperature of the conducting gas is about approximately 2000 K. The evolution of the temperature is in good accordance with a computational model based on the resolution of two-dimensional Navier-Stokes equations.
Configuration-interaction wave functions are constructed for the lowest 11 atomic target states of neutral fluorine. These wave functions are used to calculate target-state energies and absorption oscillator strengths for the dipole-allowed transitions. In general, a good agreement is found between the length and velocity forms of [ital f] values. However, [ital f] values for some transitions show significant discrepancies between these two forms. All these target states are retained in the [ital R]-matrix basis function and the ([ital N]+1)-electron collision wave functions are expanded in terms of these basis functions. The calculations are performed for the electron-impact excitation collision strengths for all transitions between these states using the [ital R]-matrix method. In the low-partial-wave region (total angular momentum [ital L][le]12) the full exchange [ital R]-matrix method is employed while a no-exchange [ital R]-matrix method is used for the calculations in the partial-wave region with 13[le][ital L][le]40. The effect of this procedure is most evident in the case of dipole-forbidden transitions for which collision strengths increase by about 10--60 % due to the contribution from higher partial waves. Beyond this value of the total angular momentum, the Burgess sum rule is applied to determine the higher partial-wave contribution to the total collision strengths for dipole-allowed transitions. The collision strengths are obtained for a wide range of incident electron energy from the first excitation threshold to 3.0 Ry. The calculations are performed in the [ital LS]-coupling scheme.
A kinetics model has been developed to study the chemical composition of a decaying SF6 arc plasma in the presence of impurities such as copper, carbon and water, proceeding from electrode and nozzle erosion or desorption in real SF6 circuit-breakers. The model is based on the following main assumptions: the plasma is in thermal equilibrium (only one temperature for all the species); the plasma is homogeneous; the pressure remains constant during the decay; the transient temperature evolution is previously imposed. Experimental gas analysis by chromatography, after arcing in a circuit-breaker has confirmed the main results of the calculation: proportion of SOF2 is much more important than that of SO2F2 and very low formation of S2F10 molecules.
We have calculated ..cap alpha.. and eta, the ionization and attachment coefficients, and (E/N) *, the limiting breakdown electric-field--to--gas-density ratio, in SF/sub 6/ and SF/sub 6/ mixtures by numerically solving the Boltzmann equation for the electron energy distribution. The calculations require a knowledge of several electron collision cross sections. Published momentum transfer and ionization cross sections for SF/sub 6/ were used. We measured various attachment cross sections for SF/sub 6/ using electron-beam techniques with mass spectrometric ion detection. We determined a total cross section for electronic excitation of SF/sub 6/ by comparing the predicted values of ..cap alpha.., eta, and (E/N) * with our measured values obtained from spatial current growth experiments in SF/sub 6/ in uniform fields over an extended range of E/N. With this self-consistent set of SF/sub 6/ cross sections, together with published He and N/sub 2/ cross sections, it was then possible to predict the dielectric properties of SF/sub 6/-He and SF/sub 6/-N/sub 2/ mixtures. Published experimental values of ..cap alpha.. for the SF/sub 6/-He mixtures lie between the values of ..cap alpha.. calculated with and without ionization of SF/sub 6/ by excited He atoms. Published experimental values of (E/N) * agree with our calculations to within 5% in both the SF/sub 6/-He and the SF/sub 6/-N/sub 2/ mixtures.
Self-consistent dissociative attachment and vibrational excitation cross sections for F2 have been calculated using Herzenberg’s theory of resonant electron scattering. It has been found that the observed electron–F2 attachment data can be explained by a low energy shape resonance. Potential parameters for the 2Σ+u negative ion were varied in order to fit predicted attachment cross sections to measured rate constant data. The best fit was obtained for a negative ion curve which crosses the F2 ground state in the vicinity of the equilibrium internuclear separation, in good agreement with an abinitio calculation for this state. The associated total vibrational cross section has a peak of about 2.0×10−16 cm2 at an incident electron energy of 0.45 eV. A strong dependence of attachment rate on F2 vibrational state is predicted.
An analytic atomic independent particle model potential adjusted to experimental single-particle energy levels is used to generate wave functions for the valence and excited states of sulfur. Using these wave functions in conjunction with the Born approximation and LS coupling, we calculate generalized oscillator strengths and integrated cross sections up to 5 keV for various electron impact excitations from the 1{ital s}²2{ital s}²2{ital p}â¶3{ital s}²3{ital p}â´(³{ital P}â) ground state.
The net emission coefficient of SF6-N2 mixtures was calculated for temperatures between 8000 and 24000 K and pressures between 1 and 8 bar. The calculation of the radiative transfer of the lines required a study of line broadening and was performed assuming that line overlapping had a negligible influence. The results show that the resonance lines, although they are strongly absorbed, make up a large part of the net radiation-about as much as the continuum. Also, the nitrogen lines are more strongly absorbed than the lines of sulphur or fluorine. At low temperatures the radiation of SF6 is stronger than that of nitrogen. When T>12000 K the net radiation of the mixture is not proportional to the net radiations of the gases owing to variations in emissivity and line broadening with temperature and composition of the mixture.
The rate of recombination and the characteristics of the afterglow line emission have been measured in magnetically confined plasmas of helium and hydrogen, with electron densities of the order of 1013 cm-3 and degree of ionization initially of the order of 50%. Electron densities and temperatures are deduced from absolute intensity measurements of spectrum line intensities originating from highly excited states, in good agreement with those obtained from microwave phase shift and plasma conductivity measurements. The results are explained in terms of an electron-electron-ion three-body recombination process. The recombination coefficient for this process is calculated as a function of electron temperature and density.
Radiative attachment coefficients for the process A+e-->A-+hv are investigated in the temperature range 10--104 K using a number of experimental and theoretical sets of photodetachment cross sections. The behaviour of the rate coefficients obtained using different sets of data resembles with that of the previous investigations. A discussion for their reliability is also given.
Thus, while the foregoing makes it clear that Koehler's syn thesis of planar precipitates using centers of dilatation may be meaningful, the differences he noted between the displacements associated with precipitates and dislocation loops arose simply because he constructed his loops from force dipoles rather than displacement dipoles. The aim of the present note is to make clear the distinction between the two entities. Full use of the tensor Green's function as a basic solution for the elastic fields of crystalline defects can only be made when this distinction is appreciated.
The recent measurement of the transition probability for the double-quantum detachment of an electron from I- has prompted a new theoretical study of this problem. A central-field model for bound and free states is used, in which a parameter is adjusted in the potential to yield the observed binding energies of the negative ions. An implicit-sum method, requiring the solution of inhomogeneous radial equations, is used to evaluate the sums over intermediate states. The results for I- lie almost within the experimental uncertainty. The cross sections for single-quantum photodetachment and electron elastic scattering (from the neutral atom) are also given for the ions studied: C-, O-, F-, Si-, S-, Cl-, Br-, I-.
This comprehensive five-volume work demonstrates the applicability of knowledge of atomic collision processes to pure and applied physics and chemistry. It contains up-to-date information about recent advances in the field and discusses future directions for research.
Time-dependent fluorescence measurements were made on Ar-F2, Kr-F2, and Ar-Kr-F2 mixtures excited by a short-pulse, low-current electron beam excitation in pressure ranges appropriate for rare-gas-halide lasers. A kinetic model was assembled that correctly analyzes integrated intensities and time dependences of the various emission bands of ArF*, Ar2F*, KrF*, and Kr2F*. We present the structure of the model and several revised rate coefficients obtained from it. The model also fits other published experimental data and agrees well with KrF laser pulse shapes and efficiencies. Cross sections for electron-impact dissociative excitation of F2, which were obtained from analysis of published data, are also presented.
Particle densities are determined for a decaying axially blown SF6 are between current zero and brekdown, some 100 μs later. During the time of interest, primarily only atoms, diatomic molecules
and ions can be built up by reactions. Therefore, in a first approach equilibrium densities are derived for SF6 which has decomposed into its considemic and diatomic components. In a second approach reaction kinetics are considered.
It turns out that the development of densities occurs in two steps. During the first approx. 100 μs there is a strong deviation
from equilibrium. Afterwards the most abundant particles remain near their partial, diatomic equilibrium values. Near breakdown
the degree of ionization is of the order of 1013 cm−3 with the most abundant ions S
2
+
and F−. This density is sufficient to distort the applied electric field. Future theories of breakdown in hot gases must take into
account this principal difference as compared with the conditions in cold gases.
Swarm parameters of electrons have been calculated for fluorine by a Monte Carlo simulation and the Boltzmann equation method for the first time. Values of these parameters have been obtained for ratios of the electric field to the gas number density E/N from 100 to 3000 Td (E/p 0 =35∼1000 V/cm Torr). Available experimental and theoretical cross sections were used for the calculations.
We have calculated α and η, the ionization and attachment coefficients, and (E/N) *, the limiting breakdown electric‐field–to–gas‐density ratio, in SF 6 and SF 6 mixtures by numerically solving the Boltzmann equation for the electron energy distribution. The calculations require a knowledge of several electron collision cross sections. Published momentum transfer and ionization cross sections for SF 6 were used. We measured various attachment cross sections for SF 6 using electron‐beam techniques with mass spectrometric ion detection. We determined a total cross section for electronic excitation of SF 6 by comparing the predicted values of α, η, and (E/N) * with our measured values obtained from spatial current growth experiments in SF 6 in uniform fields over an extended range of E/N. With this self‐consistent set of SF 6 cross sections, together with published He and N 2 cross sections, it was then possible to predict the dielectric properties of SF 6 ‐He and SF 6 ‐N 2 mixtures. Published experimental values of α for the SF 6 ‐He mixtures lie between the values of α calculated with and without ionization of SF 6 by excited He atoms. Published experimental values of (E/N) * agree with our calculations to within 5% in both the SF 6 ‐He and the SF 6 ‐N 2 mixtures.
An improved set of electron‐collision cross sections is derived for SF 6 and used to calculate transport, ionization, attachment, and dissociation coefficients for pure SF 6 and mixtures of SF 6 with N 2 , O 2 , and Ne. The SF 6 cross sections differ from previously published sets primarily at very low and high electron energies. At energies below 0.03 eV the attachment cross section is adjusted to fit recent electron swarm experiments, while the elastic momentum transfer cross section is increased to the theoretical limit. At high energies an allowance is made for the excitation of highly excited levels as observed in electron beam experiments. The cross‐section sets used for the admixed gases have previously been published. Electron kinetic energy distributions computed from numerical solutions of the electron‐transport (Boltzmann) equation using the two‐term, spherical harmonic expansion approximation were used to obtain electron‐transport and reaction coefficients as functions of E/N and the fractional concentration of SF 6 . Here E is the electric field strength and N is the gas number density. Attachment rate data for low concentrations of SF 6 in N 2 are used to test the attachment cross sections. Particular attention is given to the calculation of transport and reaction coefficients at the critical E/N=(E/N) c at which the ionization and attachment rates are equal.
ELENDIF calculates the time evolution of the electron energy distribution function in a mixture of partially ionized gases with or without an applied electric field. The code can treat inelastic and superelastic processes, electron-electron and electron-ion collisions, photon-electron (free-free) processes, attachment and recombination, ionization including a distribution of secondary electrons, and an external source of electrons (e.g. an electron beam). The code also computes the mean electron energy, drift velocity, diffusion coefficient, rate coefficients and energy flow rates for the processes being included in the calculation.
The Born approximation is used to calculate cross sections for the ionization by electron and proton impact of all neutral atomic systems in the sequences boron to neon and aluminium to argon. Possible exchange between the incident and atomic electrons is approximately taken into account using the Ochkur approximation to the exchange amplitude. In the cases where experimental data exist for comparison there is agreement at high energies to within about a factor of 2, a discrepancy which may be partly explained by the simple approximation made to the true wave function of the ejected electron.
The rates of radiative capture by atomic systems is computed for the first four ionization stages of the abundant elements C, N, O, Ne, Mg, Si, S, and Ar. A simple prescription is given for calculating the rates for systems in higher ionization stages. Results for capture to atomic helium are also given. In the general case, recent calculations of photoionization cross sections have been used to compute capture rates to levels of the ground-state configuration of the recombined species. Captures to other levels of the valence shell and to the higher shells are evaluated using hydrogenic formulae but with a correction factor which takes into account the nonhydrogenic nature of these states. This correction factor is due to the incomplete shielding by the inner electrons and represents essentially an effective charge for the recombining ion; it is determined semiempirically from an appropriate weighting of values derived from the observed level structure for each species. In some cases, for the capture to neutral atomic systems, its application increases the resulting computed recombination rate by a significant amount (about 50%). Computed recombination rates are tabulated for the four ionization stages at an electron temperature of 10,000 K and for the first stage at 100 K. A convenient procedure is outlined for evaluating the rates at other temperatures in the general neighborhood of these values.
Summary from only given. High efficiency electrical light sources used in lighting applications are based on electrical discharges in plasmas. The systematic search for improved lighting plasmas increasingly relies on plasma discharge modeling with computers and requires better and more comprehensive knowledge of basic atomic data such as radiative transition probabilities and collision cross sections. NIST has ongoing research programs aimed at the study of thermal equilibrium plasmas such as high pressure electric arcs and non-equilibrium plasmas in radio-frequency discharges and high current hollow cathode lamps. In emission experiments we have measured branching fractions and determined absolute transition probabilities for spectral lines in Ne I, Ne II, F I, O I and O II. In case of the Ne measurements the line radiation emitted by a high current hollow cathode lamp was analyzed with a 2 m monochromator. In addition, the spectra of Ne I and Ne II were measured with a UV Fourier transform spectrometer at very high spectral resolution. The line intensities were subsequently calibrated to absolute radiances. Where complete sets of transitions from an upper level could be observed, recent lifetime data for these levels were used to determine absolute transition probabilities. The accuracy of our branching fraction data is 5% for the stronger lines
Monte Carlo simulation and Boltzmann equation solutions have been used to study the electron kinetics. All electronic excitation of SF6 is assumed to be dissociative in analogy with the known product channels in ionization and multiphoton dissociation. The electric-field-to-gas-density ratios are high (E/n ¿ 1000 Td, where 1 Td (Townsend) = 1 à 10-17 V . cm2) in low-pressure (p < 0.3 torr) radiofrequency (RF) discharges. At these high E/n values, the electron energy relaxation time is much shorter than the 74-ns period at 13.56 MHz. Furthermore, the time scale of the chemical kinetics is much longer than the period of the applied RF voltage. Therefore the electron energy distribution can "track" the time-varying electric field, and time- and space-averaged rate coefficients can be used in chemical kinetics models. A rate equation model has been used to study the chemical kinetic processes. Electron-impact dissociation and ionization are the dominant sources of chemically active species. An electron density of 1 à 108 cm-3 is estimated from the known average values of E/n and the discharge input power. Two limiting cases are studied for the positive and negative ion diffusion losses: a) trapped negative ions and positive ion loss at the ambipolar diffusion rate; and b) positive and negative ion losses at the free diffusion rates. Neutral particle diffusion losses are estimated by using an effective diffusion length which takes surface reflection into account and increases as the surface reflection probability increases.
Determination of the thermal inertia time constant of an SF
- G J Cliteur
- M Ishikawa
- H Takahashi
- K Suzuki
- I Ohshima
G. J. Cliteur, M. Ishikawa, H. Takahashi, K. Suzuki, and I. Ohshima, " Determination of the thermal inertia time constant of an SF 6 arc by measurement and theory, " in Proc. 11th Int. Conf. on Gas Discharges and Appl., 1995, vol. 1, pp. 22–25.
Applied Atomic Collision Physics
- P J Chantry
Kinetic study of a decaying SF
- A Gleizes
- E Borge
- A M Casanovas
- B Belmadani