New Method to Calculate Thermodynamic and Transport Properties of a Multi-Temperature Plasma: Application to N2 Plasma

Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently André et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N ₂ and N ₂ ⁺ partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species T_h , electrons T_e , and vibrational T _v temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio =T_e/T_h was varied between 1 and 2 as well as the ratio _v =T _v /T _h for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N ₂ are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N ⁺ . The effects of _v and _e on thermodynamic and transport properties of N ₂ are then discussed.     

Two-Temperature Transport Coefficients in Argon–Hydrogen Plasmas—I: Elastic Processes and Collision Integrals

The calculation of two-temperature transport coefficients in an argon–hydrogen plasma at atmospheric pressure is performed using a new theory of two-temperature transport properties recently presented. The latter takes into account the coupling between electrons and heavy species, coupling neglected in the already existing theories of Devoto and Bonnefoi. Transport coefficients are calculated at two-temperatures, the kinetic temperature of electrons T_e being different from that of heavy species T_h. This paper is divided into two parts. The first one is related to elastic processes and its aim is to compare the results obtained with this new theory for viscosity , translational thermal conductivities ^tr _e and ^tr _h and electrical conductivity with the previous results of Bonnefoi. The composition is calculated with the modified equilibrium constant of van de Sanden et al. and the most recent interaction potential are discussed. As it could be expected the electron translational thermal conductivity and the electrical conductivity calculated when taking into account or not the coupling between electrons and heavy species show non-negligible discrepancies. Besides this comparison, the results also show the drastic influence of the non-equilibrium parameter =T_e/T_h on the values of , , ^tr _e, and ^tr _h.     

Influence of the Excited States of Atomic Nitrogen N(<Superscript>2</Superscript>D), N(<Superscript>2</Superscript>P) and N(R) on the Transport Properties of Nitrogen. Part II: Nitrogen Plasma Properties

In this paper, the calculated values of the viscosity and thermal conductivity of nitrogen plasma are presented taking into account five (e, N, N⁺, N₂ and N₂⁺) or eight (e, N(⁴S), N(²P), N(²D), N(R), N⁺, N₂ and N₂⁺) species. The calculations are based on the supposition that the temperature dependent probability of occupation of the states is given by the Boltzmann factor. The domain for which the calculations are performed, is for p = 1 and 10 atm in the temperature range from 5,000 K to 15,000 K. Classical collision integrals are used in calculating the transport coefficients and we have introduced new averaged collision integrals where the weight associated at each interacting species pair is the probable collision frequency. The influence of the collision integral values and energy transfer between two different species is studied. These results are compared which those of published theoretical studies.     

Influence of the Excited States of Atomic Nitrogen N(<Superscript>2</Superscript>D) and N(<Superscript>2</Superscript>P) on the Transport Properties of Nitrogen. Part I: Atomic Nitrogen Properties

In this paper, calculated values of the viscosity and thermal conductivity of atomic nitrogen, taking into account three species (the ground and two excited states), are presented. The calculations, which assume that the temperature dependent probability of occupation of the states is given by the Boltzmann factor, are performed for atmospheric-pressure in the temperature range from 1,000 to 20,000 K. Six collision integrals are used in calculating the transport coefficients and we have introduced new averaged collision integrals where the weight associated at each interacting species pair is the probable collision frequency. The influence of the collision integral values and energy transfer between two different species is studied. These results are compared which those of published theoretical studies.     

Two-Temperature Transport Coefficients in Argon–Hydrogen Plasmas—II: Inelastic Processes and Influence of Composition

Recently, a two-temperature transport properties theory has been proposed that retains the coupling between electrons and heavy species in thermal plasmas where the kinetic temperature of electrons Te can be different from that of heavy species Th. This paper is devoted to the application of this approach to an argon–hydrogen mixture at atmospheric pressure, taking into account inelastic processes and considering chemical equilibrium. In this second part are studied: the development of a new method to calculate the reaction thermal conductivity (inelastic collisions) in a non-equilibrium (two-temperature) plasma taking into account the coupling between electrons and heavy species; the influence of the composition calculation methods comparing the modified equilibrium constant method used in part 1 to the stationary kinetic calculation one; the influence on the transport properties (, , ) of the composition calculation method and non-equilibrium parameter =T_e/T_h.The different plasma compositions obtained either through an equilibrium constant or a stationary kinetic method are first compared and, for example, for =1.6, a discontinuity at T_e=11,000 K and an ionization delay are observed in stationary kinetic calculation, relative to the equilibrium constant method. Electrical conductivity, viscosity as well as thermal conductivity, including the translational, internal and reactional contributions, are calculated up to 25,000 K. It is shown that the plasma composition has a strong influence on transport coefficients, inducing shifts or discontinuities in the curves of transport coefficients, depending on the chosen method of calculation.     

A New Modified Pseudoequilibrium Calculation to Determine the Composition of Hydrogen and Nitrogen Plasmas at Atmospheric Pressure

This paper proposes a modified pseudoequilibrium calculation, which gives almost the same results as those of kinetic calculations to determine the composition of hydrogen and nitrogen plasmas at atmospheric pressure. The computing time is two to three orders of magnitude faster than that of the kinetic calculations. First, according to experimental results, a relationship between the electron temperature T_e and the heavy species one T_h has been proposed. The ratio T_e/T_h varies as a function of the logarithm of the ratio n_e/n _e ^max , _e ^max being the electron density in the plasma core for which equilibrium is achieved _e ^max ~ 10 ²³ ). The kinetic calculations have been performed assuming the microreversibility where the backward kinetic rate coefficient k_b is calculated by k_d/k_b=K_x, where k_d is the direct kinetic coefficient and K_x the molar fraction equilibrium constant. When electrons are involved in both direct and backward reactions, k_d and K_x are expressed as functions of T_e . However, when the direct reaction involves electrons while the backward one is due to collisions between heavy species (or the reverse), a temperature T* between T_e and T_h is introduced. T* is determined as a function of the ratio of the electron flux to that of neutral species in such a way that T*=T^e for n_e > 10²³ and T*=T_h for low values of n_e(n_e < 10¹⁵ m^–3). Compared to hydrogen, the nitrogen composition exhibits a very abrupt variation between 6000 and 6500 K, corresponding to a shift from the dissociation-dominated regime to that of ionization. It occurs because dissociation of nitrogen starts almost simultaneously with its ionization, which is not the case of H₂, for which dissociation is terminated long before ionization starts. If the charge transfer reaction, whose activation energy is low for both gases, is neglected, in both cases the electron density increases drastically below 9000 K. These results are quite similar to those obtained when calculating the composition with the multitemperature mass action law. The kinetic calculations are dominated by the reactions with a low activation energy: dissociation, dissociative recombination and charge transfer. Thus, a modified pseudoequilibrium calculation has been introduced, the plasma composition being calculated with the equilibrium constants corresponding to low activation energies[X₂ 2X, e+X ₂ ⁺ 2X, X ₂ ⁺ +X X⁺ + X₂ both for hydrogen (X=H) and nitrogen (X=N)] at the temperature T* between T_e and T_h. The results are in very good agreement with those of the kinetic calculations.     

Deposition of silicon nitride thin films by reaction of SiH4 in a nitrogen post-discharge

Silicon nitride thin films are deposited on silicon wafers at room temperature when silane gas is injected in a nitrogen flowing post-discharge. Reactive processes involving siane molecules and long-lifetime nitrogen species are studied, pointing out the nonreactivity of the N₂(A³ _u ⁺ ) metastable state, the low contribution of the vibrationally excited nitrogen ground-state molecules, and the high reactivity of N(⁴S) atoms. Spectroscopic observations performed in the reaction region are correlated with thin-film characteristics.     

Using dithering for implementing geometric moment function estimation in a correlation retina

Correlation retinas measure the correlation product of an image projected on a sensor by optical means and a function f(x, y) stored in the retina. This optical correlation is well suited for the measurement of geometric moments, and this is why one can find in the literature several correlation retina circuits dedicated to it. Unfortunately, these architectures are not programmable and are dedicated to specific applications. Moment functions are of great interest in pattern recognition. This application needs to compute, for example, geometric moments whose order can depend on the application. Thus, the implementation of this function in a correlation retina requires a flexible architecture where the function f(x, y) can be modified to allow the measurement of the product of the image under analysis and f(x, y). The most robust solution is to memorize f(x, y) in memory devices distributed in the array of pixels constituting the retina. But, for technological problems, it is necessary to limit the number of bits used to store f(x, y) in the sensor. In this article, we propose to use dithering algorithms to code f(x, y) on only one bit. We present herein the architecture of the retina circuit on which we are currently working and show that it is possible to obtain approximate geometric moment values with it. The text was submitted by the authors in English.     

Nucleation of wave defects and formation of optical localized structures in bi-directional ring lasers

This work is a contribution to the calculation of transport coefficients for nitrogen, hydrogen, Mars and Titan atmospheres plasmas. The calculation which assumes local thermodynamic equilibrium is performed using Lennard-Jones potential and simple combining rules for the potential parameters for neutral-neutral interaction. A discussion is made for the other interactions: neutral-charged, charged-charged and electron-neutral. The results are compared with those of published theoretical studies for a temperature up to 30 000 K.     

Calculation of Combined Diffusion Coefficients from the Simplified Theory of Transport Properties

The aim of this study is to check if it is possible to use the combined diffusion coefficients introduced by Murphy at equilibrium in a two-temperature model (electron temperature T_e different from that of heavy species T_h), such as that defined by Devoto and Bonnefoi for transport properties. On the one hand, the two-temperature (2-T) theory of transport properties was established by Devoto and Bonnefoi by separating electrons and heavy species because of their mass difference. Their simplified theories allow the calculation of transport coefficients (except diffusion) out of thermal equilibrium, but it has to be noted that when T_e tends toward T_h, the results are those obtained with an equilibrium calculation. On the other hand, Murphy's combined diffusion coefficients describe the diffusive mixing of two nonreactive ionized gases at equilibrium. First, the exact combined diffusion coefficients of Murphy are calculated for an Ar–N₂ (50 wt.%) mixture at atmospheric pressure. Expressions of combined diffusion coefficients are then obtained by using the simplified theory of Bonnefoi at thermal equilibrium. The results of the calculation of combined diffusion coefficients from the simplified theory of transport properties, assuming Te=Th, are compared with those of Murphy at equilibrium. It is shown that large discrepancies occur as soon as the ionization degree is over 10%. These results prove that the simplified 2-T theory of transport coefficients cannot be used for the treatment of diffusion, probably because the mass flux of electrons is no longer constrained. Thus, a new theory of transport coefficients has to be developed, taking into account the coupling of electrons and heavy species.