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 ~ 10²³ ). 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^efor 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+X₂⁺ 2X, X₂⁺+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.