Self-consistent kinetics

An important aspect of modeling weakly ionized gases is to describe the chemical transformations occurring in the system. Thermal and non-thermal plasmas are commonly used in material processing [1], etching [2], deposition [3], waste treatment [4-6], combustion [7-9], pollutant reduction [10], and so on, applications where chemistry plays a fundamental role [11]. In non-thermal plasmas, the understanding of chemical kinetics is not a trivial issue, because of non-equilibrium conditions: commonly, the gas temperature is low, usually Tg < 1000 K, while the electron temperature, Te, is above 10 000 K. The population of internal states is determined, in a first approximation, by the balance between excitation induced by free electron collisions, quenching by heavy particle interaction, and radiative decay. Another contribution comes from chemical reactions which can have a preferential path through excited states [12, 13]. On the other hand, the electron energy distribution is strongly influenced by the population of excited levels, in particular vibrational and long-living metastable states, not decaying by radiative emission [14, 15]. This scenario demonstrates the complex interaction among the different plasma components, in particular, the interplay between heavy-particle internal levels and free electrons. To describe these features, the self-consistent approach must be used, determining, at the same time, the chemical composition, the internal level, and the free electron energy distributions [16], the latter calculated by solving the Boltzmann equation, as described in chapter 2. The main difficulty of this approach is the size of the chemical problem. For diatomic molecules, such as N2, the number of vibrational levels in the ground electronic state is of the order of one hundred, while for triatomic molecules, such as CO2, this number reaches the order of ten thousand [17]. Level kinetics should also be coupled with the radiative transport equation. Part of the emitted photons are reabsorbed, exciting atoms and molecules, or inducing stimulated emission, and the speed of these processes depends linearly on the densityof photons. Usually, collisional-radiative (CR) models avoid the solution of the radiative transport equation by introducing the escape factor [18-20], the fraction of emitted photons reabsorbed locally. This approach cannot account for some interesting phenomena observed in non-homogeneous plasmas, such as the modification of the line shape,1 a consequence of the reabsorption of photons far from the emission zone, introducing non-local effects that can be described only by solving the radiative transport equation. This aspect is relevant not only to optical emission spectroscopy, but also to vehicles entering planetary atmospheres, where part of the global heat flux to the vehicle surface is due to radiation, especially in regions where the conductive and convective fluxes are small [22, 23]. The line-by-line solution of the photon transport equation is a highly demanding computational problem due to the large number of wavelength sampling points to be considered. To reduce the computational load for calculating radiative properties, a multi-group approach can be used [24], considering a limited number of spectral intervals where emissivity and absorbance are estimated. This chapter introduces the reader to the state-to-state (StS) approach, providing at the same time the fundamentals of the self-consistent coupling and showing its application in modeling discharges and high-enthalpy flows.