Thermo-chemical dynamics and chemical quasi-equilibrium of plasmas in thermal non-equilibrium

PDF available at http://www.stanford.edu/group/ctr/ResBriefs/ARB09.htmlPlasmas have a broad field of applications, such as air-breathing hypersonic vehicles (plasma control for scramjet engine), spacecraft atmospheric entries (influence of precursor electrons and prediction of blackout phenomenon), high-enthalpy wind tunnels (plasmatron, arc-jet, and shock tube facilities), lightning phenomena, discharges at atmospheric pressure, laboratory nuclear fusion and astrophysics. Graille, Magin and Massot have derived from kinetic theory a unified fluid model for multicomponent plasmas by accounting for thermal non-equilibrium between the translational energies of the electrons and heavy particles, such as atoms and ions, given their strong mass disparity. The following ionization mechanism, comprising the reactions involving electrons, ions and neutrals was considered. for a 3-species plasma. A recurrent topic in theoretical works on plasmas is the derivation of a modified Saha equation, describing systems in chemical quasi-equilibrium and thermal non-equilibrium, with the consequent debate regarding which of the forms of this equation is the correct one to apply (See the works of Giordano and co-authors and references cited therein). In particular, Morro and van Sanden have derived an equation for the electron-impact ionization reaction based on techniques issued from thermodynamics of homogeneous systems at equilibrium. This approach is questionable for plasmas in both thermo-chemical non-equilibrium, seeing the strong coupling between chemical evolution and thermal exchange. In particular, it is not obvious to choose a suitable set of constraints associated with the optimization of the thermodynamic functions. In this work, we propose to study both processes of ionization by electron impact and by heavy-particle impact. We propose to examine systems in chemical quasi-equilibrium and thermal non-equilibrium by means of a singular perturbation analysis, as opposed to a standard thermodynamic approach, by extending the work of Massot to thermal non-equilibrium. This analysis is based on a set of differential equations derived by the authors for the following physical scenario, in which the thermal relaxation becomes much slower than the chemical reactions. The singular perturbation analysis, consistent with the scale separation associated with this scenario, is used to study the dynamics of the system in two cases. First, electron-impact ionization is investigated. The dynamics of the system rapidly becomes close to a slow dynamics manifold that allows for defining a unique chemical quasi-equilibrium for two-temperature plasmas and proving that the second principle is satisfied. Then, all ionization reactions are taken into account simultaneously, leading to a surprising conclusion: when ionization through both electron and heavy-particle impact is considered, the inner layer for a short time scale (or time boundary layer) directly leads to thermal equilibrium. Thus, the global thermo-chemical equilibrium is reached within a short time scale, involving only chemical reactions, even if thermal relaxation through elastic collisions is not efficient and slow. To our knowledge, this approach sheds some completely new light on this matter and has not been used previously for such multicomponent reactive plasmas out of thermal equilibrium