This paper reviews the basics of kinetic modelling in low-temperature N 2 -O 2 plasmas, including the strong coupling between electron, vibrational, chemical and surface kinetics. The main approaches to investigate each of these kinetics are outlined and the most widely used ones are discussed in some detail. The interdependency of the different kinetics is also considered. In such a formulation, the building blocks of kinetic models in molecular plasmas are the electron Boltzmann equation, a system of rate balance equations describing the creation and loss of the most important neutral and charged heavy-particles, including the relevant vibrationally excited states and all vibration energy transfers, a proper description of transport of charged particles, and a description of heterogeneous particle destruction and molecule formation. All the details required to build a model for N 2 -O 2 plasmas are given either explicitly or by indicating relevant references, so that the interested reader has all the necessary information to build a similar model. Some new calculations are presented to illustrate and study a few specific phenomena, including the electron power transfer in air plasmas, the formation of the vibrational distribution function in O 2 dc discharges, the calculation of gas heating in pulsed air plasmas, and the heterogeneous formation of ozone in an oxygen afterglow. Finally, some open challenges and directions for further research are pointed out.

A kinetic model describing the time evolution of ∼70 individual CO 2 (X 1 Σ + ) vibrational levels during the afterglow of a pulsed DC glow discharge is developed in order to contribute to the understanding of vibrational energy transfer in CO 2 plasmas. The results of the simulations are compared against in situ Fourier transform infrared spectroscopy data obtained in a pulsed DC glow discharge and its afterglow at pressures of a few Torr and discharge currents of around 50 mA. The very good agreement between the model predictions and the experimental results validates the kinetic scheme considered here and the corresponding vibration-vibration and vibration-translation rate coefficients. In this sense, it establishes a reaction mechanism for the vibrational kinetics of these CO 2 energy levels and offers a firm basis to understand the vibrational relaxation in CO 2 plasmas. It is shown that first-order perturbation theories, namely, the Schwartz-Slawsky-Herzfeld and Sharma-Brau methods, provide a good description of CO 2 vibrations under low excitation regimes.

The LisbOn KInetics Boltzmann (LoKI-B) is an open-source simulation tool (https://github. com/IST-Lisbon/LoKI) that solves a time and space independent form of the two-term electron Boltzmann equation, for non-magnetised non-equilibrium low-temperature plasmas excited by DC/HF electric fields from different gases or gas mixtures. LoKI-B was developed as a response to the need of having an electron Boltzmann solver easily addressing the simulation of the electron kinetics in any complex gas mixture (of atomic/molecular species), describing first and second-kind electron collisions with any target state (electronic, vibrational and rotational), characterized by any user-prescribed population. LoKI-B includes electron-electron collisions, it handles rotational collisions adopting either a discrete formulation or a more convenient continuous approximation, and it accounts for variations in the number of electrons due to nonconservative events by assuming growth models for the electron density. On input, LoKI-B defines the operating work conditions, the distribution of populations for the electronic, vibrational and rotational levels of the atomic/molecular gases considered, and the relevant sets of electron-scattering cross sections obtained from the open-access website LXCat (http://lxcat. net/). On output, it yields the isotropic and the anisotropic parts of the electron distribution function (the former usually termed the electron energy distribution function), the electron swarm parameters, and the electron power absorbed from the electric field and transferred to the different collisional channels. LoKI-B is developed with flexible and upgradable object-oriented programming under MATLAB ® , to benefit from its matrix-based architecture, adopting an ontology that privileges the separation between tool and data. This topical review presents LoKI-B and gives examples of results obtained for different model and real gases, verifying the tool against analytical solutions, benchmarking it against numerical calculations, and validating the output by comparison with available measurements of swarm parameters.

This is the second of two papers presenting the study of vibrational energy exchanges in nonequilibrium CO 2 plasmas in low-excitation conditions. The companion paper addresses a theoretical and experimental investigation of the time relaxation of ∼70 individual vibrational levels of ground-state CO X 2 1 S + ( )molecules during the afterglow of a pulsed DC glow discharge, operating at pressures of a few Torr and discharge currents around 50mA, where the rate coefficients for vibration-translation (V-T) and vibration-vibration (V-V) energy transfers among these levels are validated (Silva et al 2018 Plasma Sources Sci. Technol. 27 015019). Herein, the investigation is focused on the active discharge, by extending the model with the inclusion of electron impact processes for vibrational excitation and de-excitation (e-V). The time-dependent calculated densities of the different vibrational levels are compared with experimental data obtained from time-resolved in situ Fourier transform infrared spectroscopy. It is shown that the vibrational temperature of the asymmetric stretching mode is always larger than the vibrational temperatures of the bending and symmetric stretching modes along the discharge pulse-the latter two remaining very nearly the same and close to the gas temperature. The general good agreement between the model predictions and the experimental results validates the e-V rate coefficients used and provides assurance that the proposed kinetic scheme provides a solid basis to understand the vibrational energy exchanges occurring in CO 2 plasmas.

A kinetic model for a flowing microwave discharge in N2–O2 at ω/(2π) = 2450 and 915 MHz, in the pressure range p = 1–10 Torr, is constructed with the purpose of studying the conditions that maximize the concentrations of NO(B 2Σ) molecules and O(3P) atoms, which are known to play a central role in the sterilization processes. The former are responsible for the emission of UV photons associated with the NOβ bands. The NO(B) concentration is found to pass through a maximum, at approximately 1–3% of O2 added to the mixture, which is in good agreement with the measured maximum of UV emission intensity, and with the shortest time required for the inactivation of spores. For such an O2 percentage, the NO(B) also remains in the afterglow, with only a small reduction, up to a few ∼100 ms. Furthermore, the NO(B) concentration peaks with increasing pressure, with the corresponding maximum shifted to lower O2 percentages, in agreement with the observations of UV intensity. The concentration of O(3P) atoms is practically unchanged along the afterglow, at least up to times as high as 100 ms.

A self-consistent model is developed to study the temporal variation of the gas temperature in millisecond single dc pulsed discharges and their afterglows in air-like mixtures (N 2 -20%O 2 ) at low pressures. The model is based on the solutions to the time-dependent gas thermal balance equation, under the assumption of a parabolic gas temperature profile across the discharge tube, coupled to the electron, vibrational and chemical kinetics. Modelling results provide a satisfactory explanation for recently published time-resolved experimental data for the gas temperature in a 5 ms pulsed air plasma with a current of 150 mA and the corresponding afterglow at a pressure of 133 Pa (1 Torr). It is shown that the main heating mechanisms during the first millisecond of the pulse come predominantly from O 2 dissociation by electron impact through the pre-dissociative excited state O 2 (B 3 − u ) and the quenching of nitrogen electronically excited states N 2 (A 3 + u , B 3 g , a 1 − u , a 1 g , w 1 u ) by O 2 , agreeing with other studies on fast gas heating in air plasmas. As the pulse duration increases, other gas heating sources become important, namely V-T N 2 -O energy exchanges, recombination of oxygen atoms at the wall, N 2 (A) quenching by O( 3 P) and reaction N( 4 S) + NO(X) → N 2 (X, v ∼3) + O, contributing altogether to an additional smooth increase in the gas temperature until the end of the pulse. In the first instants of the early afterglow, the gas temperature decreases very rapidly as a consequence of the minor role played by electronic collisions and due to a fast decay of N 2 electronic states. For afterglow times up to 10 ms, the gas temperature continues to decrease, following the time-dependent kinetics of [N 2 (X,v)], [N( 4 S)], [O( 3 P)] and [NO(X)]. Sensitivity of the model to different input parameters such as thermal accommodation coefficient and probabilities for atomic recombination at the wall are reported.

A time-dependent kinetic model is presented to study low-pressure (133 and 210 Pa) pulsed discharges in air for dc currents ranging from 20 to 80 mA with a pulse duration from 0.1 up to 1000 ms. The model provides the temporal evolution of the heavy species along the pulse within this range time, where the coupling between vibrational and chemical kinetics is taken into account. This work shows that the predicted values for NO(X) molecules and O( 3 P) atoms reproduce well previous measured data for these two species. A systematic analysis is carried out on the interpretation of experimental results. It is observed that the N 2 (X, v 13) + O → NO(X) + N( 4 S) and the reverse process NO(X) + N( 4 S) → N 2 (X, v ∼ 3) + O have practically the same rates for a pulse duration longer than 10 ms, each of them playing a dominant role in the populations of NO(X), N( 4 S) and, to a lesser extent, in O( 3 P) kinetics. Our simulations show that for shorter pulse durations, from 0.1 to 10 ms, NO(X) is produced mainly via the processes N 2 (A) + O → NO(X) + N( 2 D) and N( 2 D) + O 2 → NO(X) + O, while the oxygen atoms are created mostly from electron impact dissociation of O 2 molecules and by dissociative collisions with N 2 (A) and N 2 (B) molecules.

Mass spectrometry and optical emission spectroscopy are used in a N 2 -xCH 4 glow discharge with x = 0.5-2%, at low pressures (1-2 Torr) and small flow rates (6 sccm), in order to determine the CH 4 and H 2 absolute concentrations and the N 2 (B 3 g ) and N 2 (C 3 u ) relative concentrations. A kinetic model is developed based on the steady-state solutions to the homogeneous electron Boltzmann equation coupled to a system of rate balance equations for the most populated neutral and ionic species produced, either from active nitrogen and CH 4 dissociation or as a result of reactions between radicals from N 2 and CH 4 . It is observed that CH 4 is very efficiently decomposed through a sequence of reactions in which at the end HCN and H 2 appear as the most abundant products in the discharge. A brown deposition on the tube walls has been detected which is attributed to HCN, in agreement with other investigations of Titan's atmosphere, since this species is poorly destroyed in volume. The accordance between theory and experiment is very satisfactory allowing an insight to be obtained into the basic elementary mechanisms in these discharges.