Abstract: This work explains the need for plasma models, introduces arguments for choosing the type of model that better fits the purpose of each study, and presents the basics of the most common nonequilibrium low-temperature plasma models and the information available from each one, along with an extensive list of references for complementary in-depth reading. The paper presents the following models, organised according to the level of multi-dimensional description of the plasma: kinetic models, based on either a statistical particle-in-cell/Monte-Carlo approach or the solution to the Boltzmann equation (in the latter case, special focus is given to the description of the electron kinetics); multi-fluid models, based on the solution to the hydrodynamic equations; global (spatially-average) models, based on the solution to the particle and energy rate-balance equations for the main plasma species, usually including a very complete reaction chemistry; mesoscopic models for plasma–surface interaction, adopting either a deterministic approach or a stochastic dynamical Monte-Carlo approach. For each plasma model, the paper puts forward the physics context, introduces the fundamental equations, presents advantages and limitations, also from a numerical perspective, and illustrates its application with some examples. Whenever pertinent, the interconnection between models is also discussed, in view of multi-scale hybrid approaches.

Abstract: Plasma generation inside catalyst pores is of utmost importance for plasma catalysis, as the existence of plasma species inside the pores affects the active surface area of the catalyst available to the plasma species for catalytic reactions. In this paper, the electric field enhancement, and thus the plasma production inside catalyst pores with different pore shapes is studied with a two-dimensional fluid model. The results indicate that the electric field will be significantly enhanced near tip-like structures. In a conical pore with small opening, the strongest electric field appears at the opening and bottom corners of the pore, giving rise to a prominent ionization rate throughout the pore. For a cylindrical pore, the electric field is only enhanced at the bottom corners of the pore, with lower absolute value, and thus the ionization rate inside the pore is only slightly enhanced. Finally, in a conical pore with large opening, the electric field is characterized by a maximum at the bottom of the pore, yielding a similar behavior for the ionization rate. These results demonstrate that the shape of the pore has a significantly influence on the electric field enhancement, and thus modifies the plasma properties.

Abstract: The electrical asymmetry effect is realized by applying multiple frequency power sources
(13.56 MHz and 27.12 MHz) to a capacitively biased substrate electrode in a specific inductively
coupled plasma reactor. On the one hand, by adjusting the phase angle θ between the multiple
frequency power sources, an almost linear self-bias develops on the substrate electrode, and
consequently the ion energy can be well modulated, while the ion flux stays constant within a
large range of θ. On the other hand, the plasma density and ion flux can be significantly
modulated by tuning the inductive power supply, while only inducing a small change in the self-
bias. Independent control of self-bias/ion energy and ion flux can thus be realized in this specific
inductively coupled plasma reactor.

Abstract: In this work we study energy transport in a gliding arc discharge with two diverging flat
electrodes in argon gas at atmospheric pressure. The discharge is ignited at the shortest electrode
gap and it is pushed downstream by a forced gas flow. The current values considered are
relatively low and therefore a non-equilibrium plasma is produced. We consider two cases, i.e.
with high and low discharge current (28 mA and 2.8mA), and a constant gas flow of 10 lmin −1 ,
with a significant turbulent component to the velocity. The study presents an analysis of the
various energy transport mechanisms responsible for the redistribution of Joule heating to the
plasma species and the moving background gas. The objective of this work is to provide a
general understanding of the role of the different energy transport mechanisms in arc formation
and sustainment, which can be used to improve existing or new discharge designs. The work is
based on a three-dimensional numerical model, combining a fluid plasma model, the shear stress
transport Reynolds averaged Navier–Stokes turbulent gas flow model, and a model for gas
thermal balance. The obtained results show that at higher current the discharge is constricted
within a thin plasma column several hundred kelvin above room temperature, while in the low-
current discharge the combination of intense convective cooling and low Joule heating prevents
discharge contraction and the plasma column evolves to a static non-moving diffusive plasma,
continuously cooled by the flowing gas. As a result, the energy transport in the two cases is
determined by different mechanisms. At higher current and a constricted plasma column, the
plasma column is cooled mainly by turbulent transport, while at low current and an unconstricted
plasma, the major cooling mechanism is energy transport due to non-turbulent gas convection. In
general, the study also demonstrates the importance of turbulent energy transport in
redistributing the Joule heating in the arc and its significant role in arc cooling and the formation
of the gas temperature profile. In general, the turbulent energy transport lowers the average gas
temperature in the arc, thus allowing additional control of thermal non-equilibrium in the
discharge.

Abstract: A gliding arc (GA) plasma has great potential for CO2 conversion into value-added chemicals, because of its high energy efficiency. To improve the application, a 2D/3D fluid model is needed to investigate the CO2 conversion mechanisms in the actual discharge geometry. Therefore, the complex CO2 chemical kinetics description must be reduced due to the huge computational cost associated with 2D/3D models. This paper presents a chemistry reduction method for CO2 plasmas, based on the so-called directed relation graph method. Depending on the defined threshold values, some marginal species are identified. By means of a sensitivity analysis, we can further reduce the chemistry set by removing one by one the marginal species. Based on the socalled flux-sensitivity coupling, we obtain a reduced CO2 kinetics model, consisting of 36 or 15 species (depending on whether the 21 asymmetric mode vibrational states of CO2 are explicitly included or lumped into one group), which is applied to a GA discharge. The results are compared with those predicted with the full chemistry set, and very good agreement is reached. Moreover, the range of validity of the reduced CO2 chemistry set is checked, telling us that this reduced set is suitable for low power GA discharges. Finally, the time and spatial evolution of the CO2 plasma characteristics are presented, based on a 2D model with the reduced kinetics.

Abstract: This study focuses on a magnetically stabilized gliding arc (MGA) plasma. Two fully coupled flow-plasma models (in 3D and 2D) are presented. The 3D model is applied to compare the arc dynamics of the MGA with a traditional gas-driven gliding arc. The 2D model is used for a detailed parametric study on the effect of the external magnetic field. The results show that the relative velocity between the plasma and feed gas is generated due to the Lorentz force, which can increase the plasma-treated gas fraction. The magnetic field also helps to decrease the gas temperature by enhancing heat transfer and to increase the electron number density. This work shows the potential of an external magnetic field to control the gliding arc behavior, for enhanced gas conversion at low gas flow rates.

Abstract: We studied the evolution of an isolated pulsed plasma in a vortex flow stabilised microwave (MW) discharge in N2 at 25 mbar via the combination of 0D kinetics modelling, iCCD imaging and laser scattering diagnostics. Quenching of electronically excited N2 results in fast gas heating and the onset of a thermal-ionisation instability, contracting the discharge volume. The onset of a thermal-ionisation instability driven by vibrational excitation pathways is found to facilitate significantly higher N2 conversion (i.e. dissociation to atomic N2 ) compared to pre-instability conditions, emphasizing the potential utility of this dynamic in future fixation applications. The instability onset is found to be instigated by super-elastic heating of the electron energy distribution tail via vibrationally excited N2 . Radial contraction of the discharge to the skin depth is found to occur post instability, while the axial elongation is found to be temporarily contracted during the thermal instability onset. An increase in power reflection during the thermal instability onset eventually limits the destabilising effects of exothermic electronically excited N2 quenching. Translational and vibrational temperature reach a quasi-non-equilibrium after the discharge contraction, with translational temperatures reaching ∼1200 K at the pulse end, while vibrational temperatures are found in near equilibrium with the electron energy (1 eV, or ∼11 600 K). This first description of the importance of electronically excited N2 quenching in thermal instabilities gives an additional fundamental understanding of N2 plasma behaviour in pulsed MW context, and thereby brings the eventual implementation of this novel N2 fixation method one step closer.

Abstract: Nanosecond pulsed discharge plasma shows a high degree of non-equilibrium, and exhibits relatively high conversions in the dry reforming of methane. To further improve the application, a good insight of the underlying mechanisms is desired. We developed a chemical kinetics model to explore the underlying plasma chemistry in nanosecond pulsed discharge. We compared the calculated conversions and product selectivities with experimental results, and found reasonable agreement in a wide range of specific energy input. Hence, the chemical kinetics model is able to provide insight in the underlying plasma chemistry. The modeling results predict that the most important dissociation reaction of CO₂and CH₄is electron impact dissociation. C₂H₂is the most abundant hydrocarbon product, and it is mainly formed upon reaction of two CH₂radicals. Furthermore, the vibrational excitation levels of CO₂contribute for 85% to the total dissociation of CO₂.

Abstract: Vibrational excitation represents an efficient channel to drive the dissociation of CO₂in a non-thermal plasma. Its viability is investigated in low-pressure pulsed discharges, with the intention of selectively exciting the asymmetric stretching mode, leading to stepwise excitation up to the dissociation limit of the molecule. Gas heating is crucial for the attainability of this process, since the efficiency of vibration–translation (V–T) relaxation strongly depends on temperature, creating a feedback mechanism that can ultimately thermalize the discharge. Indeed, recent experiments demonstrated that the timeframe of V–T non-equilibrium is limited to a few milliseconds at ca. 6 mbar, and shrinks to the<italic>μ</italic>s-scale at 100 mbar. With the aim of backtracking the origin of gas heating in pure CO₂plasma, we perform a kinetic study to describe the energy transfers under typical non-thermal plasma conditions. The validation of our kinetic scheme with pulsed glow discharge experiments enables to depict the gas heating dynamics. In particular, we pinpoint the role of vibration–vibration–translation relaxation in redistributing the energy from asymmetric to symmetric levels of CO₂, and the importance of collisional quenching of CO₂electronic states in triggering the heating feedback mechanism in the sub-millisecond scale. This latter finding represents a novelty for the modelling of low-pressure pulsed discharges and we suggest that more attention should be paid to it in future studies. Additionally, O atoms convert vibrational energy into heat, speeding up the feedback loop. The efficiency of these heating pathways, even at relatively low gas temperature and pressure, underpins the lifetime of V–T non-equilibrium and suggests a redefinition of the optimal conditions to exploit the ‘ladder-climbing’ mechanism in CO₂discharges.

Abstract: In this paper, an O2 inductively coupled plasma used for plasma enhanced atomic layer deposition of Al2O3 thin films is investigated by means of modeling. This work intends to provide more information about basic plasma properties such as species densities and species fluxes to the substrate as a function of power and pressure, which might be hard to measure experimentally. For this purpose, a hybrid model developed by Kushner et al is applied to calculate the plasma characteristics in the reactor volume for different chamber pressures ranging from 1 to 10 mTorr and different coil powers ranging from 50 to 500 W. Density profiles of the various oxygen containing plasma species are reported as well as fluxes to the substrate under various operating conditions. Furthermore, different orientations of the substrate, which can be placed vertically or horizontally in the reactor, are taken into account. In addition, special attention is paid to the recombination process of atomic oxygen on the different reactor walls under the stated operating conditions. From this work it can be concluded that the plasma properties change significantly in different locations of the reactor. The plasma density near the cylindrical coil is high, while it is almost negligible in the neighborhood of the substrate. Ion and excited species fluxes to the substrate are found to be very low and negligible. Finally, the orientation of the substrate has a minor effect on the flux of O2, while it has a significant effect on the flux of O. In the horizontal configuration, the flux of atomic oxygen can be up to one order of magnitude lower than in the vertical configuration.

Abstract: A combined Monte Carlo (MC)/analytical surface model is developed to study the plasma processes occurring during the reactive sputter deposition of TiOx thin films. This model describes the important plasma species with a MC approach (i.e. electrons, Ar+ ions, {\rm O}_2

Abstract: The electron behaviour in an Ar/CF4 inductively coupled plasma is investigated by a Langmuir probe and a hybrid model. The simulated and measured results include electron density, temperature and electron energy distribution function for different values of Ar/CF4 ratio, coil power and gas pressure. The hybrid plasma equipment model simulations show qualitative agreement with experiment. The effect of F2 electron attachment on the electron behaviour is explored by comparing two sets of data based on different F atom boundary conditions. It is demonstrated that electron attachment at F2 molecules is responsible for the depletion of low-energy electrons, causing a density decrease as well as a temperature increase when CF4 is added to an Ar plasma.