Abstract: Electrical breakdown by the application of an electric field occurs more easily in hot gases than in cold gases because of the extra electron-species interactions that occur as a result of dissociation, ionization and excitation at higher temperature. This paper discusses some overlooked physics and clarifies inaccuracies in the evaluation of the effective ionization coefficients and the critical reduced breakdown electric field of CO2 at elevated temperature, considering the influence of excited states and ion kinetics. The critical reduced breakdown electric field is obtained by balancing electron generation and loss mechanisms using the electron energy distribution function (EEDF) derived from the Boltzmann transport equation under the two-term approximation. The equilibrium compositions of the hot gas mixtures are determined based on Gibbs free energy minimization considering the ground states as well as vibrationally and electronically excited states as independent species, which follow a Boltzmann distribution with a fixed excitation temperature. The interaction cross sections between electrons and the excited species, not reported previously, are properly taken into account. Furthermore, the ion kinetics, including electron–ion recombination, associative electron detachment, charge transfer and ion conversion into stable negative ion clusters, are also considered. Our results indicate that the excited species lead to a greater population of high-energy electrons at higher gas temperature and this affects the Townsend rate coefficients (i.e. of electron impact ionization and attachment), but the critical reduced breakdown electric field strength of CO2 is only affected when also properly accounting for the ion kinetics. Indeed, the latter greatly influences the effective ionization coefficients and hence the critical reduced breakdown electric field at temperatures above 1500 K. The rapid increase of the dissociative electron attachment cross-section of molecular oxygen with rising vibrational quantum number leads to a larger electron loss rate and this enhances the critical reduced breakdown electric field strength in the temperature range where the concentration of molecular oxygen is relatively high. The results obtained in this work show reasonable agreement with experimental results from literature, and are important for the evaluation of the dielectric strength of CO2 in a highly reactive environment at elevated temperature.

Abstract: Solid carbon deposition is a persistent challenge in dry reforming of methane (DRM), affecting both classical and plasma-based processes. In this work, we use a microwave plasma in reverse vortex flow configuration to overcome this issue in CO₂/CH₄plasmas. Indeed, this configuration efficiently mitigates carbon deposition, enabling operation even with pure CH₄feed gas, in contrast to other configurations. At the same time, high reactor performance is achieved, with CO₂and CH₄conversions reaching 33% and 44% respectively, at an energy cost of 14 kJ L⁻¹for a CO₂ : CH₄ratio of 1 : 1. Laser scattering and optical emission imaging demonstrate that the shorter residence time in reverse vortex flow lowers the gas temperature in the discharge, facilitating a shift from full to partial CH₄pyrolysis. This underscores the pivotal role of flow configuration in directing process selectivity, a crucial factor in complex chemistries like CO₂/CH₄mixtures and very important for industrial applications.

Abstract: We present a 3D and 2D Cartesian quasi-neutral plasma model for a low current argon gliding arc discharge, including strong interactions between the gas flow and arc plasma column.
The 3D model is applied only for a short time of 0.2 ms due to its huge computational cost. It mainly serves to verify the reliability of the 2D model. As the results in 2D compare well with those in 3D, they can be used for a better understanding of the gliding arc basic characteristics. More specifically, we investigate the back-breakdown phenomenon induced by an artificially controlled plasma channel, and we discuss its effect on the gliding arc characteristics. The
back-breakdown phenomenon, or backward-jump motion of the arc, as observed in the experiments, results in a drop of the gas temperature, as well as in a delay of the arc velocity with respect to the gas flow velocity, allowing more gas to pass through the arc, and thus increasing the efficiency of the gliding arc for gas treatment applications.

Abstract: In this study we quantitatively investigate for the first time the plasma characteristics of an argon gliding arc with a 3D model. The model is validated by comparison with available experimental data from literature and a reasonable agreement is obtained for the calculated gas temperature and electron density. A complete arc cycle is modeled from initial ignition to arc decay. We investigate how the plasma characteristics, i.e., the electron temperature, gas temperature,
reduced electric field, and the densities of electrons, Ar+ and Ar2+ ions and Ar(4s) excited states, vary over one complete arc cycle, including their behavior in the discharge and post-discharge. These plasma characteristics exhibit a different evolution over one arc cycle, indicating that either the active discharge stage or the post-discharge stage can be beneficial for certain applications.

Abstract: In recent years there has been growing interest in the use of plasma technology for CO2 conversion. To improve this application, a good insight into the underlying mechanisms is of great importance. This can be obtained from modeling the detailed plasma chemistry in order to understand the chemical reaction pathways leading to CO2 conversion (either in pure form or mixed with another gas). Moreover, in practice, several plasma reactor types are being investigated for CO2 conversion, so in addition it is essential to be able to model these reactor geometries so that their design can be improved, and the most energy efficient CO2 conversion can be achieved. Modeling the detailed plasma chemistry of CO2 conversion in complex reactors is, however, very time-consuming. This problem can be overcome by using a combination of two different types of model: 0D chemical reaction kinetics models are very suitable for describing the detailed plasma chemistry, while the characteristic features of different reactor geometries can be studied by 2D or 3D fluid models. In the first instance the latter can be developed in argon or helium with a simple chemistry to limit the calculation time; however, the ultimate aim is to implement the more complex CO2 chemistry in these models. In the present paper, examples will be given of both the 0D plasma chemistry models and the 2D and 3D fluid models for the most common plasma reactors used for CO2 conversion in order to emphasize the complementarity of both approaches. Furthermore, based on the modeling insights, the paper discusses the possibilities and limitations of plasma-based CO2 conversion in different types of plasma reactors, as well as what is needed to make further progress in this field.

Abstract: A gliding arc plasmatron (GAP) is very promising for CO2 conversion into value-added chemicals, but to further improve this important application, a better understanding of the arc behavior is indispensable. Therefore, we study here for the first time the dynamic arc behavior of the GAP by means of a high-speed camera, for different reactor configurations and in a wide range of operating conditions. This allows us to provide a complete image of the behavior of the gliding arc. More specifically, the arc body shape, diameter, movement and rotation speed are analyzed and discussed. Clearly, the arc movement and shape relies on a number of factors, such as gas turbulence, outlet diameter, electrode surface, gas contraction and buoyance force. Furthermore, we also compare the experimentally measured arc movement to a state-of-the-art 3D-plasma model, which predicts the plasma movement and rotation speed with very good accuracy, to gain further insight in the underlying mechanisms. Finally, we correlate the arc dynamics with the CO2 conversion and energy efficiency, at exactly the same conditions, to explain the effect of these parameters on the CO2 conversion process. This work is important for understanding and optimizing the GAP for CO2 conversion.

Abstract: An inductively coupled plasma connected to a mass spectrometer interface (sampling cone) is computationally investigated. Typical plasma characteristics, such as gas flow velocity, plasma temperature and electron density, are calculated in two dimensions (cylindrical symmetry) and compared with and without a mass spectrometer sampling interface. The results obtained from our model compare favorably with experimental data reported in the literature. A dramatic increase in the plasma velocity is reported in the region close to the interface. Furthermore, a cooled metal interface lowers the plasma temperature and electron density on the axial channel very close to the sampling cone but the corresponding values in the off axial regions are increased. Therefore, the effect of the interface strongly depends on the measurement position. It is shown that even a small shift from the actual position of the sampler leads to a considerable change of the results.

Abstract: Molecular dynamics simulations were used to investigate the size-dependent melting mechanism of nickel nanoclusters of various sizes. The melting process was monitored by the caloric curve, the overall cluster Lindemann index, and the atomic Lindemann index. Size-dependent melting temperatures were determined, and the correct linear dependence on inverse diameter was recovered. We found that the melting mechanism gradually changes from dynamic coexistence melting to surface melting with increasing cluster size. These findings are of importance in better understanding carbon nanotube growth by catalytic chemical vapor deposition as the phase state of the catalyst nanoparticle codetermines the growth mechanism.

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: Although plasma catalysis is gaining increasing interest for various environmental applications, the underlying mechanisms are still far from understood. For instance, it is not yet clear whether and how plasma streamers can propagate in catalyst pores, and what is the minimum pore size to make this happen. As this is crucial information to ensure good plasma-catalyst interaction, we study here the mechanism of plasma streamer propagation in a catalyst pore, by means of a twodimensional particle-in-cell/Monte Carlo collision model, for various pore diameters in the nm range to μm-range. The so-called Debye length is an important criterion for plasma penetration into catalyst pores, i.e. a plasma streamer can penetrate into pores when their diameter is larger than the Debye length. The Debye length is typically in the order of a few 100 nm up to 1 μm at the conditions under study, depending on electron density and temperature in the plasma streamer. For pores in the range of ∼50 nm, plasma can thus only penetrate to some extent and at
very short times, i.e. at the beginning of a micro-discharge, before the actual plasma streamer reaches the catalyst surface and a sheath is formed in front of the surface. We can make plasma streamers penetrate into smaller pores (down to ca. 500 nm at the conditions under study) by increasing the applied voltage, which yields a higher plasma density, and thus reduces the Debye length. Our simulations also reveal that the plasma streamers induce surface charging of the catalyst pore sidewalls, causing discharge enhancement inside the pore, depending on pore diameter and depth.

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: An inductively coupled plasma, connected to a sampling cone of a mass spectrometer, is computationally investigated. The effects of the sampler orifice diameter (ranging from 1 to 2 mm) and distance of the sampler cone from the load coil (ranging from 7 to 17 mm) are studied. An increase in sampler orifice diameter leads to a higher central plasma temperature at the place of the sampler, as well as more efficient gas transfer through the sampler, by reducing the interaction of the plasma gas with the sampling cone. However, the flow velocity at the sampler position is found to be independent of the sampler orifice diameter. Moreover, by changing the sampler orifice diameter, we can control whether only the central gas or also the auxiliary gas can exit through the sampler. Finally, with the increasing distance of the sampler from the load coil, the plasma temperature at the place of the sampler decreases slightly, which might also have consequences for the ion generation and transport through the sampling cone.

Abstract: An inductively coupled plasma, connected to the sampling cone of a mass spectrometer, is computationally investigated. The occurrence of rotational motion of the auxiliary and carrier gas flows is studied. The effects of operating parameters, i.e., applied power and gas flow rates, as well as geometrical parameters, i.e., sampler orifice diameter and injector inlet diameter, are investigated. Our calculations predict that at higher applied power the auxiliary and carrier gas flows inside the torch move more forward to the sampling cone, which is validated experimentally for the auxiliary gas flow, by means of an Elan 6000 ICP-MS. Furthermore, an increase of the gas flow rates can also modify the occurrence of rotational motion. This is especially true for the carrier gas flow rate, which has a more pronounced effect to reduce the backward motion than the flow rates of the auxiliary and cooling gas. Moreover, a larger sampler orifice (e.g., 2 mm instead of 1 mm) reduces the backward flow of the auxiliary gas path lines. Finally, according to our model, an injector inlet of 2 mm diameter causes more rotations in the carrier gas flow than an injector inlet diameter of 1.5 mm, which can be avoided again by changing the operating parameters.

Abstract: We present a zero-dimensional plasma kinetics model, including both surface and gas phase kinetics, to determine the role of vibrationally excited states in plasma-catalytic ammonia synthesis. We defined a new method to systematically capture the conditions of dielectric barrier discharges (DBDs), including those found in packed bed DBDs. We included the spatial and temporal nature of such discharges by special consideration of the number of micro-discharges in the model. We introduce a parameter that assigns only a part of the plasma power to the microdischarges, to scale the model conditions from filamentary to uniform plasma. Because of the spatial and temporal behaviour of the micro-discharges, not all micro-discharges occurring in the plasma reactor during a certain gas residence time are affecting the molecules. The fraction of power considered in the model ranges from 0.005 %, for filamentary plasma, to 100 %, for uniform plasma. If vibrational excitation is included in the plasma chemistry, these different conditions, however, yield an ammonia density that is only varying within one order of magnitude. At only 0.05 % of the power put into the uniform plasma component, a model neglecting vibrational excitation clearly does not result in adequate amounts of ammonia. Thus, our new model, which accounts for the concept in which not all the power is deposited by the micro-discharges, but some part may also be distributed in between them, suggests that vibrational kinetic processes are really important in (packed bed) DBDs. Indeed, vibrational excitation takes place in both the uniform plasma between the micro-discharges and in the strong micro-discharges, and is responsible for an increased N2 dissociation rate. This is shown here for plasma-catalytic ammonia synthesis, but might also be valid for other gas conversion applications.