Special Issue on Verification, Validation and Benchmarking of Low-temperature Plasma Models

Packed bed reactor (PBR) is the commonly used configuration in plasma catalysis, and its plasma characteristics have been extensively investigated. The filled catalysts in PBR make it challenging to carry out in-situ measurements of electric fields, and limited experimental data have been obtained. We investigated the surface streamer propagation and electric field distribution in a simplified PBR through simulations and experiments. The simplified PBR in the experiments is comprised of a blade-plate electrode structure filled with an Al₂O₃ column (_r = 9) in the discharge gap. An ICCD camera and an electric field diagnosis method called EFISH (electric field induced second harmonic generation) were employed, and a two-dimensional fluid model was established for the simulation. Four discharge types in the PBR were identified based on ICCD images and simulation results, including polar discharge at the contact areas, surface streamer along the dielectric column, expansion of surface discharge along the dielectric column, and surface ionization waves along the dielectric plate. Surface streamers with opposite propagation directions were found in the model, namely the forward streamer during the pulse rising time and the reverse streamer during the pulse falling time. Notably, the reverse streamer exhibits a significantly lower velocity compared to the forward streamer. Both experimental measurements and simulation were conducted to investigate the spatiotemporal electric field near the surface of the packing material. The results of both E_exp and E_sim showed peaks with opposite polarities, and exhibited similar trends. In the simulation, the forward streamer head showed a higher electric field compared to the reverse streamer head. Moreover, during the rest pulse time, the surface electric field was more intense at the contact areas than in other regions. The findings of this work provide valuable insights into the discharge mechanism and electric field on the catalytic material surface within the PBR.

In this work, a fluid/Monte Carlo collision (fluid/MCC) hybrid model is developed based on the framework of multi-physics analysis of plasma sources. This hybrid model could be highly accurate in predicting the nonequilibrium phenomena in capacitively coupled plasmas and meanwhile avoid the limitation caused by the computational cost. Benchmarking against the well-established particle-in-cell/MCC (PIC/MCC) method and comparison with experimental data have been presented both in electropositive N₂ discharges and electronegative O₂ discharges. The results indicate that in N₂ discharges, the ion density evolves from a uniform distribution to an edge-high profile as power increases. Besides, the electron energy distribution function (EEDF) at the bulk center exhibits a 'hole' at about 3 eV, and the 'hole' becomes less obvious at the radial edge, because more low energy electrons are generated there. In O₂ discharges, the EEDF exhibits a Druyvesteyn-like distribution in the bulk region, and it evolves to a Maxwellian distribution in the sheath, indicating the dominant influence of the electric field heating there. The results obtained by the hybrid model agree well with those calculated by the PIC/MCC method, as well as those measured by double probe, except for a slight discrepancy in absolute values. The qualitative agreement achieved in this work validates the potential of this hybrid model as an effective tool in the deep understanding of plasma properties, as well as in the improvement of plasma processing.

The kinetics of excited atoms in a low-pressure argon capacitively coupled plasma source are investigated by an extended particle-in-cell/Monte Carlo Collisions simulation code coupled with a diffusion-reaction-radiation code which considers a large number of excited states of Ar atoms. The spatial density distribution of Ar atoms in the 1s₅ state within the electrode gap and the gas temperature are also determined experimentally using tunable diode laser absorption spectroscopy. Processes involving the excited states, especially the four lower-lying 1s states are found to have significant effects on the ionization balance of the discharge. The level of agreement achieved between the computational and experimental results indicates that the discharge model is reasonably accurate and the computations based on this model allow the identification of the populating and de-populating processes of the excited states.

This work analyses the influence of different charged-particle transport models on the global modeling of low-temperature plasmas. The simulations use the LisbOn KInetics simulation tool, calculating the charged-particle loss frequency due to transport with various formulations, categorized into two large groups: ambipolar-based and h-factor transport models. The models are applied to the description of (i) a DC discharge in oxygen (as example of an electronegative multi-ion plasma), at low to intermediate pressures, adopting a validated kinetic scheme as reference model; (ii) a microwave discharge in helium (as example of an electropositive multi-ion plasma), from low to atmospheric pressures, proposing and validating an updated kinetic scheme that bridges two previous models, adjusted separately for low to intermediate pressures and for atmospheric pressure. The analysis shows that using different charged-particle transport models can result in uncertainties of 20%–60% and 8%–115% in the discharge characteristics of oxygen and helium, respectively, with larger dispersion at low pressure and low electron density. The spreading in the results is observed also in the densities of the main plasma species, corresponding to uncertainties up to $60\%$ and within 50%–150% in oxygen and helium, respectively. Since transport accounts for more than $50\%$ of total charge losses, this mechanism should always be part of the quantitative sensitivity analysis of a kinetic scheme, considering several models with different validity domains, according to the electro-positive/-negative single-/multi-ion plasma under study and the low/high pressure conditions considered.

Compared to other computational physics areas such as codes for general computational fluid dynamics, the documentation of verification methods for plasma fluid codes remains under developed. Current analytical solutions for plasma are often highly limited in terms of testing highly coupled physics, due to the harsh assumptions needed to derive even simple plasma equations. This work highlights these limitations, suggesting the method of manufactured solutions (MMSs) as a potential option for future verification efforts. To demonstrate the flexibility of MMS in verifying these highly coupled systems, the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework was utilized. Thanks to the MOOSE framework's robustness and modularity, as well as to its physics module capabilities and ecosystem applications (i.e. Zapdos and the chemical reaction network) developed for plasma physics modeling and simulation, this report lays the groundwork for a structured method of conducting plasma fluid code verification.

This work explores the effect of N₂ addition on CO₂ dissociation and on the vibrational kinetics of CO₂ and CO under various non-equilibrium plasma conditions. A self-consistent kinetic model, previously validated for pure CO₂ and CO₂–O₂ discharges, is further extended by adding the kinetics of N₂. The vibrational kinetics considered include levels up to v = 10 for CO, v= 59 for N₂ and up to v₁= 2 and v₂= v₃= 5, respectively for the symmetric stretch, bending and asymmetric stretch modes of CO₂, and account for electron-impact excitation and de-excitation (e–V), vibration-to-translation (V–T) and vibration-to-vibration energy exchange (V–V) processes. The kinetic scheme is validated by comparing the model predictions with recent experimental data measured in a DC glow discharge operating in pure CO₂ and in CO₂–N₂ mixtures, at pressures in the range 0.6–4 Torr (80.00–533.33 Pa) and a current of 50 mA. The experimental results show a higher vibrational temperature of the different modes of CO₂ and CO and an increased dissociation fraction of CO₂, that can reach values as high as 70%, when N₂ is added to the plasma. On the one hand, the simulations suggest that the former effect is the result of the CO₂–N₂ and CO–N₂ V–V transfers and the reduction of quenching due to the decrease of atomic oxygen concentration; on the other hand, the dilution of CO₂ and dissociation products, CO and O₂, reduces the importance of back reactions and contributes to the higher CO₂ dissociation fraction with increased N₂ content in the mixture, while the N₂(B³Π_g) electronically excited state further enhances the CO₂ dissociation.

In the past three decades, first principles-based fully kinetic particle-in-cell Monte Carlo collision (PIC/MCC) simulations have been proven to be an important tool for the understanding of the physics of low pressure capacitive discharges. However, there is a long-standing issue that the plasma density determined by PIC/MCC simulations shows quantitative deviations from experimental measurements, even in argon discharges, indicating that certain physics may be missing in previous modeling of the low pressure radio frequency (rf) driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission (SEE) and excited state atoms play an important role in low pressure rf capacitive argon plasma discharges. The ion-induced secondary electrons are accelerated by the high sheath field to strike the opposite electrode and produce a considerable number of secondary electrons that lead to additional ionizing impacts and further increase of the plasma density. Importantly, the presence of excited state species even further enhances the plasma density via excited state neutral and resonant state photon-induced SEE on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1–10 Pa) that is commonly used for etching in the semiconductor industry. At the highest pressure (20 Pa) and driving voltage amplitudes 250 and 350 V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced SEE are quantitatively higher than observed in the experiments, requiring further investigation on high pressure discharges.

Phenomena taking place in capacitively coupled plasmas with large electrodes and driven at very high frequencies are studied numerically utilizing a novel energy- and charge-conserving implicit fully electromagnetic particle-in-cell (PIC)/Monte Carlo code ECCOPIC2M. The code is verified with three model problems and is validated with results obtained in an earlier experimental work (Sawada et al 2014 Japan. J. Appl. Phys.53 03DB01). The code shows a good agreement with the experimental data in four cases with various collisionality and absorbed power. It is demonstrated that under the considered parameters, the discharge produces radially uniform ion energy distribution functions for the ions hitting both electrodes. In contrast, ion fluxes exhibit a strong radial nonuniformity, which, however, can be different at the powered and grounded electrodes at increased pressure. It is found that this nonuniformity stems from the nonuniformity of the ionization source, which is in turn shaped by mechanisms leading to the generation of energetic electrons. The mechanisms are caused by the interaction of electrons with the surface waves of two axial electric field symmetry types with respect to the reactor midplane. The asymmetric modes dominate electron heating in the radial direction and produce energetic electrons via the relatively inefficient Ohmic heating mechanism. In the axial direction, the electron energization occurs mainly through an efficient collisionless mechanism caused by the interaction of electrons in the vicinity of an expanding sheath with the sheath motion, which is affected by the excitation of the surface modes of both types. The generation of energetic electron populations as a result of such mechanisms is shown directly. Although some aspects of the underlying physics were demonstrated in the previous literature with other models, the PIC method is advantageous for the predictive modeling due to a complex interplay between the surface mode excitations and the nonlocal physics of the corresponding type of plasma discharges operated at low pressures, which is hard to reproduce in other models realistically.

In the present study, we computationally investigate the splitting of CO₂ to carbon monoxide and oxygen in an atmospheric pressure microwave (MW) plasma torch. We demonstrate different stages of CO₂ conversion while using 2D and 1D models. For both models, we use identical sets of chemical reactions, cross sections, power profiles and dimensions of the plasma region. Based on the real MW plasma torch device, we first constructed two-dimensional geometry and obtained results using the 2D model. Then, the 1D plug-flow model was employed. With 1D model we expected to obtain the results close to those we already had from the 2D approach. However, we revealed that the gas temperature and plasma species behaviour in 1D model was quite different from those obtained with the 2D code. We revisited the 2D results and found that the reverse (upstream) gas flow near the central electrode was responsible for the observed discrepancies. In 2D model, the residence time of a certain portion of gas was much longer. When the flow rate in 1D model was adjusted, the reasonable agreement between both models was achieved.

The steady-state criterion for plasma numerical simulations can be determined by the particle balance relation. In this study, we utilized a one-dimensional (1D) particle-in-cell/Monte Carlo model to investigate particle transport in a capacitively coupled plasma discharge, including particle density change, flow, generation, and loss. Our analysis revealed that the generation rate and loss rate are equivalent in both time and space, indicating a fine balance in the steady state of the discharge system. Additionally, we presented the spatio-temporal distribution and time-averaged particle transport term for electrons and ions to demonstrate how particles attain equilibrium at varying pressures. This validation method can be particularly useful in numerical simulations where determining steady state can be challenging. Our findings establish the correctness and reliability of the method.

We report results obtained by our 0D, time-dependent self-consistent model for the description of the CO₂ plasma kinetics in glow discharge conditions, comparing our results with the simulation and experimental results reported by Grofulovic et al (2018 Plasma Sources Sci. Technol. 27 115009; 2019 PhD Thesis) and Klarenaar et al (2017 Plasma Sources Sci. Technol. 26 115008). Our model is based on the simultaneous solution of the kinetic equations describing the vibrational, the electronic excited states and the plasma chemistry and of the electron Boltzmann equation for the calculation of the electron energy distribution function (eedf). The results for the vibrational level densities of CO₂ show a satisfactory agreement with the Grofulovic's model results, despite the differences in the vibrational energy level scheme and in the kinetic processes included with the correspondent rate coefficients, with a good match also with the corresponding experimental results. Moreover, conditions characterized by higher power density (5–50 W cm⁻³) have been investigated to understand the behavior of the CO₂ plasma discharge when a higher vibrational excitation is present. Large deviations of the vibrational distributions of CO₂ and CO from equilibrium ones are predicted both in discharge and post discharge conditions. In particular, the CO₂ vibrational distribution presents a behavior similar to a Treanor distribution for v < 15 while a deactivation of the plateau in the vibrational distribution function after v > 15 appears as a consequence of the dissociation induced by vibrational excitation mechanism, i.e. pure vibrational mechanism, becoming important at higher power densities. Finally, the results dependence on the selection of the CO₂ electron molecule dissociation cross section, i.e. Phelps (1973 J. Appl. Phys. 44 4464 or Cosby (1993 Report No. AD-A266 464 WL-TR-93-2004 (Dayton, OH: Wright-Patterson Airforce Base)), has been investigated, showing that its more opportune choice is still a problem to be discussed for the description of conditions in which the electron impact dissociation dominates the kinetics, while once vibrational excitation is activated, CO₂ dissociation is essentially driven by vibrational-induced dissociation, depending to a minor extent from that choice.

We study positive streamers in air propagating along polycarbonate dielectric plates with and without small-scale surface profiles. The streamer development was documented using light-sensitive high-speed cameras and a photo-multiplier tube, and the experimental results were compared with 2D fluid streamer simulations. Two profiles were tested, one with 0.5 mm deep semi-circular corrugations and one with 0.5 mm deep rectangular corrugations. A non-profiled surface was used as a reference. Both experiments and simulations show that the surface profiles lead to significantly slower surface streamers, and also reduce their length. The rectangular-cut profile obstructs the surface streamer more than the semi-circular profile. We find quantitative agreement between simulations and experiments. For the surface with rectangular grooves, the simulations also reveal a complex propagation mechanism where new positive streamers re-ignite inside the surface profile corrugations. The results are of importance for technological applications involving streamers and solid dielectrics.

The present work investigates the kinetics of catalytic ammonia synthesis in a N₂/H₂ mixture activated by a nanosecond pulsed discharge plasma experimentally and numerically. X-ray diffraction, high-resolution transmission electron microscopy and x-ray photoelectron spectroscopy are combined to characterize the morphology and surface electronic properties of the catalyst. Special attention is placed on the role of excited species in promoting the formation of important intermediates and the plasma-enhanced surface chemistry. A detailed kinetic mechanism consisting of atoms, radicals, excited species, molecules, ions, and surface species is developed and studied by incorporating a set of the electron impact reactions, reactions involving excited species, ionic reactions, direct and dissociative adsorption reactions, and surface reactions. A zero-dimensional model incorporating the plasma kinetics solver is used to calculate the temporal evolution of species densities in a N₂/H₂ plasma catalysis system. The results show that the coupling of Fe/γ–Al₂O₃ catalyst with plasma is much more effective in ammonia synthesis than the Fe/γ–Al₂O₃ catalyst alone and plasma alone. The numerical model has a good agreement with experiments in ammonia formation. The path flux analysis shows the significant roles of excited species N(²D), H₂(v1), N₂(v) in stimulating the formation of precursors NH, NH₂, and adsorbed N(s) through the pathways N(²D) + H₂ → NH + H, H₂(v1) + NH → NH₂ + H and N₂(v) + 2Fe(s) → N(s) + N(s), respectively. Furthermore, the results show that the adsorption reaction N + Fe(s) → N(s) and Eley–Ridel interactions N(s) + H → NH(s), N + H(s) → NH(s), NH + H(s) → NH₂(s) and NH₂ + H(s) → NH₃(s) can kinetically enhance the formation of ammonia, which further highlights the plasma-enhanced surface chemistry. This work provides new insights into the roles of excited species and plasma-enhanced surface chemistry in the plasma catalytic ammonia synthesis.

This paper introduces the finite element discharge modelling (FEDM) code, which was developed using the open-source computing platform FEniCS (https://fenicsproject.org). Building on FEniCS, the FEDM code utilises the finite element method to solve partial differential equations. It extends FEniCS with features that allow the automated implementation and numerical solution of fully coupled fluid-Poisson models including an arbitrary number of particle balance equations. The code is verified using the method of exact solutions and benchmarking. The physically based examples of a time-of-flight experiment, a positive streamer discharge in atmospheric-pressure air and a low-pressure glow discharge in argon are used as rigorous test cases for the developed modelling code and to illustrate its capabilities. The performance of the code is compared to the commercial software package COMSOL Multiphysics^® and a comparable parallel speed-up is obtained. It is shown that the iterative solver implemented by FEDM performs particularly well on high-performance compute clusters.

Space-charge effects limit the beam-extraction capability of the ion optics and thus hinder the miniaturization and other performance improvements of ion thrusters. This paper presents numerical studies of the space-charge effects in ion optics using hybrid and full particle-in-cell (PIC) simulations, and proposes a modified Child–Langmuir (CL) law. As the injected current increases, the parallel-plane electrode system which corresponds to the classical CL law will reach an unstable and oscillatory state, while the ion optics system remains stable because the electrons from the bulk plasma compensate for the space-charge effects. Furthermore, the radial expansion of the ion beam and the loss of ions on the grids can counteract the space-charge effects when the injected current increases. In general, the space-charge effects in ion optics are self-consistently adjusted by the compensating electrons and the variation of the beam radius. Accordingly, we identify a region in ion optics where, generally, no electrons exist to exclude the influence of electron compensation, and then we modify the CL law of this region by taking into account the effect of the change in the beam radius. We validate the modified CL law and demonstrate its effectiveness in predicting the operating points of the ion optics, such as the perveance-limit point.

The modeling of neutral atoms is important for the full-particle simulations of Hall thrusters. In previous studies, researchers have developed various algorithms to model the neutral kinetics. The choice of those algorithms can influence significantly the computational speed, simulation convergence, and physical results. In this work, we perform a full-particle simulation of a typical 1 kW-class SPT-100 Hall thruster using four neutral algorithms, including the fixed-neutral algorithm (FNA), the algorithm of direct simulation of Monte Carlo (DSMC), the collisionless-neutral algorithm (CLNA), and the fluid algorithm (FA), to analyze the effects of different neutral iteration approaches on the simulation results. We found that FNA is sensitive to the initial number density of neutrals, and is difficult to converge properly, while the other algorithms not neglecting the atomic dynamics can get stable results. We count the parameters of the thruster, that is, thrust, specific impulse, and plasma density using different neutral algorithms. The time-averaged results match well with those of the experiment. However, the results differ in the time scale due to the low-frequency oscillations in Hall thrusters. We verify that the oscillations are due to the periodic change of neutrals and establish a zero-dimensional model to analyze the properties of the oscillations in the time scale. It indicates that the ratio of ion migration to neutral migration is the essential factor that significantly affects the calculation results. The model reveals that the direct neutral iteration methods, like DSMC and CLNA, can better simulate the characteristics of discharge fluctuations in Hall thrusters than the quasi-steady-state method, like FA. Finally, we proposed practical suggestions for the selection of the neutral algorithms for the SPT-100 thruster, which can also be generalized to other low- and medium-power Hall thrusters.

This work focuses on the comparison between a zero-dimensional (0D) global model (LoKI) and a one-dimensional (1D) radial fluid model for the positive column of oxygen DC glow discharges in a tube of 1 cm inner radius at pressures between 0.5 Torr and 10 Torr. The data used in the two models are the same, so that the difference between the models is reduced to dimensionality. A good agreement is found between the two models on the main discharge parameters (gas temperature, electron density, reduced electric field and dissociation fraction), with relative differences below 5%. The agreement on other species average number densities, charged and neutral, is slightly worse, with relative differences increasing with pressure from 11% at 0.5 Torr to 57% at 10 Torr. The success of the 0D global model in describing these plasmas through volume averaged quantities decreases with pressure, due to pressure-driven narrowing of radial profiles. Hence, in the studied conditions, we recommend the use of volume-averaged models only in the pressure range up to 10 Torr.

Verification of numerical simulations is an important step in code development as it demonstrates the correctness of the code in solving the underlying physical model. Analytical solutions represent a strong tool in code verification, but due to the complexity of the fundamental equations, such solutions are often not always available. This is particularly true in the case of kinetic models. Here we present a family of fully analytical solutions describing current transmission between two electrodes and which apply to both fluid, and kinetic, descriptions of the system. The solutions account for the finite initial particle injection velocity and are valid for all injection currents between zero and the maximum at the space-charge limit. In addition to determining this space-charge limited current, spatial profiles of all physical quantities (such as the particle density and velocity) are also obtained at all injection currents. This provides a means to not only verify fluid and kinetic simulations, but also to assess the error and accuracy of the numerical simulation methods and parameters used. The analytical solutions extend the classical Child–Langmuir law (which only applies to the maximum transmissible current and an initial injection velocity equal to zero), and provide new insight into space-charge affected current flow.

Iodine is emerging as an attractive alternative propellant to xenon for several electric propulsion technologies due to its significantly lower cost and its ability to be stored unpressurized as a solid. Because of the more complex reaction processes and energy-loss channels in iodine plasmas however, as well as the historical lack of reliable collision cross-section data, the development of accurate theoretical and numerical models has been hindered. Using recently calculated theoretical cross-sections, we present an iodine plasma model and perform a comparison with experimental data obtained from an iodine-fuelled gridded ion thruster. The model is in reasonable agreement with experimental measurements of the ion beam current, propellant mass utilization efficiency, and ion beam composition, and is able to quantitatively and qualitatively reproduce system behaviour as the input mass flow rate and RF power are varied. In addition, both the model and experiment show that the use of iodine can lead to a performance enhancement when compared with xenon. This occurs because of the combination of different iodine reaction processes, collision cross-section values, and inelastic energy thresholds which result in lower collisional energy losses, as well as an increased antenna-plasma power transfer efficiency for thrusters using a radio-frequency inductive coil.

Electrostatic probe and thrust balance measurements of a coaxial electron-cyclotron-resonance plasma thruster with magnetic nozzle are compared against numerical simulations of the device that solve self-consistently the plasma transport problem with a hybrid particle-in-cell/fluid approach and the microwave electromagnetic fields using mixed finite elements. A simple phenomenological anomalous transport model similar to those used in Hall thruster modeling is applied. Reasonable average relative errors are reported on the ion current density (8.7%) and plasma density (12.8%) profiles along the plume. Good agreement is found in terms of relative errors on thruster performance parameters as the 90%-current divergence angle (0%–3%), utilization efficiency (3%–10%), peak ion energy (9%–15%), and energy efficiency (2%–17%). The comparison suggests that enhanced cross-field diffusion is present in the plasma. Differences in the experimental and numerical behavior of electron temperature point to the areas of the model that could be improved. These include the electron heat flux closure relation, which must correctly account for the axial electron cooling observed.

Numerical and analytical approaches to plasma density determination from the ion current to cylindrical Langmuir probe are validated on hairpin probe measurements. An argon inductively coupled plasma discharge in a pressure range from 4.5 mTorr to 27 mTorr is studied. The discharge input power is varied in the range from 200 to 800 W, giving a plasma density in the range from 10⁹ to 10¹¹ cm⁻³. The approaches used for plasma density determination are analytical collisionless orbital motion limit theory, fluid semianalytical model of ion radial motion with ion collisions and particle-in-cell with a Monte Carlo collisions model of ion current collection by the cylindrical Langmuir probe. The relative error of different models is shown. The ion collisions should be taken into account, even at relatively low pressures, in order to get a reliable plasma density value from the ion current to the Langmuir probe.

Here, we compare the ionization region model (IRM) against experimental measurements of particle densities and electron temperature in a high power impulse magnetron sputtering discharge with a tungsten target. The semi-empirical model provides volume-averaged temporal variations of the various species densities as well as the electron energy for a particular cathode target material, when given the measured discharge current and voltage waveforms. The model results are compared to the temporal evolution of the electron density and the electron temperature determined by Thomson scattering measurements and the temporal evolution of the relative neutral and ion densities determined by optical emission spectrometry. While the model underestimates the electron density and overestimates the electron temperature, the temporal trends of the species densities and the electron temperature are well captured by the IRM.

The electron cyclotron resonance (ECR) effect in a weakly magnetized capacitively coupled radio frequency (RF) plasma was previously observed with optical emission spectroscopy (OES) in experiments and analyzed by particle-in-cell/Monte Carlo collision (PIC/MCC) simulations (Zhang et al 2022 Plasma Sources Sci. Technol.31 07LT01). When the electron cyclotron frequency equals the RF driving frequency, the electron can gyrate in phase with the RF electric field inside the plasma bulk, being continuously accelerated like microwave ECR, leading to prominent increases in the electron temperature and the excitation or ionization rate in the bulk region. Here, we study further the basic features of the RF ECR and the effects of the driving frequency and the gas pressure on the RF ECR effect by OES and via PIC/MCC simulations. Additionally, a single electron model is employed to aid in understanding the ECR effect. It is found that the maximum of the measured plasma emission intensity caused by ECR is suppressed by either decreasing the driving frequency from 60 MHz to 13.56 MHz or increasing the gas pressure from 0.5 Pa to 5 Pa, which shows a qualitative agreement with the change of the excitation rate obtained in the simulations. Besides, the simulation results show that by decreasing the driving frequency the electron energy probability function (EEPF) changes from a convex to a concave shape, accompanied by a decreased electron temperature in the bulk region. By increasing the gas pressure, the EEPF and the electron temperature show a reduced dependence on the magnitude of the magnetic field. These results suggest that the ECR effect is more pronounced at a higher frequency and a lower gas pressure, primarily due to a stronger bulk electric field, together wih a shorter gyration radius and lower frequency of electron–neutral collisions.

A diffusive ionization wave can be generated by an ultrafast high voltage far exceeding the inception threshold, and is featured by its unique and repetitive conical morphology. A combinative experimental and numerical study of the diffusive ionization waves is conducted in this work to investigate the role of photoionization in different N₂/O₂ mixtures with oxygen concentrations of 20%, 2%, 0.2%, 1 ppm, and pure nitrogen. In all gas mixtures, the ionization wave first forms a spherical shape after its inception then a conical when it approaches the plane electrode. Compared with typical filamentary streamers and inception cloud generated by low overvoltage, photoionization in a diffusive ionization wave takes effects mainly before the formation of the spherical ionization wave, and affects slightly the propagation velocity, discharge morphology, and the width (diameter) of the ionization wave. When the pin-to-plane electrode gap distance is kept 16 mm, in the atmospheric pressure simulation with an 85 kV voltage pulse, the maximum ionization width decreases from 11.4 mm in the 20% mixture to 9.1 mm in pure nitrogen. In the 200 mbar pressure experiment with a 16 kV voltage pulse, the maximum ionization width decreases from 12.5 mm in the 20% mixture to 11.6 mm in pure nitrogen. E in the inception cloud diameter estimation function (D= 2 U E⁻¹) is modified to estimate the width of the ionization wave during its spherical propagation stage. It is shown that the estimation results at 180–205 kV cm⁻¹ are in good agreement with the simulation results at atmospheric pressure air.

Spatiotemporal dynamics in a capacitively coupled plasma discharge generated using a combination of 13.56 MHz sinusoidal voltage and 271.2 kHz tailored rectangular voltage is examined both experimentally and computationally. In the experiments, a fast-gated camera is used to measure the space and time-resolved emission at a wavelength of 750.39 nm from the Ar 2p₁ $\rightarrow$ 1s₂ transition. A particle-in-cell model is used to simulate the Ar plasma. The rectangular waveform is formed using 20 consecutive harmonics of 271.2 kHz, and the waveform duty cycle (DC) is varied between 5%–50%. The experiments and simulation show that excitation and argon metastable (Ar$^*$) production are primarily caused by electrons accelerated by the expanding sheath. Species generation occurs asymmetrically with more production happening adjacent to the powered electrode when the low frequency (LF) voltage is positive and vice versa. Densities of charged and excited-state neutral species decrease with increasing LF voltage due to the thinning of the plasma region and enhanced charged species loss at surfaces. At DC = 10%, the plasma responds strongly when the LF rectangular voltage switches from a small negative to a large positive voltage. Emission from the plasma and Ar$^*$ production decrease considerably during this phase. When the LF voltage becomes negative again, species production and excitation remain suppressed for some time before returning to the pre-positive-pulse conditions. This reduction in plasma production is linked to the spike in electron current to the powered electrode during the positive LF voltage period, which depletes the electrons in the plasma bulk and adjacent to the grounded electrode and also raises the mid-chamber plasma potential. Plasma production suppression after the LF positive $\rightarrow$ negative voltage transition lasts longer at higher LF voltage and lower high frequency voltage due to lower plasma density.

Plasma jets are sources of repetitive and stable ionization waves, meant for applications where they interact with surfaces of different characteristics. As such, plasma jets provide an ideal testbed for the study of transient reproducible streamer discharge dynamics, particularly in inhomogeneous gaseous mixtures, and of plasma–surface interactions. This topical review addresses the physics of plasma jets and their interactions with surfaces through a pedagogical approach. The state-of-the-art of numerical models and diagnostic techniques to describe helium jets is presented, along with the benchmarking of different experimental measurements in literature and recent efforts for direct comparisons between simulations and measurements. This exposure is focussed on the most fundamental physical quantities determining discharge dynamics, such as the electric field, the mean electron energy and the electron number density, as well as the charging of targets. The physics of plasma jets is described for jet systems of increasing complexity, showing the effect of the different components (tube, electrodes, gas mixing in the plume, target) of the jet system on discharge dynamics. Focussing on coaxial helium kHz plasma jets powered by rectangular pulses of applied voltage, physical phenomena imposed by different targets on the discharge, such as discharge acceleration, surface spreading, the return stroke and the charge relaxation event, are explained and reviewed. Finally, open questions and perspectives for the physics of plasma jets and interactions with surfaces are outlined.

In electronegative radiofrequency plasmas, striations (STRs) can appear if the bulk plasma is dominated by positive and negative ions that can react to the driving frequency. Here, we investigate such self-organized structures in dual-frequency (2/10 MHz) capacitively coupled CF₄ plasmas by phase-resolved optical emission spectroscopy and particle-in-cell/Monte Carlo collision simulations. This choice of the frequencies is made to ensure that the ions can react to both the lower (2 MHz, 'low frequency', LF) and the higher (10 MHz, 'high frequency', HF) components of the excitation waveform. A strong interplay of the two excitation components is revealed. As the STRs appear in the plasma bulk, their number depends on the length of this region. By increasing the LF voltage, ϕ_LF, the sheath widths at both electrodes increase, the bulk is compressed and the number of STRs decreases. The maximum ion density decreases slightly as a function of ϕ_LF, too, due to the compressed plasma bulk, while the minimum of the ion density remains almost constant. The spatio-temporal distributions of the excitation and ionization rates are modulated both by the LF and HF with maxima that occur at the first HF period that follows the complete sheath collapse at a given electrode. These maxima are caused by a high local ambipolar electric field. At a given phase within a HF period the current density is different at different phases within the LF period because of frequency coupling. The LF components of the F⁻ ion velocity and of the electric field are much lower than the respective HF components due to the lower LF component of the displacement current in the sheaths. The LF component of the total current is dominated by the ion current at low values of ϕ_LF but by the electron current at high values. The HF component of the total current is dominated by the electron current and decreases slightly as a function of ϕ_LF.

Particle-in-cell (PIC) with Monte Carlo collisions is a fully kinetic, particle based numerical simulation method with increasing popularity in the field of low temperature gas discharge physics. Already in its simplest form (electrostatic, one-dimensional geometry, and explicit time integration), it can properly describe a wide variety of complex, non-local, non-linear phenomena in electrical gas discharges at the microscopic level with high accuracy. However, being a numerical model working with discretized temporal and (partially) spatial coordinates, its stable and accurate operation largely depends on the choice of several model parameters. Starting from four selected base cases of capacitively coupled, radio frequency driven argon discharges, representing low and intermediate pressure and voltage situations, we discuss the effect of the variation of a set of simulation parameters on the plasma density distribution and the electron energy probability function. The simulation parameters include the temporal and spatial resolution, the PIC superparticle weight factor, as well as the electron reflection and the ion-induced electron emission coefficients, characterizing plasma–surface interactions.

The particle-in-cell/Monte Carlo collisions (PIC/MCC) simulation approach has become a standard and well-established tool in studies of capacitively coupled radio frequency (RF) plasmas. While code-to-code benchmarks have been performed in some cases, systematic experimental validations of such simulations are rare. In this work, a multi-diagnostic experimental validation of 1d3v electrostatic PIC/MCC simulation results is performed in argon gas at pressures ranging from 1 Pa to 100 Pa and at RF (13.56 MHz) voltage amplitudes between 150 V and 350 V using a custom built geometrically symmetric reference reactor. The gas temperature, the electron density, the spatio-temporal electron impact excitation dynamics, and the ion flux-energy distribution at the grounded electrode are measured. In the simulations, the gas temperature and the electrode surface coefficients for secondary electron emission and electron reflection are input parameters. Experimentally, the gas temperature is found to increase significantly beyond room temperature as a function of pressure, whereas constant values for the gas temperature are typically assumed in simulations. The computational results are found to be sensitive to the gas temperature and to the choice of surface coefficients, especially at low pressures, at which non-local kinetic effects are prominent. By adjusting these input parameters to specific values, a good quantitative agreement between all measured and computationally obtained plasma parameters is achieved. If the gas temperature is known, surface coefficients for different electrode materials can be determined in this way by computationally assisted diagnostics. The results show, that PIC/MCC simulations can describe experiments correctly, if appropriate values for the gas temperature and surface coefficients are used. Otherwise significant deviations can occur.

We compare simulations and experiments of single positive streamer discharges in air at 100 mbar, aiming toward model validation. Experimentally, streamers are generated in a plate–plate geometry with a protruding needle. We are able to capture the complete time evolution of reproducible single-filament streamers with a ns gate-time camera. A 2D axisymmetric drift-diffusion-reaction fluid model is used to simulate streamers under conditions closely matching those of the experiments. Streamer velocities, radii and light emission profiles are compared between model and experiment. Good qualitative agreement is observed between the experimental and simulated optical emission profiles, and for the streamer velocity and radius during the entire evolution. Quantitatively, the simulated streamer velocity is about 20% to 30% lower at the same streamer length, and the simulated radius is about 1 mm (20% to 30%) smaller. The effect of various parameters on the agreement between model and experiment is studied, such as the used transport data, the background ionization level, the photoionization rate, the gas temperature, the voltage rise time and the voltage boundary conditions. An increase in gas temperature due to the 50 Hz experimental repetition frequency could probably account for some of the observed discrepancies.