Abstract A machine learning framework was developed for real-time prediction of electron temperature and electron density in lowtemperature argon plasmas from optical emission spectroscopy (OES). Training data were generated using a multi-parameter collisional-radiative (CR) model assuming a Maxwellian electron energy distribution, which accounts for electron temperature, electron density, radiation trapping, wall quenching, wall neutralisation, and ion temperature. From 14 emission lines, 91 spectral line ratios were constructed as input features, and a random forest algorithm was trained using a dual-target strategy: electron temperature and electron density as co-targets for temperature prediction, and electron density and radiation trapping factor as co-targets for density prediction. The model was validated against Langmuir probe measurements across 40 operating conditions (20-90 mTorr, 100-300 W) in an argon inductively coupled plasma. Electron temperature predictions showed highly consistent trends with probe measurements, with closer agreement as the electron energy distribution function (EEDF) evolved from non-Maxwellian towards Maxwellian. Electron density prediction accuracy was strongly influenced by the degree of Maxwellianisation, and SHAP analysis revealed that the spectral features encode radiation trapping information more strongly than electron density itself, identifying radiation trapping as the dominant spectral signature in OES-based density diagnostics. UMAP dimensional reduction analysis demonstrated inherent limitations in spectral distinguishability at low electron densities. Two-dimensional fluid simulations quantified the measurement geometry differences between local probe diagnostics and line-integrated OES observations, providing an explanation for the systematic underestimation of electron density by OES-based predictions. Finally, the framework was deployed for real-time prediction using OES data acquired at 100 ms intervals, demonstrating stable diagnostic performance throughout continuous plasma operation. Under non-Maxwellian conditions, the predictions exhibited distinctive features correlated with the degree of non-Maxwellianisation, including bimodal prediction patterns and increased variance. These observations suggest the possibility of inferring the electron energy distribution function from Maxwellian-based OES prediction models.
Abstract A fundamental understanding of repetitive dielectric barrier discharge (DBD) is crucial for advancing plasma physics and related applications. This study investigates a single-filament DBD operated at 100 kHz in atmospheric-pressure air. The repetitive filamentary discharge is simulated using a simplified two-dimensional (2D) plasma fluid model, complemented by one‑dimensional (1D) simplified and kinetic models as well as experiments. The simulated current reproduces the experimental feature of a single discharge pulse per positive and negative half‑cycle, with reasonable discharge phase agreement. The transition processes from the first discharge to the steady state are revealed by the model. Steady-state volumetric and surface streamers show distinctly different shapes and densities from the first discharge due to the memory effects. An asymmetric single-period (AP1) state and a ‘bistable’ phenomenon relying on the initial electron density are observed. The key factors influencing current symmetry are found to include photoionization, ion dynamics (e.g., mobility and ion-ion recombination processes), and electron detachment. This study provides deeper insights into the evolution mechanism of repetitive streamers in air DBD and highlights the role of ion dynamics in asymmetric discharge behavior.
Abstract The impact of substrate cooling on electron energy probability function (EEPF) is investigated in an inductively coupled plasma. For Ar plasma, the electron density triples at 60 mTorr as the substrate temperature decreases. The dependence is observed over a wide temperature range from 200 K (cryogenic) to 330 K (above room temperature). The electron density enhancement is attributed to a decrease in neutral gas temperature, which increases gas density and subsequently enhances electron-neutral collisions, promoting ionization. The effect is more pronounced at higher pressures, and the impact of substrate temperature varies with the gas species (Ar, He, N₂, and O₂). In molecular gas plasma, the electron density enhancement is suppressed. These results demonstrate that substrate temperature serves as a primary determinant of plasma characteristics in cryogenic etching processes, offering a fundamental basis for optimizing cryogenic processes in semiconductor manufacturing applications.
Abstract The atomic iodine number density is measured in a capacitively coupled iodine discharge by two-photon laser-induced fluorescence (TALIF). The radio frequency (RF) discharge is created in a cylindrical quartz glass cell with a temperature-controlled cold finger that allows the pressure regulation within the cell. The atomic number density is measured for initial pressures of 4.1 Pa and 10.9 Pa with an RF net forward power ranging from 3 W to 30 W. The atomic iodine ground state is excited to the upper level 3 P 2 6p 2 [1] o 3/2 at a laser wavelength of 298.2 nm and the fluorescence is recorded at 804.6 nm. A novel approach based on the ratio of the TALIF signal measured in the iodine plasma to a reference signal recorded in iodine vapor under plasma-off conditions is used to determine the ground state number density. Under plasma-off conditions the laser dissociates molecules and excites the resulting atoms by two-photon absorption at the same wavelength. A relation between the atomic ground state number density and the ratio of the two TALIF signals, the number of atoms created by photolysis, the laser spatial and temporal properties, and the detection volume of the setup is derived. The atomic ground state number densities of 1.31 +0.38 -0.29 ×10 21 m -3 and 4.10 +1.18 -0.92 ×10 21 m -3 were measured at an initial pressure of 4.1 Pa and 10.9 Pa at 30 W.
Abstract We investigated the influence of humidity on development of helium sinusoidal-driven atmospheric-pressure plasma streamers using Intensified Charge-Coupled Device (ICCD) imaging, mass spectrometry (MS), and laser-induced fluorescence (LIF). A critical humidity threshold of ∼20 ppm was identified, below which streamers become diffuse and unstable. Importantly, the origin of water vapor (adsorbed in the gas line vs bubbler injection) was found to significantly affect streamer morphology. ICCD observations of streamer length correlate with changes in dominant ion species detected by MS, and with spatial OH distributions revealed by LIF. Although OH density was measured only at 250 ppm, the results confirm that humidity is the main source of reactive OH radicals. These findings highlight the crucial role of trace humidity in plasma jet behavior and demonstrate the need for precise humidity control in plasma diagnostics and applications.
Abstract Nitric oxide (NO) is a multifunctional small molecule central to vascular regulation, wound healing, cellular signalling, and antimicrobial defence, while also functioning as a reactive intermediate in sustainable nitrogen and catalytic cycles. However, its rapid oxidation and poor stability in aqueous environments critically limit both biomedical and environmental applications of NO. Here, we report microwave-plasma-generated NO water ( μ PG-NOW) as a high-concentration and long-lived aqueous NO reservoir, providing a reagent-free and scalable platform for controlled NO generation. Electrochemical analyses using cyclic voltammetry and electrochemical impedance spectroscopy reveal record-high NO concentrations (300–2100 µ M) and exceptional stability (>1800 h), corresponding to a twelve-fold lifetime enhancement over conventional NO solutions. These properties originate from synergistic self-deoxygenation and disproportionation-driven regeneration, which continuously sustain free NO and accelerate the redox kinetics, yielding an exchange current density nearly fifty-five times higher than that of an acidified nitrite-derived NO-generating reference solution. For sustainable applications, μ PG-NOW also serves as a mild and eco-friendly reagent for surface modifications of NiO x semiconductors, enabling reproducible tuning of their electronic structures and interfacial energetics. The combined attributes of chemical durability, a high concentration, and enhanced redox efficiency establish μ PG-NOW as a next-generation aqueous NO platform bridging biomedical, catalytic, and sustainable domains. This integrated approach unites plasma–liquid chemistry with functional materials engineering, advancing NO-based technologies for both life and energy sciences.
Abstract Direct current glow discharges organize into patterns at the surface of liquid anode interfaces, where the pattern mode depends on the discharge current and the liquid ionic strength. Earlier work showed that the transition of a simple uniform mode to a ring pattern can be effectively described and predicted by a reaction-diffusion-based Turing stability analysis, where the theory identifies ionic strength, or solution conductivity, and plasma current as the two primary variables that dictate the transition to a patterned state. In this work, we expand this approach and show that adjusting the electric field to a ring charge distribution enables the application of the Turing stability analysis to the next higher order of pattern behavior: ring-to-spot pattern transitions. Validation of this theory was conducted via experimentally photographed plasma patterns at various plasma currents and ionic strengths. Using a machine learning approach, a pre-trained convolutional neural network model was applied to classify experimental images into different pattern modes. The theory matches well with experimental observations and demonstrates how a simple theoretical framework can be used for understanding multiple stable states in a plasma with a liquid electrode for a given ionic strength and plasma current.
Abstract Plasma is a dielectric material with strong dispersion effect, and the higher the frequency of electromagnetic waves, the stronger the penetration in the plasma. Due to the shorter wavelength of terahertz, the focal spot size after passing through the focusing lens is smaller. When using terahertz wave focused transmission for plasma propagation, the area of terahertz wave propagation in the plasma is smaller (about 2 λ ∼ 4 λ ), resulting in higher spatial resolution for plasma parameter diagnosis. This article proposes a diagnostic method for focusing and transmitting terahertz waves with a frequency of 0.22 THz through multiple paths in a cylindrical plasma with radial non-uniform electron density. Firstly, the amplitude and phase characteristics of terahertz waves propagating through multiple paths were studied through numerical simulation, and the diagnostic method with high spatial resolution was validated. A terahertz wave diagnostic system with water-cooled chamber protection was built in a high-temperature and low-pressure plasma environment, and multi-path focused transmission plasma diagnostic experiments were conducted. By using the multi-path transmission diagnostic method, high spatial distribution rate diagnostic results can be obtained with a spatial resolution of up to 5 mm.
Abstract We developed a two-dimensional self-consistent model of the CRAFT RF-driven dual-driver negative ion source to quantify how RF power deposition, gas inflow, neutral heating, and pressure evolution jointly determine the precursor-plasma conditions. The model couples charged-particle drift-diffusion transport, neutral diffusion, inductive RF power deposition, hydrogen plasma chemistry, gas heating, and boundary conditions that include secondary electron emission, surface recombination, and neutral inflow and outflow. Unlike models that prescribe the filling pressure, the present formulation uses the gas inflow as the external control parameter and computes the neutral pressure self-consistently during discharge. The model is validated against Langmuir-probe measurements over 33–125 kW, reproducing the electron density distribution near the plasma grid (PG) with an overall root-mean-square deviation of 22%. The simulations capture localized plasma generation in the RF drivers, diffusive expansion into the chamber, strong molecular dissociation, and substantial gas heating in the expansion region. They further show that source operation is controlled by the coupled balance between RF power deposition and neutral replenishment. At reduced gas inflow, the discharge enters a depletion-limited regime, in which the electron density saturates with increasing RF power. Rovibrational excitation and relaxation of hydrogen molecules provide an additional channel of neutral-gas heating and contribute to the non-monotonic dependence of gas temperature and plasma parameters on RF power and gas feed. These results provide a physically consistent framework for interpreting precursor-plasma conditions in the CRAFT negative ion source and for identifying operating regimes favorable for stable high-density plasma and enhanced atomic-hydrogen production near the PG.
Abstract For reduced electric fields between 80 and 500 Td, the energy deposited in nanosecond discharges applied in the burnt gases of a lean-premixed methane–air flame mainly excites N 2 electronic states. The quenching of these electronic states is responsible for the main effects of nanosecond discharges on a timescale of tens of nanoseconds: ultrafast heating and ultrafast dissociation. In this work, the products, energy release, and rate constants of N 2 (B) and N 2 (C) quenching by N 2 , O 2 , H 2 O, CO 2 , O, CO, H 2 , and CH 4 are reported from an extensive literature review of numerical studies and experiments performed mostly near ambient conditions. These quenching rate constants successfully describe the measured decay of N 2 (B) and N 2 (C) number densities in the burnt gases of the lean premixed methane–air flame studied in part I. This result indicates that the quenching rate coefficients reviewed in this work can be employed when simulating plasma kinetics at combustion temperatures or when building phenomenological models of nanosecond discharges.
In this Letter, we reveal the underlying physics of the rotating spoke morphology-the axially extended leading edge and internal substructures-in magnetron discharges using a two-dimensional particle-in-cell/Monte Carlo collisions (PIC/MCC) approach. It is found that the spoke morphology is controlled by the axial profile of the external magnetic field. As the magnetic field gradient becomes more uniform, the cathode presheath penetrates further toward the anode. Consequently, the Simon-Hoh instability, which distorts the azimuthal equipotential lines and generates azimuthal electric fields, occurs closer to the anode. The resulting del B induced electron heating then drives the formation of a spoke characterized by an axially extended leading edge. The internal substructures are identified as a lower hybrid drift instability, driven by the electron diamagnetic drift and E & times;B drift along the potential hump channel extending from the spoke region to the anode. These spoke morphology features-the axially extended leading edge and its internal substructures-are in good agreement with previous experimental observations.
Abstract Plasma-catalysis holds great potential for efficient CO 2 recycling but the effectiveness of this approach depends on how plasma sources and catalytic materials are coupled. Fluidized bed (FB) reactors are interesting because they exhibit increased surface contact area between material particles and gas phase, and improved heat transfer. A low-pressure DC glow discharge (GD) in FB configuration, ignited with or without fluidized Al 2 O 3 particles, is investigated with optical emission spectroscopy. A decrease in oxygen atom density through the fluidization of the material and an increase in the intensity of CO systems, attributed to increased CO density and to a lesser extend to electric field changes, is observed in comparison to the plasma alone. This indicates that fluidized particles indeed cause a reduction in the O presence leading to an increase in CO density. The rotational temperature does not significantly change, despite the more efficient heat transfer to the wall expected in FB-GDs. This is attributed to the higher current density induced by the confinement of the plasma in the center of the tube by the charged particles. The plasma-assisted catalytic behavior is further investigated by infrared absorption spectroscopy downstream of the FB-GD, showing superior conversion performance compared to the GD alone. The development of this innovative route is crucial to understanding the enhancement of plasma-surface interaction for CO 2 recycling.
The plasma discharge of the small CHT200 cylindrical Hall thruster has been simulated using the axisymmetric hybrid code HYPHEN. Experimental data from three operating points with xenon have been used to fit empirical parameters of the plasma model and partially validate it. The dynamics of four heavy species (up to Xe 3+) are tracked. The analysis covers the 2D maps of the main plasma magnitudes, the 1D profiles of the plasma-wall interaction variables, and the performance figures (based on current and power balances). The differences with the plasma discharge in annular Hall thrusters are highlighted. In the cylindrical thruster the discharge is more complex and there exist two well-distinguished ionization regions. The one close to the annular anode/injector, at the rear corner of the chamber, is the main source of Xe + ions, which are accelerated obliquely towards the channel axis and the exit. By geometrical convergence, a high peak of Xe + density is formed around the axis, which results in a region of high ionization for Xe 2+ and Xe 3+, which inherit the energy of the ionized Xe +. This explains the large current-based propellant utilizations characteristic of CHTs. Downstream energies per unit of charge of the three ion species are found of the same order. Ion velocity distribution functions computed at two locations in the thruster axis illustrate more in detail the behavior of the different ion species. For the selected operating points of the CHT200, about 2/3 of the cathode-emitted electrons drift inwards, leading to a low thrust efficiency. Simulations demonstrate that this is related to large energy losses in the chamber (up to 65% of the total power), which are shown to be due mainly to an extended wall region with large secondary electron emission. Alternatives for modeling the electron energy equation and its boundary conditions to reproduce the plasma cooling in the plume are discussed and their effects on the electron current topology are commented.
Electrical characteristics of a capacitively coupled plasma (CCP) excited at very high frequency (VHF) are very sensitive to parasitic impedances of a chamber, and thus the optimization of a chamber impedance is of significance in improving the power coupling efficiency. In this work, the influence of the reactance of the RF path on grounded-electrode side on the electrical characteristics of the CCP chamber and the power efficiency under 40.68 MHz is systematically investigated using multi-fold diagnostics supplemented by equivalent circuit-based analysis. By introducing a fixed inductor and a tunable capacitor in the grounded-electrode side RF path, the reactance of the grounded RF path (with respect to the zero-potential point) can be intentionally adjusted. It was found that for a certain value of the adjustable capacitor (or grounding reactance), a local series resonance occurs between the interelectrode CCP and the inductively-dominated ground-side RF chain, leading to maxima of the interelectrode voltage, the plasma current, and the plasma power absorption efficiency for a fixed RF power at the input of the matching network. Accordingly, the optical emission intensity, and the electron density also reach their peaks. This work provides a quantitative framework for impedance engineering and optimization of electromagnetic structure of a plasma reactor under VHF excitation.
Temporally-resolved two-dimensional numerical simulations of microwave discharge dynamics in helium at medium and high pressures are carried out using an extended fluid model. The range of applicability for the similarity laws is analyzed. It is shown that, at the end of the breakdown phase at the center of the plasmoid, with pressure changes from 47.5 Torr to 95 Torr and then to 190 Torr, the maximum of electron density changes by a factor of 3.4 and 3.2, which yields a deviation from the similarity laws within 15%. With an increase in pressure to 285 Torr and 380 Torr, variations in the electron density at the end of the breakdown phase already lead to a 20% error, and with an increase in pressure to 760 Torr, an error of 40% is observed. It has been shown that with increasing pressure, various scenarios of self-organization of plasma structures in the discharge region are observed: diffuse, diffuse with filaments, strictly filamented, and diffuse forms with multiple filaments. This indicates a violation of the similarity laws, which is associated with both the kinetics of elementary processes and thermophysical and gas-dynamic processes.
In capacitively coupled radio frequency (RF) plasmas sustained in electronegative gases, ionization-attachment feedback can induce periodic discharge instabilities. Based on particle-in-cell simulations of oxygen plasmas combined with a diffusion model, we demonstrate that such instabilities are accompanied by self-induced temporal mode transitions of the electron power absorption mode between the alpha-, Detachment Induced/ gamma-, and Drift-Ambipolar-modes. While the RF period averaged ion energy and ion flux at the electrodes are insensitive to the instability and increase monotonically with increasing driving voltage, the atomic oxygen production is found to be sensitive to such periodic temporal mode transitions, with its production rate exhibiting a pronounced non-monotonic dependence on the driving voltage. These phenomena are explained by the effects of such temporal mode transitions on the spatio-temporal electric field structure and electron kinetics.
Abstract The accurate determination of the electron temperature ( T e ) and density ( N e ) is critical for understanding argon plasma characteristics, yet inverse solutions to the collisional-radiative (CR) model often suffer from non-uniqueness, complicating data interpretation. The core contribution of this study is the visualization of band-like solution structures within the CR inverse problem and the development of a practical strategy for handling this non-uniqueness. The results reveal band-like residual regions in the T e – N e space, representing continuous zones where fitting residuals are insensitive to coupled T e – N e variations, thereby corresponding to multiple solutions. These regions exhibit a change in monotonicity at T e ≈ 1.77 eV under the Maxwellian assumption, reflecting a transition in the dominant electron-collision kinetics governing the excited states. The structures of these regions are highly sensitive to spectral line selection and EEPF assumptions: higher excited-level sets shift the solutions toward higher N e to balance the relative population distribution, whereas EEPF assumptions with greater high-energy depletion shift them toward higher T e to maintain the necessary excitation rates. The proposed optimization approach efficiently identifies these solutions while maintaining physical consistency. This strategy resolves the non-uniqueness of the inverse problem, ensuring reliable tomographic determinations of T e and N e in argon inductively coupled plasmas.
Ion beam processing applications require adjustments to the process parameters, in order to operate efficiently and with the optimal precision. Global plasma models offer a fast and reliable approach, to characterize and optimize such ion beam sources. In the scope of this work, a self-consistent global plasma model for inductively coupled plasmas (ICPs) using argon as process gas was developed. Targeting surface modification applications in particular, two novel features are implemented and investigated, describing the ion beam extraction process. The plasma boundary above extraction apertures is calculated in an iterative scheme, solving the balance between extracted ions and charge carriers inside the plasma volume self-consistently. Combined with consideration of spatial varying plasma densities, the model is able to predict plasma properties and extracted ion currents for arbitrary ICP systems, extraction geometries and operating conditions. Thereby, multiple ion beam source configurations validate the model, by comparing simulation results with experimentally investigated plasma and ion beam properties, obtained by electrical measurements and Langmuir probe diagnostics in the low pressure environment ( pch=0.06-0.12Pa) of multiple vacuum chambers.
Abstract CO 2 with an admixture of C 4 F 7 N could serve as an eco-friendly alternative to the extreme greenhouse gas SF 6 in high-voltage insulation. Streamer discharges in such gases are different from those in air due to the rapid conductivity decay in the streamer channels. Furthermore, since no effective photoionisation mechanism is known, we expect discharge growth to be more stochastic than in air. In this paper we investigate whether conventional fluid models provide an good approximation to a particle-in-cell model for negative streamers in CO 2 with admixtures of 1 or 10% C 4 F 7 N Higher fractions were not included, as C 4 F 7 N admixtures in high-voltage insulation rarely exceed 10% C 4 F 7 N. We focus on 3D simulations of negative streamers. First we review cross section databases for C 4 F 7 N and CO 2 . Then we compare a two-term Boltzmann solver with a Monte Carlo method to compute reaction and transport coefficients from the cross sections. Afterwards we compare 3D fluid simulations with the local field (LFA) or local energy approximation (LEA) against particle simulations. In general, we find that the results of particle and fluid models are quite similar. One difference we observe is that particle simulations are intrinsically stochastic, leading to more branching. Furthermore, the LEA model does not show better agreement with the particle simulations than the LFA model. We also discuss the effect and choice of different boundary conditions on the negative rod electrode.
Abstract In radio frequency plasma experiments, external matching networks are essential for power delivery, while perfect matching is not always achievable in practice. Often L-type matching networks are used, consisting of a tunable parallel capacitor, a fixed serial inductance and a tunable serial capacitor. The influence of such a matching network on capacitively coupled plasmas is investigated for a representative argon discharge at 30 Pa, 13.56 MHz, and V rf,0 = 125 V, using a kinetic plasma simulation coupled self-consistently with a model of the external circuit, with particular emphasis on the effects of tuning the serial and parallel capacitors on the mode of plasma operation and process relevant plasma parameters. Tuning the serial capacitor near its ideal value is found to strongly influence the power transferred to the plasma and to modify the mode of plasma operation, the sheath electric field and particle energy distributions. Variations of the parallel capacitor, in contrast, affect the power dissipation in the plasma only to a minor extent. These results show that and explain how matching conditions control not only the total power dissipated in the plasma, but also its distribution as a function of spatial position and time within the radio-frequency period through its effects on the discharge mode. These results are relevant for experiments, which often operate under imperfect matching conditions.
