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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.

A new unstructured, massively parallel code dedicated to low temperature plasmas, AVIP, is presented to simulate plasma discharges in interaction with combustion. The plasma species are modeled in a drift-diffusion formulation and the Poisson equation is solved consistently with the charged species. Plasma discharges introduce stiff source terms on the reactive Navier-Stokes equations and Riemann solvers, more robust than the schemes available in AVBP, have been implemented in AVIP and reported back in AVBP to solve the reactive Navier-Stokes equations. The validation of all the numerical schemes is carried out in this paper where numerous validation cases are presented for the plasma drift-diffusions equations and the reactive Navier-Stokes equations., 40 pages, 44 figures; added GENCI grant in acknowledgments

In Paper I, we successfully used an external circuit to significantly damp the Breathing Mode (BM) oscillations in 2D particle-in-cell self-consistent simulations of the axial–azimuthal plane of a Hall thruster. We also introduced the two-point power spectral density reconstruction method (PSD2P) used to analyze electrostatic instabilities and generate dispersion diagrams in azimuthal and axial directions, at various times during the BM period. Here, a 3D Dispersion Relation (DR) for electrostatic modes is calculated by linearizing the continuity/momentum fluid equations for electrons and ions. We show that by taking the appropriate limits, this relation can be simplified to derive the DRs of some well-known [Formula: see text] instabilities, such as the electron cyclotron drift instability and its evolution to the Ion Acoustic Wave (IAW), and the Ion Transit-Time Instability (ITTI). The PSD2P diagrams demonstrate the importance of considering the 2D nature of the IAW and ITTI, which have been previously considered to be mono-dimensional (azimuthal and axial, respectively). In particular, we show that the IAW grows near the maximum of the magnetic field and due to its axial components propagates toward both the anode and the cathode (in addition to the well-known azimuthal propagation). The resulting wavefront is, therefore, bent. By analogy to the propagation of acoustic waves in gases, it is proposed that the cause of the IAW wavefront bending is the strong electron temperature gradients in the axial direction. We also show that the ITTI has a strong positive growth rate when a small azimuthal component is present. Finally, we observe that the ITTI significantly affects the discharge current.

Using 2D particle-in-cell (PIC) simulations coupled to a fluid description of the gas dynamics, we study the electrostatic instabilities developing in the axial–azimuthal plane of a Hall thruster, during several periods of a low-frequency oscillation (the so-called breathing mode at [Formula: see text]). As done in experiments, the 2D PIC-MCC (Monte Carlo collision) code is coupled to an electrical circuit in order to partially damp the (otherwise large) discharge current fluctuations at the breathing mode frequency. The different electrostatic higher frequency modes that develop in the plasma are analyzed using a two-point power spectral density reconstruction method, which allows us to generate the dispersion diagrams (in the frequency-wavenumber space) along the axial and azimuthal directions and at different times during the low-frequency breathing mode oscillations. This technique allows us to distinguish between different well-identified instabilities: the electron cyclotron drift instability and its evolution toward an ion acoustic wave and the ion transit time instability. These instabilities are usually considered unidirectional (either axial or azimuthal); however, it is shown here that they exist in both directions. This two-dimensional character is instrumental in understanding where these instabilities grow and how they propagate in the thruster channel and plume. A theoretical discussion of this aspect is proposed in Paper II. The effects of (i) the azimuthal length of the simulation box and (ii) the electron temperature injection at the cathode are also discussed.

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A model for electrons in partially ionized plasmas that self-consistently captures non-Maxwellian electron energy distribution function (EEDF) effects is presented. The model is based on the solution of scalar and vectorial velocity moments up to the contracted fourth-order moment. The set of fluid (macroscopic) equations is obtained with Grad's method and exact expressions for the collision production terms are derived, considering the electron–electron, electron–gas, and electron–ion elastic collisions as well as for electron–gas excitation and ionization collisions. A regularization of the equations is proposed in order to avoid spurious discontinuities, existing in the original Grad's moment model, by using a generalized Chapman–Enskog expansion that exploits the disparity of mass between the electrons and the heavy particles (ions and atoms) as well as the disparity of plasma and gas densities, typical of gas discharges. The transport model includes non-local effects due to spatial gradients in the EEDF as well as the impact of the EEDF in the calculation of the elastic and inelastic collision rates. Solutions of the moment model under spatially homogeneous conditions are compared to direct simulation Monte Carlo and a two-term Boltzmann solver under conditions that are representative of high plasma density discharges at low-pressure. The moment model is able to self-consistently capture the evolution of the EEDF, in good quantitative agreement with the kinetic solutions. The calculation of transport coefficients and collision rates of an argon plasma in thermal non-equilibrium under the effect of an electric field is in good agreement with the solutions of a two-term Boltzmann solver, largely improving models with a simplified Bhatnagar–Gross–Krook collisional operator.

The large differential drift motion between electrons and ions that is created by the E × B current can produce different instabilities, such as the electron cyclotron drift instability, perpendicular to the magnetic field, and the Modified Two-Stream Instability (MTSI), with a component along the magnetic field. In this paper, we derive and validate a stability condition for the apparition of the MTSI modes in 2D particle-in-cell simulations of E × B discharges in the radial-azimuthal plane of a Hall thruster. We verify that, by choosing properly the domain dimensions, it is possible to capture correctly the MTSI growth and its corresponding number of azimuthal periods. In particular, we show that an azimuthal length that is smaller than a certain threshold prevents the MTSI from growing. Moreover, we show that the MTSI growth does not depend on the plasma density, but is affected by the axial electric field (perpendicular to the simulation domain). Additionally, we show that during its linear growth in the early times of the simulations, the MTSI produces an enhanced heating of the electrons in the magnetic field direction as well as an increased cross field mobility. For longer times, in the nonlinear regime, the system evolves toward a more chaotic state with the presence of structures that mostly exhibit large azimuthal wavelengths.

The dynamics of a nanosecond positive ionization front generated in a pin-to-plane geometry in atmospheric pressure air is simulated using a 2D axisymmetric drift-diffusion fluid model. For a 16 mm gap and a sharp pin electrode, the plateau of the applied voltage is varied between 40 and 60 kV and the rise time is varied between 0.5 and 1.5 ns or a DC voltage is applied. The discharge ignition time and the voltage at ignition are shown to depend mostly on the voltage rise time. The connection time, i.e. the time for the ionization wave to ignite, propagate and connect to the plane is shown to strongly depend on both the values of the voltage plateau and rise time. For all cases, the discharge has a conical shape with a maximal radius of about 8 mm as it connects to the grounded plane. The average propagation velocity of the ionization front is found to vary in the range 3.1 to 8.5 mm ns−1. These values are in rather good agreement with experiments. Temporal evolutions of the electric field are recorded on the symmetry axis at different positions in the gap. At each location, an increase and decrease of the electric field is observed as the ionization front, propagating from the pin to the plane, passes the studied point, in accordance with experimental observations. Finally, for a voltage plateau of 55 kV and a rise time of 0.5 ns, a temporal sampling of 100 ps is shown to be sufficient to capture the dynamics of the electric field during the ionization front propagation when it passes close to the middle of the gap. Conversely, a temporal sampling of 10 ps is required when the ionization wave is close to both electrodes, or during the fast redistribution of the electric field after the connection of the ionization front at the cathode.

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International audience; Using both 0D and 1D fluid models, we revisit the formation of the breathing mode in Hall thrusters and show that it is an ionization instability associated with nonlinearity in the electron power absorption. As the plasma density increases, the axial electric field profile changes and the magnitude of the electric field is enhanced in the ionization zone. This causes a nonlinear increase in the power absorbed by electrons, and an increase in the electron temperature and ionization rate factor that is able to partially compensate for the decreasing neutral density to keep the ionization rate high. This sets up a positive feedback mechanism where the electric field continues to be enhanced as the plasma density increases, and consequently the neutral density needs to decrease even further before plasma growth can be halted. At this point the neutral density is so low that the plasma can no longer be "sustained", and time is needed for neutrals to refill the thruster channel before "re-ignition" can occur and the process repeated. By treating the breathing mode as an AC excitation, a carefully designed external circuit can be used to counteract the change in axial electric field by appropriately varying the anode voltage to stabilise the discharge.

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International audience; This paper provides perspectives on recent progress in understanding the physics of devices in which the external magnetic field is applied perpendicular to the discharge current. This configuration generates a strong electric field that acts to accelerate ions. The many applications of this set up include generation of thrust for spacecraft propulsion and separation of species in plasma mass separation devices. These “E × B” plasmas are subject to plasma–wall interaction effects and to various micro- and macroinstabilities. In many devices we also observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena and state-of-the-art computational results, identifies critical questions, and suggests directions for future research.

The interaction of kHz μs-pulsed atmospheric pressure He jets with metallic targets is studied through simulations and experiments, focusing on the differences between floating and grounded targets. It is shown that the electric potential of the floating target is close to grounded in the instants after the impact of the discharge, but rises to a high voltage, potentially more than half of the applied voltage, at the end of the 1 μs pulse. As a result, a return stroke takes place after the discharge impact with both grounded and floating targets, as a redistribution between the high voltage electrode and the low voltage target. Electric field, electron temperature and electron density in the plasma plume are higher during the pulse with grounded target than with floating target, as gradients of electric potential progressively dissipate in the latter case. Finally, at the fall of the pulse, another electrical redistribution takes place, with higher intensity with the highly-charged floating target than with the grounded target. It is shown that this phenomenon can lead to an increase in electric field, electron temperature and electron density in the plume with floating target.

International audience; Plasma transport in magnetized discharges is a long-standing problem because it strongly depends on instabilities whose properties and influence on the plasma transport are difficult to predict. A magnetized plasma column is investigated with 2D PIC simulations in the plane transverse to the magnetic field, at gas pressures between 3 and 12 mTorr and magnetic field intensities between 0 and 40 mT. At high magnetic field, instabilities develop and rotate in the diamagnetic drift direction. It is shown theoretically and by simulation that the magnetic field confinement is destroyed by the instability. Predictive formulas of the main parameters of the instability-enhanced plasma transport such as the edge-to-center plasma density ratio (or h factor), and the effective collision frequency are provided and successfully compared with the PIC simulations.

The genesis of the ion axial velocity distribution function (VDF) is analyzed for collisionless Hall thruster discharges. An analytical form for the VDF is obtained from the Vlasov equation, by applying the Tonks–Langmuir theory in the thruster channel, under the simplifying assumptions of monoenergetic creation of ions and steady state. The equivalent set of 1D unsteady anisotropic moment equations is derived from the Vlasov equation, and simple phenomenological closures are formulated, assuming a polynomial shape for the ion VDF. The analytical results and the anisotropic moment equations are compared to collisionless particle-in-cell simulations, employing either a zero heat flux (Euler-like equations) or the polynomial-VDF closure for the heat flux. The analytical ion VDF and its moments are then compared to experimental measurements.

This paper quantitatively characterizes a kHz atmospheric pressure He plasma jet without target powered by a pulse of positive applied voltage. It focuses on a quantitative comparison between experimental measurements and numerical results of a two-dimensional fluid model using the same configuration, for different values of magnitude and width of pulsed applied voltage. Excellent agreement is obtained between experiments and simulations on the gas mixture distribution, the length and velocity of discharge propagation and the electric field in the discharge front. For the first time in the same jet, the experimentally measured increase of the electric field in the plume is confirmed by the simulations. The electron density and temperature, measured behind the high field front, are found to agree qualitatively. Moreover, the comparison with simulations shows that discharge propagation stops when the potential in the discharge head is lower than a critical value. Hence, pulse width and magnitude allow to control propagation length. For long pulses, the potential in the discharge front reaches this critical value during the pulse. For shorter pulses, propagation is determined by the pulse shape, as the critical value is reached around 90-130 ns after the fall of the pulse. The results suggest that the magnitude of this critical value is defined by the gas mixture at the position of the front.

International audience; This work presents a study of the influence of dielectric permittivity on the interaction between a positive pulsed He plasma jet and a 0.5 mm-thick dielectric target, using a validated two-dimensional numerical model. Six different targets are studied: five targets at floating potential with relative permittivities ϵr= 1, 4, 20, 56 and 80; and one grounded target of permittivity ϵr=56. The temporal evolution of the charging of the target and of the electric field inside the target are described, during the pulse of applied voltage and after its fall. It is found that the order of magnitude of the electric field inside the dielectric targets is the same for all floating targets with ϵr≥4. For all these targets, during the pulse of applied voltage, the electric field perpendicular to the target and averaged through the target thickness, at the point of discharge impact, is between 1 and 5 kV cm−1. For the two remaining targets (ϵr=1 and grounded target with ϵr=56), the field is significantly higher than for all the other floating targets.

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Electric field induced second harmonic (E-FISH) generation has emerged as a versatile tool for measuring absolute electric field strengths in time-varying, non-equilibrium plasmas and gas discharges. Yet recent work has demonstrated that the E-FISH signal, when produced with tightly focused laser beams, exhibits a strong dependence on both the length and shape of the applied electric field profile (along the axis of laser beam propagation). In this paper, we examine the effect of this dependence more meaningfully, by predicting what an E-FISH experiment would measure in a plasma, using 2D axisymmetric numerical fluid simulations as the true value. A pin-plane nanosecond discharge at atmospheric pressure is adopted as the test configuration, and the electric field evolution during the propagation of the ionization wave (IW) is specifically analysed. We find that the various phases of this evolution (before and up to the front arrival, immediately behind the front and after the connection to the grounded plane) are quite accurately described by three unique electric field profile shapes, each of which produces a different response in the E-FISH signal. As a result, the accuracy of an E-FISH measurement is generally predicted to be comparable in the first and third phases of the IW evolution, and significantly poorer in the second (intermediate) phase. Fortunately, even though the absolute error in the field strength at certain time instants could be large, the overall shape of the field evolution curve is relatively well captured by E-FISH. Guided by the simulation results, we propose a procedure for estimating the error in the initial phase of the IW development, based on the presumption that the starting field profile mirrors that of its corresponding Laplacian conditions before evolving further. We expect that this approach may be readily generalized and applicable to other IW problems or phenomena, thus extending the utility of the E-FISH diagnostic.

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A numerical parametric study on positive diffuse discharges in point-to-plane geometry in air at atmospheric pressure is presented. Different discharge characteristics are studied: ignition time, connection time to the grounded cathode plane, shape of the discharge and its maximum radius at the connection time, evolution of the maximum electric field in the discharge front and velocity of the ionization front during its propagation. First, a case at a DC voltage of 50 kV applied on a rod anode ended by a semi-sphere with a radius of 100 μm set at 1.6 cm from a grounded cathode plane is considered. The influence of the rod radius, the position of a disc holder, the shape of the anode electrode and the radial extension of the computational domain are studied. The radius of curvature of the anode tip (varied between 100 and 1000 μm) and the shape of the anode electrode (rod or hyperbola) are shown to have a negligible influence on discharge characteristics. Conversely, the presence of a disc holder or a small radial computational domain lead to a decrease of the maximum discharge radius at the connection time and a change in the discharge shape from a conical to an ellipsoidal shape. These changes on the discharge morphology have only a limited impact on the propagation velocity of the discharge front and maximum electric field on the discharge axis. Then, a point-to-plane geometry with a rod electrode of 50 μm radius, in a 1.6 cm gap, with a 100 kV voltage applied with a rise time of 1 ns is studied. The influence of a disc holder on the discharge characteristics is the same as for lower DC voltages. Finally, the time evolution of the absolute value of the electric field at different test points on the discharge axis is studied. Close to the anode tip, rapidly after the peak of electric field due to the passage of the ionization front, the electric field in the discharge channel is shown to increase to values higher than the breakdown field.

In this paper we propose a representative simulation test-case of E B discharges accounting for plasma wall interactions with the presence of both the electron cyclotron drift instability and the modified-two-stream-instability. Seven independently developed particle-in-cell (PIC) codes have simulated this benchmark case, with the same specified conditions. The characteristics of the different codes and computing times are given. Results show that both instabilities were captured in a similar fashion and good agreement between the different PIC codes is reported as main plasma parameters were closely related within a 5% interval. The number of macroparticles per cell was also varied and statistical convergence was reached. Detailed outputs are given in the supplementary data, to be used by other similar groups in the perspective of code verification.

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International audience; The increasing need to demonstrate the correctness of computer simulations has highlighted the importance of benchmarks. We define in this paper a representative simulation case to study low-temperature partially-magnetized plasmas. Seven independently developed Particle-In-Cell codes have simulated this benchmark case, with the same specified conditions. The characteristics of the codes used, such as implementation details or computing times and resources, are given. First, we compare at steady-state the time-averaged axial profiles of three main discharge parameters (axial electric field, ion density and electron temperature). We show that the results obtained exhibit a very good agreement within 5% between all the codes. As ExB discharges are known to cause instabilities propagating in the direction of electron drift, an analysis of these instabilities is then performed and a similar behaviour is retrieved between all the codes. A particular attention has been paid to the numerical convergence by varying the number of macroparticles per cell and we show that the chosen benchmark case displays a good convergence. Detailed outputs are given in the supplementary data, to be used by other similar codes in the perspective of code verification. 2D axial-azimuthal Particle-In-Cell benchmark for low-temperature partially ..

It is shown that the transport in low temperature, collisional, bounded plasma is enhanced by instabilities at high magnetic field. While the magnetic field confines the electrons in a stable plasma, the instability completely destroys the confinement such that the transport becomes independent of the magnetic field in the highly magnetized limit. An analytical expression of the instability-enhanced collision frequency is proposed, based on a magnetic field independent edge-to-center density ratio., Comment: Physics of Plasmas, American Institute of Physics, In press

International audience; The evolution of the electron mean energy in the pre-sheath and the sheath of a low pressure plasma bounded by two planes is investigated with 1D particle in cell simulations. We observed that the electron mean energy is not constant in the sheath, but instead decreases significantly from the bulk towards the wall. From the simulations, a polytropic state law is proposed, allowing us to close the fluid equations for the electrons without the isothermal hypothesis. A comparison between the fluid model and the simulations show that the non-isothermal sheath model is more accurate than the isothermal model. The impact of the electron mean energy variation on the potential sheath drop and the electron particle and heat flux is evaluated.

International audience; This work investigates the dynamical charging of a surface under exposure of a non-equilibrium plasma jet at atmospheric pressure through a quantitative comparison between modeling and experiments. We show using mono-polar pulses with variable pulse duration and amplitude that the charging time (i.e. the time from impact of the ionization wave till the fall of the high voltage pulse) is a crucial element determining the plasma-surface interaction. This is done through direct measurements of the electric field induced inside the target using the optical diagnostic technique called Mueller polarimetry and comparison with the electric field calculated using a 2D fluid model of the plasma jet interaction with the target in the same conditions as in the experiments. When the charging time is kept relatively short (less than 100 ns), the surface spreading of the discharge and consequent surface charge deposition are limited. When it is relatively long (up to microseconds), the increased surface spreading and charge deposition significantly change the electric field to which the target is exposed during the charging time and when the applied voltage returns to zero.

We present a novel numerical scheme for the efficient and accurate solution of the isothermal two-fluid (electron + ion) equations coupled to Poisson's equation for low-temperature plasmas at low-pressure. The model considers electrons and ions as separate fluids, comprising the electron inertia and space charge regions. The discretization of this system with standard explicit schemes is constrained by very restrictive time steps and cell sizes related to the resolution of the Debye length, electron plasma frequency, and electron sound waves. Both sheath and electron inertia are fundamental to fully explain the physics in low-pressure and low-temperature plasmas. However, most of the phenomena of interest for fluid models occur at speeds much slower than the electron thermal speed and are quasi-neutral, except in small charged regions. A numerical method that is able to simulate efficiently and accurately all these regimes is a challenge due to the multiscale character of the problem. In this work, we present a scheme based on the Lagrange-projection operator splitting that preserves the asymptotic regime where the plasma is quasi-neutral with massless electrons. As a result, the quasi-neutral regime is treated without the need of an implicit solver nor the resolution of the Debye length and electron plasma frequency. Additionally, the scheme proves to accurately represent the dynamics of the electrons both at low speeds and when the electron speed is comparable to the thermal speed. In addition, a well-balanced treatment of the ion source terms is proposed in order to tackle problems where the ion temperature is very low compared to the electron temperature. The scheme significantly improves the accuracy both in the quasi-neutral limit and in the presence of plasma sheaths when the Debye length is resolved. In order to assess the performance of the scheme in low-temperature plasmas conditions, we propose two specifically designed test-cases: a quasi-neutral two-stream periodic perturbation with analytical solution and a low-temperature discharge that includes sheaths. The numerical strategy, its accuracy, and computational efficiency are assessed on these two discriminating configurations.

International audience; Understanding anomalous electron transport in E × B discharges remains a key challenge in the development of self-consistent models of these systems. It has been shown that short-wavelength, high-frequency, instabilities in the azimuthal E × B direction may be responsible for increased electron transport due to an enhanced electron-ion friction force. Although a theoretical model based on quasi-linear kinetic theory has previously been proposed to describe this friction force, it has so far only undergone limited validation testing. Here we rigorously assess this theoretical model by comparison with the friction force self-consistently obtained from 2D axial-azimuthal particle-in-cell simulations. The simulation geometry is based on a recently established benchmark configuration for E × B discharges, and a broad parametric study is performed by varying the magnetic field strength, the discharge current density, and the presence of different neutral collisional processes. Overall the theory is found to be in very good agreement with the simulation results for all cases studied; verifying the underlying physical mechanisms leading to enhanced electron transport. We demonstrate however that the friction force depends sensitively on the shape of the electron velocity distribution function, thus posing significant challenges to fully self-consistent, first principles, modelling of anomalous transport in fluid simulations.

International audience; Electric propulsion can reach higher exhaust velocities compared to chemical systems and thus result in lower propellant mass requirements. Among the different electric propulsion systems, Hall effect thrusters are used for spatial propulsion since the 1970s. However inside a Hall thruster, complex physical phenomena such as erosion or electron anomalous transport which may lower thruster efficiency and lifetime, are not yet fully understood. Thanks to high performance computing, numerical simulations are now considered for understanding the plasma behavior. With the renewed interest for such electric propulsion to supply small satellites, numerical solvers able to predict accurately the real thruster efficiency have become crucial for industry. This paper presents the approach used and first validation tests of such a solver. The AVIP code solves plasma equations in complex industrial geometries using an unstructured parallel-efficient 3D fluid methodology. AVIP also includes a Particle-In-Cell (PIC) solver used as a reference for validation. While full 3D PIC simulations of a Hall thruster still require unaffor-dable computational time, fluid models provide in a reasonable time 3D results on the plasma behavior inside the discharge channel. In this category, standard drift-diffusion models [1-3] are fast and robust but at the cost of strong hypotheses and simplifications. In particular such models do not describe explicitly the sheath formation in the vicinity of walls and often use analytical models instead. They are limited to simple configurations and only provide a first insight into plasma complex phenomena. The present approach includes a more detailed two-fluid plasma model without drift-diffusion approximation. After the description of the formulation and main features of the solver, the paper focuses on wall boundary conditions which are crucial for the formation of sheaths. It is demonstrated in particular that a vacuum boundary condition is not adapted to fit PIC results. A boundary condition based on wall thermal fluxes is more realistic. The mesh resolution is also found to be critical. The simulation methodology is finally applied to a 2D simulation of a typical Hall effect thruster in order to observe the plasma properties inside the discharge chamber.

International audience; Edge-to-center plasma density ratios – so-called h factors – are important parameters for global models of plasma discharges as they are used to calculate the plasma losses at the reactor walls. There are well-established theories for h factors in the one-dimensional case. The purpose of this paper is to establish h factors in two-dimensional (2D) systems, with guidance from a 2D particle-in-cell (PIC) simulation. We derive analytical solutions of a 2D fluid theory that includes the effect of ion inertia, but assumes a constant (independent of space) ion collision frequency (using an average ion velocity) across the discharge. Predicted h factors from this 2D fluid theory have the same order of magnitude and the same trends as the PIC simulations when the average ion velocity used in the collision frequency is set equal to the ion thermal velocity. The best agreement is obtained when the average ion velocity varies with pressure (but remains independent of space), going from half the Bohm velocity at low pressure, to the thermal velocity at high pressure. The analysis also shows that a simple correction of the widely-used 1D heuristic formula may be proposed to accurately incorporate 2D effects.

International audience; This paper presents 2D simulations of atmospheric pressure discharges in helium with N2 and O2 admixtures, propagating in a dielectric tube between a point electrode and a grounded metallic target. For both positive and negative polarities, the propagation of the first ionization front is shown to correspond to a peak of the absolute value of the axial electric field inside the tube, but also outside the tube. After the impact on the metallic target, a rebound front is shown to propagate from the target to the point electrode. This rebound front is 2–3 times faster than the first ionization front. Close to the high voltage point, this rebound front corresponds to a second peak of the absolute value of the axial electric field. Close to the target, as the first ionization and rebound fronts are close in time, only one peak is observed. The dynamics of the absolute value of the radial component of electric field outside the tube is shown to present an increase during the first ionization front propagation and a fast decrease corresponding to the propagation of the rebound front. These time evolutions of the electric field components are in agreement with experiments. Finally, we have shown that the density of metastable He * in 99% He—1% N2 and 99% He—1% O2 atmospheric pressure discharges are very close. Close to the grounded target, the peak density of reactive species is significantly increased due to the synergy between the first ionization and rebound fronts, as observed in experiments. Similar results are obtained for both voltage polarities, but the peak density of metastable He* close to the target is shown to be two times less in negative polarity than in positive polarity.

International audience; The mathematical modeling and computer simulation of low-temperature plasmas is gradually such a level of maturity that these simulation tools can be used not just for improving scientific understanding but also as computer-aided engineering design tools in an industrial setting. These models necessarily involve the description of multiple physical phenomena occurring over a range of times and lengths, thereby complicating their numerical implementation and solution. This special issue presents 12 invited contributions that present recent developments in the field of modeling and simulation of low-temperature plasma discharges. This editorial introduces these papers by providing an overview of the context in which these papers are presented.

International audience; Kinetic drift instabilities have been implicated as a possible mechanism leading to anomalous electron cross-field transport in E B discharges, such as Hall-effect thrusters. Such instabilities, which are driven by the large disparity in electron and ion drift velocities, present a significant challenge to modelling efforts without resorting to time-consuming particle-in-cell (PIC) simulations. Here, we test aspects of quasi-linear kinetic theory with 2D PIC simulations with the aim of developing a self-consistent treatment of these instabilities. The specific quantities of interest are the instability growth rate (which determines the spatial and temporal evolution of the instability amplitude), and the instability-enhanced electron-ion friction force (which leads to “anomalous” electron transport). By using the self-consistently obtained electron distribution functions from the PIC simulations (which are in general non-Maxwellian), we find that the predictions of the quasilinear kinetic theory are in good agreement with the simulation results. By contrast, the use of Maxwellian distributions leads to a growth rate and electron-ion friction force that is around 2–4 times higher, and consequently significantly overestimates the electron transport. A possible method for self-consistently modelling the distribution functions without requiring PIC simulations is discussed

In the last decades, new combustion regimes, such as mixtures diluted by exhaust gas recirculation or burning lean stratified fuel/air mixtures have been studied to decrease pollutant emission and fuel consumption. Classical spark discharges are known to be very inefficient to ignite in these new regimes whereas non-equilibrium plasma discharges have shown promising results. In particular, several experimental studies have shown that the nanosecond spark discharge regime is one of the most promising techniques for plasma-assisted ignition and combustion. The key advantage of these ultra-short discharges is their low power consumption to efficiently produce highly reactive plasmas in gaseous mixtures containing air or nitrogen.

International audience; In this work we study the electron drift instability in Hall-effect thrusters (HETs) using a 2D electrostatic particle-in-cell (PIC) simulation. The simulation is configured with a Cartesian coordinate system modeling the radial-azimuthal (r − θ) plane for large radius thrusters. A magnetic field, B 0 , is aligned along the Oy axis (r direction), a constant applied electric field, E 0 , along the Oz axis (perpendicular to the simulation plane), and the E 0 × B 0 direction is along the Ox axis (θ direction). Although electron transport can be well described by electron-neutral collisions for low plasma densities, at high densities (similar to those in typical HETs), a strong instability is observed that enhances the electron cross-field mobility; even in the absence of electron-neutral collisions. The instability generates high frequency (of the order of MHz) and short wavelength (of the order of mm) fluctuations in both the azimuthal electric field and charged particle densities, and propagates in the E 0 × B 0 direction with a velocity close to the ion sound speed. The correlation between the electric field and density fluctuations (which leads to an enhanced electron-ion friction force) is investigated and shown to be directly responsible for the increased electron transport. Results are compared with a recent kinetic theory, showing good agreement with the instability properties and electron transport.

International audience; Anomalous electron transport is a long-standing problem in the understanding of Hall-effect thrusters. Recent results have suggested as a possible cause a kinetic instability, but few attempts have succeeded in implementing such phenomena in a fluid simulation of the thruster. The common approach in this case relies on including an ad-hoc model of the anomalous transport and so to fit experimental results. We propose here a comparison between the friction force and the anomalous heating arising from the ad-hoc model, with the corresponding effects coming from the use of the instability-induced transport. The results are obtained through a one-dimensional fluid simulation of the Hall-effect thruster with ad-hoc anomalous transport. The comparison shows good agreement between the two approaches, suggesting indeed that the instability-induced anomalous transport is the good candidate for reproducing the ad-hoc simulations and paving the way for a full self-consistent implementation of the phenomena in a fluid simulation.

International audience; Hall-effect thrusters, which are electrostatic devices based on an E B ´ plasma discharge, have successfully been used as satellite propulsion systems for the last few decades. However, the presence of anomalous electron cross-field transport is still poorly understood, and involves complex and strongly coupled mechanisms such as azimuthal electron drift instabilities and intense secondary electron emission (SEE) from the thruster walls. The present work focuses on the relative importance of these two phenomena. We use a 2D particle-in-cell/Monte Carlo collision model configured to simulate the radial-azimuthal directions near the thruster exit plane. A constant radial magnetic field and axial electric field are imposed, and electron drift instabilities are observed in the azimuthal (E B ´) direction. A simplified SEE model is implemented and an extensive parametric study is performed to directly determine the effect on electron transport. It is found that, for the operating conditions used in our simulations, SEE enhances the near-wall electron mobility by a factor 2, while reducing the bulk plasma mobility by about 20% (due to electron cooling). However, the dominant contribution to anomalous electron transport is still observed to be caused by electron drift instabilities driven by the E B ´ discharge configuration. SEE modifies the electron mobility profile, but the spatially-averaged value remains relatively constant. Three different operating regimes are identified depending on the SEE rate value: two that are stable, and a third which shows an oscillatory behaviour. In addition to electron transport, the kinetic simulations give new insight into the plasma sheath formation at the radial walls, and comparison with typical analytical sheath models demonstrate important differences.

International audience; A vibrational collisional model based on the database of the University of Bari is used to investigate non- equilibrium phenomena in nitrogen nozzle flows. For the cases studied, the vibrational distribution in the divergent section appeared to significantly deviate from a Boltzmann distribution. Multiquanta Vibra- tion-Translation processes are shown to have a major influence on the recombination of the flow and on the shape of the vibrational distribution along the nozzle axis. Based on these results, a reduced model is derived with n groups of vibrational levels with their own internal temperatures to model the shape of the vibrational distribution. In this model, energy and chemistry source terms are calculated self-consis- tently from the rate coefficients of the vibrational database. For the studied nozzle flows, a good agree- ment is observed between the results of the vibrational collisional model with 68 levels and those of the reduced model with only 3 groups of levels.

International audience; This paper presents simulations of an atmospheric pressure air discharge in a point-to-plane geometry with a dielectric layer parallel to the cathode plane. Experimentally, a discharge reignition in the air gap below the dielectrics has been observed. With a 2D fluid model, it is shown that due to the fast rise of the high voltage applied and the sharp point used, a first positive spherical discharge forms around the point. Then this discharge propagates axially and impacts the dielectrics. As the first discharge starts spreading on the upper dielectric surface, in the second air gap with a low preionization density of 10^4~\textc\textm^-3 , the 2D fluid model predicts a rapid reignition of a positive discharge. As in experiments, the discharge reignition is much slower, a discussion on physical processes to be considered in the model to increase the reignition delay is presented. The limit case with no initial seed charges in the second air gap has been studied. First, we have calculated the time to release an electron from the cathode surface by thermionic and field emission processes for a work function φ ∈ ≤ft[3,4\right] eV and an amplification factor β ∈ ≤ft[100,220\right] . Then a 3D Monte Carlo model has been used to follow the dynamics of formation of an avalanche starting from a single electron emitted at the cathode. Due to the high electric field in the second air gap, we have shown that in a few nanoseconds, a Gaussian cloud of seed charges is formed at a small distance from the cathode plane. This Gaussian cloud has been used as the initial condition of the 2D fluid model in the second air gap. In this case, the propagation of a double headed discharge in the second air gap has been observed and the reignition delay is in rather good agreement with experiments.