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Water is often used as a medium for preparation of nanoparticles in plasma. One way to obtain plasma in liquids is a nanosecond high voltage pulse applied on micrometer sharp electrode, so that the electric discharge is developed. Liquid water under the action of sharp pulse of the electric field may be disrupted so that cavities of nanometer scale would eventually appear and expand. Owing the electric field forces, those nanocavities rapidly elongate to the form of long needle-like ruptures in the liquid bulk. We study electron acceleration in these ruptures and analyze the production of secondary electrons in the water near the nanocavity surfaces. For electron transport in the nanocavity and for electron water-interactions we use Monte Carlo model based on Geant4-DNA simulation toolkit. Nanocavities are modelled as hollow cylindrical voids in liquid water with homogeneous electric field inside oriented along the cylindrical axis. Due to the nanometric scale of these voids, electrons can move collisionless inside, where are also accelerated by the action of the electric field. Primary electrons are injected as monoenergetic isotropic source from the inner surface of the void. We seek physical conditions, a combination of electric field strength and geometry of the cavity that would lead to the production of more than one secondary electron per single primary electron. This study is relevant for understanding of initial phases of electric discharge development in liquid water.

We investigate how the geometry of nanovoids present during the (sub)nanosecond electrical breakdown in liquid water influences the electron multiplication. Our analysis uses a particle-tracing Monte Carlo simulation toolkit Geant4-DNA. The electron multiplication in nanovoids is one of the possible scenarios describing the charge generation in liquid water. In our simplified model, we assume a constant homogeneous electric field, an ellipsoidal shape of nanovoids, and isotropic distribution of the primary electron's velocity. The quantity of interest is the number of ionizations per number of launched primary electrons. We study this yield of electrons as we vary the ellipsoid eccentricity parameter while keeping the volume constant. The nanovoids with zero eccentricity (spherical case) produce smaller yield since the suppressed length does not favor electron multiplication. On the other hand, a very prolonged ellipsoid causes the loss of most electrons because of early collisions with the void-liquid interface. Therefore, for a particular value of eccentricity, the yield is maximal. The results of this study contribute to the elucidation of the initial phases of discharge evolution in polar liquids and is one of the first steps towards quantitative assessment of the importance of microscopic parameters involved. The understanding of this phenomenon promises the explanation of macroscopic parameters observed in the (sub)nanosecond electrical breakdown experiments.

Recently, a bouncing-like mechanism for electron multiplication inside long nano-ruptures during the early stages of nanosecond discharge in liquid water has been proposed in (Bonaventura 2021 Plasma Sources Sci. Technol. 30 065023). This mechanism leads to the formation of electron avalanches within nano-ruptures caused by strong electrostrictive forces. The avalanche propagation is a self-sustaining process: the electrons emitted from the water surface to the cavity support the propagation of the avalanche and the avalanche itself is a source of the parent electrons impinging on the surface of the nano-rupture and causing secondary emission. We analyze the process of the electron secondary emission directly from the simulation results of the electron avalanche propagation. This allow us to perform an in situ study of the secondary emission and related physical processes. We present the results of an extensive parametric study performed using the state-of-the-art simulation toolkit Geant4-DNA for modeling electron-liquid water interactions. It is shown that the typical lifetime of an electron in an avalanche is about 0.1 to 0.2 picoseconds and that the electron experiences about 4 bounces before ending up in liquid water. In addition, it is shown that the secondary electrons are formed in a layer adjacent to the nano-rupture surface that is only a few nanometres thin. The secondary electron velocity distribution at the moment of the electron birth, the velocity space of electrons (re-)emitted from the water, and the velocity space of electrons at the moment of their impact to the cavity surface are analyzed in detail. Electron bouncing and secondary electron generation efficiency are quantified using the secondary emission coefficient, the secondary emission efficiency, and the effective energy consumed to produce new electrons.

Electron and ion currents to a cylindrical Langmuir (electrostatic) probe were calculated using the particle-in-cell/Monte Carlo (PIC/MC) self-consistent simulation for a neutral gas in the pressure range 2–3,000 Pa. The simulation enables us to calculate the probe currents even at high neutral gas pressures when the collisions of collected charged particles with neutral gas particles near the probe are important. The main aim of this paper is the calculation of probe currents at such high gas pressures and the comparison of the results with experimentally measured probe currents. Simulations were performed for two cases: (a) probes with varying radii in a non-thermal plasma with high electron temperature at low neutral gas pressure of 2 Pa (in order to verify the correctness of our simulations), and (b) probe with the radius of 10 um in the afterglow plasma with low electron temperature and a higher neutral gas pressure (up to 3,000 Pa). The electron probe currents obtained in case (a) show good agreement with those predicted by the orbital motion limited current (OMLC) theory for probes with radii up to 100 um for the given plasma conditions. At larger probe radii and/or at higher probe voltages, the OMLC theory incorrectly predicts too high an electron probe current for the plasma parameters studied. Additionally, a formula describing the spatial dependence of the electron density in the presheath in the collisionless case is derived. The simulation at higher neutral gas pressures, i.e. case (b), shows a decrease of the electron probe current with increasing gas pressure and the creation of a large presheath around the probe. The simulated electron probe currents are compared with those of measurements by other authors, and the differences are discussed.

This work presents a study on electron multiplication in cylindrical nanovoids formed in liquid water due to strong pulsed external electric fields. The state-of-the-art simulation toolkit Geant4-DNA is used to describe electron interactions in liquid water. Scaling laws for electron propagation are introduced, concluding that the product of the electric field strength E and the cavity radius R is a suitable parameter to compare simulation results for different values of E and R, and 1/R scaling is proposed for space and time variables. It is shown that the electron avalanche can grow inside of the nanovoid if E · R > 19.4 eV. The avalanche growth is fed by the emission of the secondary electrons from the surface of the nanovoid. This electron avalanche can also provide a higher total ionization yield along the nanovoid than the simple direct flight of electrons through the nanovoid length. Characteristic electron multiplication timescale and avalanche velocity are determined. Multiplication timescale is shown to be of the order of 1 ps or shorter for electron-multiplying conditions. The velocity of the electron avalanche is about 2.8 × 106 m s-1. The multiplication timescale and the avalanche velocity are consistent with recent experimental observations on nanosecond discharge initiation in liquid water.

We postulate that basic radiative signatures observed during the initial phases of nanosecond discharge in liquid water can be attributed to the electron–neutral bremsstrahlung process. Principal characteristics of the radiation collected from developing luminous filaments consist of a sharp decrease in the emission intensity at the short-wavelength side of the spectra, followed by a maximum and subsequent decrease in intensity towards near-infrared wavelengths. All these radiative features can be attributed to the electron–neutral bremsstrahlung produced by a bell-like energy distribution of the electrons. Such an electron energy distribution function is coherent with the concept of electric field emission into electrostriction-induced nanovoids. The findings of this work help in elucidating the hitherto unclear mechanism(s) of plasma generation in liquid water.

In this work, we examine initial phases of micro-discharges produced in deionized water by high-voltage pulses of nanosecond duration. We summarize results achieved by applying opto-electrical diagnostics with extremely high temporal (down to 30 ps) as well as spatial (down to m) resolutions. We have obtained frozen interferometric and shadowgraph images evidencing three distinct events. The first one, subcritical (no-discharge) event, is characterised by periodic perturbations of the index of refraction which depart from the anode surface and are pulled away with the speed of sound as an expanding envelope defined by the shape of the anode tip. One-dimensional hydrodynamic modelling of subcritical phase under conditions mimicking curvatures of real anode tips reveals basic characteristics of perturbations caused by dynamic balance between the hydrostatic and electrostrictive pressures consistent with experimental observations. The second one, dark or non-luminous discharge event, is characterised with the onset of few isolated very tiny tree-like structures growing from anode tip. Depending on the HV amplitude, the initial structures occur with delay of 2-3) ns after onset of HV pulse and subsequently expand with average velocity of (1-2)E7 cm/s creating very dense bush-like structures made of thin hair-like filaments in few nanoseconds. The third one, luminous discharge, follows (nearly simultaneously) the dark discharge event and unveils much simpler tree-like morphology determined by the extension of non-luminous bush-like structures. Characteristic dimensions of observed events range from about 1 micrometre (typical diameter of non-luminous filaments) to tens of micrometres (characteristic diameters of luminous filaments). Furthermore, we have addressed a possible role of microbubbles developing in the anode region due to the periodic HV pulses and verified that the UV-vis-NIR spectrometric signatures of the luminous phase notably change when replacing non-degassed DI water with the degassed one.

The emergence of a streamer from an ionisation wave and its expansion are ultra-fast processes shaping the very first moments of the streamer development, and are usually accessible only by complex numerical models. In this Letter, we report experimental evidence of the emergence of a streamer from an ionisation wave in 1.3 kPa air, a laboratory analogue of early-stage streamers emerging in geophysical Blue Starters and Jets. The radially and temporally resolved electric field patterns of an expanding streamer are determined by sub-nanosecond optical emission spectroscopy. As the emerged streamer expands, the electric field decreases by a factor of 1.4 in 1 ns. We quantify the radial expansion of the streamer head and its axial acceleration, reaching the velocity of 107 m s-1. In combination with electrical measurements, the transferred charge, electron density, and mean electron energy are quantified, enabling detailed insight into this ultra-fast phenomenon at its characteristic time-scale. © 2020 IOP Publishing Ltd., This research was funded by the Academy of Sciences of the Czech Republic under project M100431201. TH was supported by the European Science Foundation Research Networking Programme TEA-IS (ex-change Grant No. 4219). ZB was supported by the Czech Science Foundation, project No. 15-04023S. FJGV was supported by the Spanish Ministry of Science and Innovation (MINECO) under project ESP2017-86263-C4-4-R. TH is grateful for the support of project LM2018097 funded by the Ministry of Education, Youth and Sports of the Czech Republic.

The review provides an up-to-date overview and discussion of phenomena related to positive streamer breakdowns in short uniform and non-uniform field (corona) gaps. The terminology used to specify different types of streamer phenomena is critically discussed in light of a unified theory of high-pressure gas discharges describing the sequence of ionization events from initial electron avalanches up to a partial or complete breakdown. The emphasis is given to the understanding of the formation of an active cathode spot by the streamer arrival to the cathode, which is the critical but still obscure phase of the breakdown development. Based on the analysis including a computer simulation model a hypothesis is advanced that also such widely studied and practically important gas discharge phenomena as negative corona Trichel pulses and fast ionization instabilities in cathode regions of high-pressure gas discharges are due to the formation of positive streamers in the immediate cathode vicinity. The proposed hypothesis offers attractive feature of the unification of a wide scale of high-pressure gas discharges within the general class of positive streamer initiated breakdown phenomena. Moreover, it provides indications for further study in the field both by experiment and computer simulations.

The Particle In Cell/Monte Carlo Collisions (PIC/MCC) simulation was used for the calculation of electron and ion currents to a spherical Langmuir (electrostatic) probe. This simulation took into account the collisions of collected charged particles with neutral gas particles around the probe and it can calculate the probe currents at higher neutral gas pressures.

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.

We developed an extension of the spectrometric method to estimate a reduced electric field (E/N), which is applicable in nitrogen-containing plasmas. The method is based on the intensity ratio of the emission bands of the first negative system (FNS) of and the second positive system (SPS) of N2. It uses the emission occurring in the wavelength interval 375–410 nm, which includes six SPS and two FNS bands. The choice of the spectral window is guided by much simpler acquisition and processing of experimental data than the SPS(0, 0) and FNS(0, 0) pair that is typically used. Following this idea, we construct a kinetic model for pure molecular nitrogen, which determines the population of the upper states responsible for the FNS and SPS emission. Moreover, we perform sensitivity analysis of the kinetic model, which allows us to reveal the most significant processes for the investigated intensity ratios. For these processes, we provide an in-depth review of the kinetic data that are available in the literature. We use the fact that the spectral window investigated contains bands to obtain three independent intensity ratios with sufficient signal-to-noise ratio ((FNS(0, 0)/SPS(0, 2), FNS(0, 0)/SPS(1, 4), FNS(0, 0)/SPS(2, 5)), which are usable for more accurate electric field determination. We also provide analytical formulas representing intensity ratio dependencies on E/N. Furthermore, we focus on different spectrometric representations of FNS and SPS bands, which also affect the precision of E/N determination. We examine the FNS/SPS band profiles in terms of different rotational temperatures and instrumental functions. Finally, we propose a simple procedure that enables the use of bandhead intensities in the intensity ratio dependencies, thus avoiding the need to evaluate integral band intensities from the recorded spectra.

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.

International audience; The runaway electron mechanism is of great importance for the understanding of the generation of x- and gamma rays in atmospheric discharges. In 1991, terrestrial gamma-ray flashes (TGFs) were discovered by the Compton Gamma-Ray Observatory. Those emissions are bremsstrahlung from high energy electrons that run away in electric fields associated with thunderstorms. In this paper, we discuss the runaway threshold definition with a particular interest in the influence of the angular scattering for electron energy close to the threshold. In order to understand the mechanism of runaway, we compare the outcome of different Fokker–Planck and Monte Carlo models with increasing complexity in the description of the scattering. The results show that the inclusion of the stochastic nature of collisions smooths the probability to run away around the threshold. Furthermore, we observe that a significant number of electrons diffuse out of the runaway regime when we take into account the diffusion in angle due to the scattering. Those results suggest using a runaway threshold energy based on the Fokker–Planck model assuming the angular equilibrium that is 1.6 to 1.8 times higher than the one proposed by [1, 2], depending on the magnitude of the ambient electric field. The threshold also is found to be 5 to 26 times higher than the one assuming forward scattering. We give a fitted formula for the threshold field valid over a large range of electric fields. Furthermore, we have shown that the assumption of forward scattering is not valid below 1 MeV where the runaway threshold usually is defined. These results are important for the thermal runaway and the runaway electron avalanche discharge mechanisms suggested to participate in the TGF generation.

An established and widely used method for remote electric field determination is based on the ratio of the spectral band intensities of the first negative and second positive spectral systems of molecular nitrogen which does, however, require theoretically or experimentally obtained dependence R ( E / N ) . The aim of this work is to reduce the overall uncertainty in the theoretical dependence R ( E / N ) calculated in part I of this work. We present an in-depth review of the kinetic and cross section data that are available in literature for the most influential processes. By tracking the historical evolution of the kinetic data, their cross-validation by independent authors and by taking into account advances in the experimental methods, we separate datasets that have not been rendered inaccurate by later works. By doing so, we reduce the uncertainty of the theoretical R ( E / N ) dependence and propose corresponding confidence band to be used by scientific community.

Microwave interferometer is a useful device in plasma diagnostics. An important advantage of this device is that it does not disturb the plasma. However, in classical arrangement, microwave interferometer measurement yields a line integrated plasma density. Localized measurement of plasma density may be carried out using microwave interferometer with dielectric rod antennae. Electromagnetic wave propagating along such a dielectric rod is, in general, influenced by dielectric properties of outer medium i. e., the plasma. Phase velocity of electromagnetic wave propagating along a dielectric waveguide surrounded by plasma is computed and the results concerning microwave interferometry diagnostics are discussed.

We investigated a plasma excited by high power pulsed microwaves (MWs) (pulse duration 2.5 µs, repetition rate 400 Hz, peak power 105 W, frequency 9.4 GHz) in nitrogen at reduced pressure (pressure range 10–2000 Pa) with the aim of a better understanding of such types of discharge. The construction of the experimental device suppresses the plasma–wall interactions and therefore the volume processes are predominant. To obtain the temporal evolution of the electron density we used two MW interferometers at frequencies of 15 and 35 GHz with dielectric rod waveguides which gives them the capability of localized measurements. We estimated the effective collision frequency from the absorption of a measurement beam. Time resolved optical emission spectroscopy of the 1st negative system and the 2nd positive system was carried out, too. Due to a high power input the discharge dynamics was fast and the steady state was typically reached in 1 µs. We found that the effective collision frequency has the same temporal behaviour as the 2nd positive system of N2, including a characteristic maximum at the beginning of the pulse.

The time development of the electron distribution function and electron macroscopic parameters was studied by solving the time-dependent Boltzmann equation for low temperature plasma. A new technique for solving the time-dependent Boltzmann equation was developed. This technique is based on a multi-term approximation of the electron distribution function expansion in Legendre polynomials. The results for electron relaxation in Reid's ramp model and argon plasma are presented. The effect of negative mobility was studied and is discussed for argon plasma. Finally, the time-dependent Boltzmann equation was solved for pulsed microwave discharge in nitrogen. The accuracy of all results was confirmed by the Monte Carlo simulation.

A pulsed microwave discharge burning in pure nitrogen was studied theoretically. The time-dependent Boltzmann equation for electrons was solved numerically in multi-term approximation. It was assumed that the discharge was ignited by a 100 kW microwave (f = 9.4 GHz) pulses with 2.5 µs duration; the repetition frequency was 400 Hz. It was shown that the electron distribution function approaches very quickly the steady state distribution function after a change of the amplitude of electric field intensity. The steady state time averaged values of electron mean energy, diffusion and rate coefficients and drift velocity were calculated for different values of electric field intensity. With these values the actual values of electric field intensity from a previous experiment were determined from the measured time dependence of electron concentration. The calculated values were compared with previous experimental results.

In the paper we study, be means of microwave interferometry, the evolution of electron density in afterglow of pulsed driven nitrogen discharge. Recombination coeffients are derived, too.

The motion of argon ions in its parent gas in the electric field was studied using standard Monte Carlo collision method in order to fit the collision cross sections for momentum transfer and for resonant charge transfer on the experimental data. The classical Langevin formula for polarization scattering was used for the latter. As a fitted parameter the momentum transfer cross section was used. The experimental dependency of the drift velocity on the ratio of the electric field intensity and the neutral gas number density was used as a fitted data. The fitted collision cross sections were used for the Monte Carlo study of the influence of ion-neutral collisions on the saturated ion probe current. The calculated ion current characteristics were compared with the results of Langmuir probe measurements under different plasma conditions.

International audience; This paper presents 2D simulations of nanosecond discharges between two point electrodes for four different H2–air mixtures defined by their equivalence ratios phgr (i.e. phi =0, air, phi =0.3, lean mixture, phi =1, stoichiometric mixture and phi =1.5, rich mixture) at atmospheric pressure and at an initial temperature of 1000 K. In a first step, we have shown that the mixture composition has only a very small influence on the discharge dynamics and structure during the streamer phase and up to the formation of the plasma channel between the two point electrodes in H2–air mixtures with phi in [0,1.5]. However, as the plasma channel is formed slightly earlier as the equivalence ratio increases, for a given voltage pulse, the duration of the nanosecond spark phase increases as the equivalence ratio increases. As expected, we have shown that excited states of N2 (and in particular N2(A)) and radicals (and in particular O(D), O(P), H and OH) are very efficiently produced during the voltage pulse after the start of the spark phase. After the voltage pulse, and up to 100 ns, the densities of excited states of N2 and of O(D) decrease. Conversely, most of the O(P), H and OH radicals are produced after the voltage pulse due to the dissociative quenching of electronically excited N2. As for radicals, the gas temperature starts increasing after the start of the spark phase. For all studied mixtures, the density of O(P) atoms and the gas temperature reach their maxima after the end of the voltage pulse and the densities of O(P), H and OH radicals and the maximal gas temperature increase as the equivalence ratio increases. We have shown that the production of radicals is the highest on the discharge axis and the distribution of species after the voltage pulse and up to 100 ns has a larger diameter between the electrodes than close to both electrode tips. As for species, the temperature distribution presents two hot spots close to the point electrode tips. The non-uniform distributions of radical densities and gas temperature obtained after the nanosecond voltage pulse provide accurate initial conditions for 2D reactive flow codes to study the combustion ignition on longer timescales and compare with experiments.

A method for treatment of boundary conditions and particle loading in a self-consistent semi-infinite Particle-In-Cell/Monte Carlo simulation is presented. A non-ionizing, collisional plasma in contact with an electrode was assumed. The simulation was performed for a spherical probe with constant probe potential. The motion of charged particles was calculated in three dimensions, but only the radial charge distribution and thus only radial electric field were assumed. The particle loading has to be done with an appropriate velocity distribution with a radial drift velocity. This drift velocity has to be calculated from the probe current, and therefore, a self-consistent (iterative) approach is necessary. Furthermore, correct values of particle densities and electric field potential at the outer boundary of the computational domain have to be set using asymptotic formulae for particle density and electric field potential. This approach removes the “source sheath” which is created artificially, if incorrect...

Many plasma applications could benefit from the versatile plasma source operable at a wide-pressure-range, e.g., from the fraction of Pa to the super-atmospheric conditions. In this paper, the basic characteristics of wide-pressure-range plasma source based on the coplanar dielectric barrier discharge is given. The operational characteristics of this plasma source were measured in nitrogen at pressures ranging from 101 Pa (resp. 10−4 Pa) to 105 Pa. Measurements of the plasma geometry, breakdown voltage, and micro-discharges' behaviour revealed three operational regimes of this plasma source: “high pressure,” “transitional” and “low-pressure” with vague boundaries at the pressures of approx. 10 kPa and 1 kPa. It was found that the plasma layer of coplanar dielectric barrier discharge could be expanded up to several centimetres to the half-space above the planar dielectric barrier when the gas pressure is reduced below 1 kPa, which provides an outstanding space to tailor the source for the specific applicat...

The generation of x- and gamma-rays in atmospheric discharges has been studied intensively since the discovery of terrestrial gamma-ray flashes (TGFs) by the Compton gamma-ray Observatory in 1991. Emissions are bremsstrahlung from high energy particles accelerated in large scale atmospheric electric fields associated with thunderstorms. Whereas observations now are many, both from lightning and the laboratory, the phases of the discharge where emissions are generated are still debated and several processes for electron acceleration have been put forward by theorists. This paper address the electron acceleration in streamer region of lightning. We present the first 'beam-bulk' model of self-consistent streamer dynamics and electron acceleration. The model combines a Monte Carlo Collision code that simulates the high-energy electrons (> 100 eV) and a fluid code that simulates the bulk of the low-energy electrons and ions. For a negative streamer discharge, we show how electrons are accelerated in the large electric field in the tip of the streamer and travel ahead of the streamer where they ionize the gas. In comparison to the results obtained with a classical fluid model for a negative streamer, the beam-bulk model predicts a decrease of the magnitude of the peak electric field and an increase of the streamer velocity. Furthermore, we show that a significant number of runaway electrons is lost by diffusion outside of the streamer tip. The results presented here do not yet include extra amplification nor acceleration far away from the streamer to explain the electron energies seen in TGFs. Still, in the light of those results, we emphasize that the production of runaway electrons from streamers needs to be simulated including the self-consistent feedback of runaways on the streamer. Simulations with a beam-bulk model may not only help to understand the fundamental atmospheric processes behind TGFs, but also pave the way for the interpretation of remote sensing of the most energetic discharges in the Earth's atmosphere and thus help to address their environmental impact.

The initial stages of transient luminous events (TLEs) occurring in the upper atmosphere of the Earth are, in a certain pressure range, controlled by the streamer mechanism. This paper presents the results of the rst laboratory experiments to study the TLE streamer phenomena under conditions close to those of the upper atmosphere. Spectrally and highly spatiotemporally resolved emissions originating from radiative states N2(C3Pi u) (second positive system) and N2+(B2Sigma u+) (first negative system) have been recorded from the positive streamer discharge. Periodic ionizing events were generated in a barrier discharge arrangement at a pressure of 4 torr of synthetic air, i.e. simulating the pressure conditions at altitudes of cca. 37 km. Employing Abel inversion on the radially scanned streamer emission and a 2D tting procedure, access was obtained to the local spectral signatures within the over 10^6 ms-1 fast propagating streamers. The reduced electric eld strength distribution within the streamer head was determined from the ratio of the band intensities with peak values up to 500 Td and overall duration of about 10 ns. The 2D pro les of the streamer head electric elds were used as an experimentally obtained input for kinetic simulations of the streamer-induced air plasma chemistry. The radial and temporal computed distribution of the ground vibrational levels of the radiative states involved in the radiative transitions analyzed (337.1 nm and 391.5 nm), atomic oxygen, nitrogen, nitric oxide and ozone concentrations are vizualized and discussed in comparison with available models of the streamer phase of Blue Jet discharges in the stratosphere.

International audience; The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the solution. For initial separation of both streamers smaller or comparable to the longest characteristic absorption length of photoionization in air, we have found that the streamers tend to merge at the moment when the ratio between their characteristic width and their mutual distance reaches a value of about 0.35 for positive streamers, and 0.4 for negative ones. Moreover it is demonstrated that these ratios are practically independent of the applied electric field, the initial seed configuration, and the pressure.

International audience; The electric field in streamer discharges in air can be easily determined by the ratio of luminous intensities emitted by N2(C) and N2+(B) if the steady-state assumption of the emitting states is fully justified. At ground pressure, the steady-state condition is not fulfilled and it is demonstrated that its direct use to determine the local and instantaneous peak electric field in the streamer head may overestimate this field by a factor of 2. However, when spatial and time-integrated optical emissions (OEs) are considered, the reported results show that it is possible to formulate a correction factor in the framework of the steady-state approximation and to accurately determine the peak electric field in an air discharge at atmospheric pressure. A correction factor is defined as G= Es/Ee, where Ee is the estimated electric field and Es is the true peak electric field in the streamer head. It is shown that this correction stems from (i) the shift between the location of the peak electric field and the maximum excitation rate for N2(C) and N2+(B) as proposed by Naidis (2009 Phys. Rev. E 79 057401) and (ii) from the cylindrical geometry of the streamers as stated by Celestin and Pasko (2010 Geophys. Res. Lett. 37 L07804). For instantaneous OEs integrated over the whole radiating plasma volume, a correction factor of G ∼ 1.4 has to be used. For time-integrated OEs, the reported results show that the ratio of intensities can be used to derive the electric field in discharges if the time of integration is sufficiently long (i.e. at least longer than the longest characteristic lifetime of excited species) to have the time to collect all the light from the emitting zones of the streamer. For OEs recorded using slits (i.e. a window with a small width but a sufficiently large radial extension to contain the total radial extension of the discharge) the calculated correction factor is G ∼ 1.4. As for OEs observed through pinholes, the reported results demonstrate that for local OEs, the G coefficient depends slightly on the radial position and is in a range [1.24, 1.28]. For line-integrated OEs, the radial variation of G is more significant and G is in the range [1.24, 1.38]. Finally, it is noted that the use of different sets of Einstein coefficients and quenching rates of excited states has negligible influence on the value of G.

This paper presents simulations of an air plasma discharge at atmospheric pressure initiated by a needle anode set inside a dielectric capillary tube. We have studied the influence of the tube inner radius and its relative permittivity εr on the discharge structure and dynamics. As a reference, we have used a relative permittivity εr = 1 to study only the influence of the cylindrical constraint of the tube on the discharge. For a tube radius of 100 µm and εr = 1, we have shown that the discharge fills the tube during its propagation and is rather homogeneous behind the discharge front. When the radius of the tube is in the range 300–600 µm, the discharge structure is tubular with peak values of electric field and electron density close to the dielectric surface. When the radius of the tube is larger than 700 µm, the tube has no influence on the discharge which propagates axially. For a tube radius of 100 µm, when εr increases from 1 to 10, the discharge structure becomes tubular. We have noted that the velocity of propagation of the discharge in the tube increases when the front is more homogeneous and then, the discharge velocity increases with the decrease in the tube radius and εr. Then, we have compared the relative influence of the value of the tube radius and εr on the discharge characteristics. Our simulations indicate that the geometrical constraint of the cylindrical tube has more influence than the value of εr on the discharge structure and dynamics. Finally, we have studied the influence of photoemission processes on the discharge structure by varying the photoemission coefficient. As expected, we have shown that photoemission, as it increases the number of secondary electrons close to the dielectric surface, promotes the tubular structure of the discharge.

International audience; This paper presents simulations of positive and negative streamers propagating between two point electrodes in preheated air at atmospheric pressure. As many discharges have occurred before the simulated one, seed charges are taken into account in the interelectrode gap. First, for a pre-ionization background of 109 cm−3, we have studied the influence of the data set used for transport parameters and reaction rates for air on the simulation results. We have compared results obtained in 1997 using input parameters from Morrow and Lowke and from Kulikovsky. Deviations as large as 20% of streamer characteristics (i.e. electric field in the streamer head and body, streamer velocity, streamer radius, streamer electron density) have been observed for this point-to-point configuration. Second, we have studied the influence of the pulsed voltage frequency on the discharge structure. For the studied discharge regime, a change in the applied voltage frequency corresponds to a change in the pre-ionization background. In this work, we have considered a wide range of pre-ionization values from 104 and up to 109 cm−3. We have noted that the value of the pre-ionization background has a small influence on the electron density, electric field and location of the negative streamer head. Conversely, it has a significant influence on the positive streamer characteristics. Finally, we have compared instantaneous and time-averaged optical emissions of the three band systems of N2 and {\rm N}_2^+ (1PN2, 2PN2 and {\rm 1NN}_2^+ ) during the discharge propagation. We have shown that the emission of the 2PN2 is the strongest of the three bands, in agreement with experimental observations. It is interesting to note that even with a short time averaging of a few nanoseconds, which corresponds to currently used instruments, the structure of the time-averaged emission of the 2PN2 is different from the instantaneous one and shows negative and positive streamers with smaller radial expansions and more diffuse streamer heads.

Recently, laser schlieren deflectometry (LSD) had been successfully employed as a temperature measurement method to reveal the heat convection generated by micro filaments of a self-organized non-thermal atmospheric plasma jet. Based on the theory of the temperature measurements using LSD, in this work, three approaches for an application of the method are introduced: (i) a hyperbolic-like model of refractive index is applied which allows an analytical theory for the evaluation of the deflection angle to be developed, (ii) a Gaussian shape model for the filament temperature is implemented which is analyzed numerically and (iii) an experimental calibration of the laser deflection with a gas mixture of helium and argon is performed. Thus, these approaches demonstrate that a universal relation between the relative maximum temperature of the filament core (T 1 /T 0 ) and a the maximum deflection angle δ 1 of the laser beam can be written as T 1 /T 0 =(1 − δ 1 /δ 0 )−1 , where δ 0 is a parameter that is defined by the configuration of the experiment and by the assumed model for the shape of the temperature profile.

This work presents a numerical model of hydrogen plasma in a microwave coaxial discharge at low pressure (25–250 Pa). The model is a mixed two-dimensional (2D)/three-dimensional (3D) model in that it combines three-dimensional geometry for the electromagnetic field and two-dimensional geometry for the transport equations. The model is validated against experimental results available in the literature and, where possible, simulations of comparable discharges. The model shows reasonable agreement in the relevant pressure range. A parametric study with respect to pressure is carried out and it is observed that the plasma contracts towards the quartz tube with increasing pressure. Increasing the pressure also influences the abundance of H + ions but on the other hand it has little impact on hydrogen dissociation degree and electron temperature. Furthermore, the uniformity of the plasma above the substrate holder is analyzed. It is observed that at pressures over 150 Pa, the plasma gets non-uniform in the direction parallel to the plasma lines. Finally, the uniformity of particle and energy fluxes to the substrate holder are analyzed. Knowing the fluxes is especially useful for the material applications of the device.

A spatio-temporal theoretical model of pulsed microwave discharge was developed. This model is based on the macroscopic continuity equation for electrons and on the wave equation for an electromagnetic wave passing through the discharge plasma. These equations were solved together and in a self-consistent manner. For simplicity, the continuity equation was solved in one dimension only and the electromagnetic wave was assumed to be plane and transversal. Both equations were solved numerically and the spatio-temporal dependences of electron concentration and the amplitude of the microwave electric field were obtained. It was found that the discharge development depends, significantly, on the initial spatial distribution of electron concentration. Two different cases were studied: the discharge development during the first microwave pulse only and after several successive pulses. The calculations were performed particularly for the discharge in nitrogen. The results were compared with experimental data from our previous work.