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Terrestrial gamma ray flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by relativistic runaway electron avalanches (RREAs). It is usually admitted that the number of high‐energy electrons produced in the brightest TGFs remains mostly confined within a range from 1017 to 1019. To understand the constraints in the development of RREAs, we perform self‐consistent simulations using a newly developed model with a finite acceleration region and various injection rates. We find that RREAs should naturally self‐quench for a fixed total number of runaway electrons, and hence a fixed number of bremsstrahlung photons. From the idea that TGF sources quench themselves, we derive a simple equation controlling the total number of runaway electrons. In this framework, the existence of a saturation in the electron density discovered in a previous work places a lower limit on TGF durations. Plain Language Summary: Terrestrial gamma ray flashes (TGFs) are short bursts of high‐energy photons occurring during thunderstorms. They are believed to be produced by energetic electrons accelerating due to the intense electric field, forming a Relativistic Runaway Electron Avalanche (RREA). Discovered fairly recently, many of the TGF features remain unexplained. In this article, we aim to understand the constraint on the number of high‐energy electrons produced during TGFs, that always remains confined between 1017 and 1019. Using a newly developed simulation model, we find that RREAs naturally quench themselves when the number of high‐energy electrons and photons reach the range previously mentioned. Based on a limited number of fundamental processes, we were able to derive a simple equation controlling the total number of runaway electrons and deduce a lower limit for TGF durations. Key Points: There is a maximum low‐energy electron density reachable in Terrestrial Gamma Ray Flashe (TGF) sources when relativistic runaway electron avalanches (RREAs) reach saturation: nesat∼1015 ${n}_{e}^{\mathit{sat}}\sim 1{0}^{15}$ m−3There exists a minimum TGF timescale equal to the RREA timescale: τmin ∼ 1 μsThe self‐quenching of the TGF sources implies a maximum number of electrons Ne ∼ 1017 [ABSTRACT FROM AUTHOR]

Gas Insulated Switchgear (GIS) is extensively utilized in power grid systems. However, the existence of numerous photoelectrons in the SF6 gas during X-ray non-destructive testing in ultra-high-voltage (UHV) GIS equipment may induce gas streamer discharge in a strong electric field. To address this issue, in this work, the impact of X-ray irradiation on the SF6 gas discharge in GIS equipment was systematically analyzed. Firstly, one GIS engineering mode with a three-dimensional electric field was established, and a physical GIS model was established by the Geant4 and Garfield++ codes. Secondly, the electrons’ ionization, and multiplication processes in SF6 gas during the X-ray irradiation were studied. Finally, a test platform with an equivalent electric field tube, which had the same intensity as in the GIS equipment, was established to verify the physical GIS model. X-ray beams with 0.1 MeV, 0.16 MeV, 0.3 MeV, and 1.25 MeV energy were used during the test process. From our analysis, it was concluded that X-ray irradiation can cause an electron avalanche in SF6 gas and the intensity of the avalanche is low, which is far away from the appearance of the streamer discharge. [ABSTRACT FROM AUTHOR]

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Terrestrial Gamma Ray Flashes (TGFs) are short bursts of gamma rays occurring during thunderstorms. They are believed to be produced by Relativistic Runaway Electron Avalanches (RREAs). In this paper, we present a new numerical model based on the Particle‐In‐Cell (PIC) method to simulate the interactions between the electromagnetic fields and the electron avalanche self‐consistently. The code uses a cylindrical Yee lattice to numerically solve the electromagnetic fields, a Monte Carlo approach to simulate collisions with air molecules, and a plasma fluid model to calculate the effects of low‐energy electrons and ions. The model is first tested through the reproduction of dispersion relations in a hot plasma. RREAs propagating under a homogeneous background electric field are then simulated. Owing to the self‐consistent nature of this description, we report here new physical properties such as saturation processes in the electron density and in the number of high‐energy electrons, detailed dynamical screening of the electric field in the ion trail of the avalanche, and the associated electric currents. We find that the saturation of RREAs is obtained when the numbers of high‐energy electrons and photons is consistent with those believed to be representative of TGF sources. Key Points: Development of a self‐consistent model coupling a Monte Carlo code with an electromagnetic particle‐in‐cell code to simulate Relativistic Runaway Electron Avalanches (RREAs)We identify a saturation phenomenon of the RREA, constraining the maximum number of high‐energy electrons and photons in terrestrial gamma‐ray flashesOnce saturation is reached, the electric field is partially screened, preventing the subsequently injected electrons from accelerating [ABSTRACT FROM AUTHOR]

We deals with the Monte Carlo simulation of the Townsend discharge current in a vicinity of minimum of Paschen's curve when the high reduced electric fields, E/p = (200–660) V/(cm Torr), are achievable. The main idea in description of the steady-state mode is that a great number of electron avalanches simultaneously generated in the gap provides the current in the external electric circuit. The impact ionization coefficient α (the first Townsend coefficient), obtained in modeling, is in a good agreement with the experiments on measuring the prebreakdown current. However, the interpretation of the process of electron multiplications needs in corrections. The classical impact ionization coefficient is conventionally introduced with invoking the notion of electron drift velocity. In the case of high reduced electric fields, the runaway electrons, which move in the regime of continuous acceleration, essentially contribute both in the expansion of the electron cloud and in the ionization multiplication of the initial emission current. [ABSTRACT FROM AUTHOR]

A mathematical model for the development of an electron avalanche and an avalanche-streamer transition in the discharge gaps of an ozonizer is proposed, taking into account the influence of an electric field created by the avalanche itself and the effect of electron attachment to neutral particles, as well as the processes of recombination of electrons with positive ions and photoionization of neutral particles. Based on the model, an iterative method has been developed that makes it possible to determine the size dependence of an electron avalanche, the number of electrons formed in it, and the number of emitted photons leading to the initialization of secondary avalanches on the distance traveled by the front of the primary avalanche. [ABSTRACT FROM AUTHOR]

Transfer of bulk electric power required in the modern world can be realized only through Extra High Voltage and Ultra High Voltage transmission lines. The scenario is dominated by overhead lines in which electromagnetic noise generated by corona is an important concern. Corona-induced currents propagate along line conductors producing electromagnetic noise, which is essential to be quantified. Towards this end, the present work aims to investigate basic mechanism of current induction using an isolated avalanche developing under space charge modulated background field. Beginning with the complete electric field produced by an avalanche, the corresponding induced currents are quantified, and the structure of electric and magnetic fields is extracted. The well-known time-domain electric field integral equation is employed for the purpose. The basic issue with long transmission line modelling is amply demonstrated. Since single avalanche is the basic mechanism behind corona, general inferences drawn are applicable for corona on transmission lines. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

It is shown that, in addition to the well-known Townsend and streamer discharges in gas, there is a third type of discharge, namely nanosecond diffuse-channel discharge. It occurs in a highly overvolted gas gap. The study is carried out on the example of air at normal conditions in a uniform electric field. In this case, the ratio , where d is the gap spacing and xc is the electron avalanche critical length. The electric field at the head of such an avalanche reaches 106 V cm–1 and higher, therefore, it emits runaway electrons, which create new electrons ahead of the old ones. An avalanche chain is formed, formally similar to a streamer but with low electrical conductivity. The runaway electrons and ultraviolet photoemission from the cathode contribute to the accumulation of secondary electrons in the gap. This leads to the appearance of a diffuse glow discharge, which then turns into a channel discharge and in an arc. The dependence of the overvoltage coefficient η on the product pd is calculated, where p is the gas pressure at d/xc = 10. It is compared with the well-known curve that separates Townsend and streamer discharges in air. [ABSTRACT FROM AUTHOR]

A mathematical model of electron avalanches and avalanche–streamer transitions in air is presented that is based on the drift–diffusion model of discharges and takes into account the drift of electrons in an electric field, impact ionization of molecules by electrons, and their adhesion and detachment. The transition criterion is the appearance of a quasi-neutral plasma channel between the avalanche and its wake. An estimate is given of the critical number of electrons and the minimum tension between the avalanche and its wake at the moment of the avalanche transformation into a streamer in air under normal atmospheric conditions. Discharges were studied in intervals of 0.1–0.5-cm length with a homogeneous field with an intensity of (5–8) × 104 V/cm. It is shown that the critical number of electrons weakly depends on the value of the intensity and is in the range of (3.9–5.5) × 107. The stability of the applied mathematical model to changes in its parameters and the correspondence of the calculation results in confirmation of the known patterns of development of avalanches and avalanche–streamer transitions. [ABSTRACT FROM AUTHOR]

The dynamics of an electron avalanche starting from the flat cathode surface and from the tops of microtips of different heights on the cathode surface is compared. The dynamics of avalanches was simulated in a changing electric field of the forming cathode sheath of a self-sustained high-pressure volume discharge with preliminary ionization of the gaseous medium. The aim of this work was to study the possibility of the development of instability during the formation of the cathode sheath. It is shown that the start from the top of the microtip gives the avalanche an advantage both in the increase in the number of electrons and in the distance traveled in comparison with the avalanche that started from a flat surface. This advantage is due to the region of enhancement of the electric field produced by the microtip and increases with the height of the tip. Areas of increased plasma density formed by avalanches that start from microtips can create an initial inhomogeneity necessary for the development of instability during the formation of the cathode sheath. The possible mechanisms of the development of instability in the cathode sheath are analyzed. [ABSTRACT FROM AUTHOR]

Breakdown voltage (BDV) is calculated for two electrode structures, namely, sphere and donut gaps, operating in air at atmospheric pressure. The calculation is based on the streamer BD criterion. COMSOL software package is used for field analysis and calculation of critical number of electrons by assessing integrals of the efficient ionization coefficient along field lines. Thus, also lengths of critical avalanches that can propagate from both electrodes were obtained. First, simulations were performed for sphere gaps at conditions standardized by IEEE to derive critical number of electrons for highly reliable experimental data. It was shown that these numbers deviate greatly from the widely accepted 108 number, and that clear tendencies for the deviations exist depending on the gap to sphere diameter ratio. This assisted us in the second part of this work, which is a description of a spark gap (SG) formed by two donuts. Such gaps are compact and can serve as closing switches, and as a crude HV measurement means. Experimental results and comparison to calculated BDVs are reported. These two examples illustrate a simple and effective method of BDV calculation in arbitrary geometries with weakly nonuniform field for well-characterized gases at moderate pressures; it can be used with industry-standard software in HV practice. [ABSTRACT FROM AUTHOR]

Electron multiplication in high-pressure pure xenon was studied in the 0.5–3.0 MPa pressure range using a cylindrical proportional counter. The electron multiplication factor and the first Townsend ionization coefficient were determined, thus expanding collective knowledge beyond the previous studies, which were limited to 1.0 MPa. The measured electron multiplication factor falls between 15 and 2400 for the investigated pressure range. The density-reduced first Townsend ionization coefficient in this work is larger than that obtained for low-pressure xenon. In addition, the density-reduced first Townsend ionization coefficient was found to be density dependent. It was also found that the energy resolution deteriorates with increasing pressure. However, when the electron multiplication factor is several hundred, the energy resolution in high-pressure pure xenon was found to be better than that in commonly used xenon-based gas mixtures. [ABSTRACT FROM AUTHOR]

The insulation design of high-voltage equipment is based on physical information about surface discharge mechanism. However, few studies have provided the information. This paper presents a peculiar-surface discharge characteristic in the presence of particle around an epoxy surface. Surface discharge experiments were conducted to measure partial discharge (V P) and surface flashover voltage (V F) with particle locations from the epoxy surface in atmospheric air. There was no the significant change in V P on the particle location. In contrast, V F revealed the distinctive-insulation characteristic that showed its peak. This characteristic was described from the space charge and the proposed surface discharge mechanism. • Discharge experiments were performed in the presence of a particle around an epoxy. • The flashover voltage showed a peak at a particular position of the particle. • The surface discharge mechanism was proposed to interpret the peak of flashover. [ABSTRACT FROM AUTHOR]

The simulation of electron avalanches and avalanche size distributions in methane is presented in this paper. A model for electron transport under the influence of a constant electric field based on the Monte Carlo method is described in detail. The model is verified and then used to simulate the avalanche development, to calculate the number of electrons in the avalanche (avalanche size), and to determine the avalanche size distribution. The simulated avalanche size distributions in methane are compared with the experimental results, and a good agreement is observed. The influence of inter‐electrode distance, pressure, and reduced electric field on the shape of the avalanche size distribution is discussed. The assumption from the literature that for a constant reduced electric field the shape of the reduced avalanche size distribution is independent of the mean size of the avalanche is confirmed for a wide range of experimental conditions. The simulations have shown that avalanche size distributions depend only on the reduced electric field, confirming the similarity principle. [ABSTRACT FROM AUTHOR]

Current research on gas discharge theory has made significant development in terms of numerical simulation, but its analytical description of streamer mechanism remains overly simplified, as it is still based on the electron avalanche model characterized with the exponential growth and infinite breakdown current. This paper presents a simple analytical method of gas discharge based on the classic logistic model and covers four aspects. First, it gives the exact definition of generation and mortality rate of electron number, establishes a logistic differential equation and a logistic iteration model for streamer mechanism, and derives deterministic analytical and iterative solution. Second, we also extend the mortality rate to include negative value, thus allowing the logistic model to describe both exponential growth and S shape growth scenarios, and provide criteria for categorizing spark breakdown, Townsend discharge, and stable discharge (glow, arc, aka saturated streamer). Third, the logistic differential model can be transformed into an iterative model. From that we derive the criteria for evaluating discharge instability. Last, although our model is 1-D, but it is still practical and easy to use given its clear analytical expression of underlying physical mechanism. [ABSTRACT FROM AUTHOR]

High electric breakdown strength of insulating materials is essential to improving the reliability of the electricity grid, reducing the size of electric devices, saving energy, protecting the environment, and reducing costs. Traditionally, dielectric breakdown strength is increased by exploiting its dependence on the thickness of the dielectric material, based on the electron impact ionization and avalanche theory by Townsend (1900) and Seitz (1949) [9]. However, at present there has been little research addressing the role of the transverse dimension (perpendicular to the direction of the electric field) in the avalanche breakdown process, and no results about research in nanoscale. An insulation breakdown prototype of a 1D nanocell was constructed. It consisted of an air-column and Al 2 O 3 solid wall. Based on the analysis and comparison between nanocell geometrical dimensions and avalanche physical dimensions, it was found that the properties of the 1D nanocell diverges from the gas/solid discharge theories of Townsend and Seitz. Along with the I-V results of 1D nanocell by C-AFM (Conductive-Atomic Force Microscope), it was demonstrated that electrical breakdown cannot be caused by electron avalanche in 1D nanocell. The discharge properties of Al 2 O 3 NPT (nano pore template) with nanocells array and when it inserted into the air gap as a barrier were studied to further demonstrate the capability of 1D nanocells on the electrical characteristic of macroscale material. Results showed that the scale effect of nanocells have an obvious role in improving the dielectric breakdown voltage, with singular discharge phenomena identified. This study proposes a new super-insulator prototype of 1D nanocell and supplies a novel thought for constructing high performance nanostructured dielectrics for more wide applications, and provides a scientific basis on the interconnection among Micro-Meso-Macro scales. [ABSTRACT FROM AUTHOR]

We present an improved numerical model for anode initiated electron avalanche breakdown of a dielectric-vacuum interface. An initiating event occurs in the high field region near the anode triple junction to start the first avalanche. The first avalanche grows and then stops, and a new one starts closer to the cathode. The breakdown process is modeled as a sequence of avalanches progressing from the anode to the cathode. [ABSTRACT FROM PUBLISHER]

[Display omitted] • A phenomenological model for anodic growth of TiO 2 nanotube arrays is developed. • Nucleation of O 2 bubbles is the porous layer initiation step. • First anodization stages play a key role in the evolution of oxide nanostructuration. • Oxide layer dissolution is not a field activated process. • Simultaneous fitting of j/t profiles and morphological layer features were described. In this work, we develop a phenomenological model describing the growth of TiO 2 nanotube arrays (NTA-TiO 2) by titanium anodization in ethylene glycol-based electrolytes containing fluoride. NTA-TiO 2 formation is described in terms of the well-known High-Field mechanism (HFM) considering film thinning by dissolution, and the electronic current contribution according to the Oxygen Bubble Mold (OBM) model, as it has been previously reported. For the first time, the inclusion of the nucleation of oxygen bubbles as the rate determining step at early anodization times is considered. By simultaneous fitting of the potentiostatic j / t profiles and the time evolution of morphological features such as pore radius, layer thickness and density of pores, the behavior observed for several experimental conditions is accurately described, in contrast to previously reported Field Assisted Dissolution (FAD) and OBM models. Proposed model allows obtaining physical and phenomenological information concerning the formation and growth of nanoporous oxide films as well as their morphological properties. Results also indicate that fluoride species play a key role at the early anodization stages, determining the subsequent film morphology evolution. Also, conclusive evidence for a chemical-type instead of field-assisted film dissolution process is obtained. [ABSTRACT FROM AUTHOR]

Some problems of the theory of electron transfer in gases under the action of a strong external electric field is considered in the paper. Based on the three-dimensional ELSHOWalgorithm, samples of states of particles in an electron avalanche are obtained for a given time moment in order to calculate the corresponding 'diffusion radii' and diffusion coefficients. Randomized projection estimators and kernel estimators (for test purpose) are constructed with the use of grouped samples for evaluation of the distribution density of particles in an avalanche. Test computations demonstrate a high efficiency of projection estimators for calculation of diffusive characteristics. [ABSTRACT FROM AUTHOR]

The audible noise (AN) production mechanism caused by corona discharge in ultrahigh voltage transmission lines is less understood. The study on sound pressure characteristic is necessary to obtain the inherent relation between AN and corona discharge. In this paper, the experimental research on single-point direct current (dc) corona discharge was evolved and the time-domain sound pressure waveform was obtained using capacitor microphone. The experiment results show that the dc corona discharge comprises multiple subsequent discharge pulses. The discharge voltage and the electrode polarity have a direct effect on the rising time and pulsed width of the single current pulse. The waveform of sound pressure produced by single discharge is a bipolar microsecond pulse, which lags behind the current pulse in time domain. The time delay is propagation time of sound signal from the discharge spot to the measurement spot. Based on the corona discharge characteristic in dc voltage, the experiment platform for nanosecond pulsed discharge was built to obtain the relation between discharge parameter and sound parameter. The characteristics of sound pressure in different discharge conditions were analyzed. The study results indicate that the sound pressure produced by pulsed discharge is similar with that produced by corona discharge. The experiment platform for pulsed discharge can be used to research the AN production mechanism by dc corona discharge. [ABSTRACT FROM AUTHOR]

A cathode-directed streamer in air is modeled using the hypothesis that branching is initiated by large electron avalanches that develop in a strong electric field in the front of streamer head. A series of streamer discharge simulations are carried out using a three-dimensional numerical model. The possibility of streamer branching is shown as a result of the interaction with two electron avalanches that arise in front of its head. They are directed to the sides from streamer propagation direction. Such a mechanism of branching is brought about by the fact, that at the moment of contact with the streamer, the avalanches have already undergone an avalanche-streamer transition or are close to it. The equality of the number of electrons in these avalanches at the moment of contact is not important. If this equality is violated, branching is asymmetric. If one of the avalanches interacting with the streamer is far from the avalanche-streamer transition, it does not trigger perfect branching, but it may produce an underdeveloped branch that does not evolve further. The streamer trajectory then deviates toward a larger avalanche, interacting with it. [ABSTRACT FROM AUTHOR]