Secondary Electron Emission Avalanche Research Articles

DC surface flashover characteristics of Al2O3/epoxy composites at cryogenic temperature

Epoxy resin is essential in the superconducting system as an insulating and supporting material. Extreme conditions such as cryogenic temperature, high vacuum, and high electric field could result in insulation failure for Epoxy resin. Surface flashover voltage is usually lower than breakdown voltage for solid materials. In this paper, the DC surface flashover characteristics of nano-Al2O3/epoxy composites (0, 1, 2, 3, 4, and 5%) have been investigated at cryogenic and room temperature. The nano-Al2O3 particles were modified by silane coupling agent (KH560). Epoxy doped with nano-Al2O3 was poured into a self-made mold and experienced a thermosetting process for 14 h. DC flashover tests were performed according to the IEC 60243–1:2013 international standard. The results were evaluated by the Weibull distribution method. The result shows that the DC surface flashover voltage of nano-Al2O3/epoxy composite is strongly related to the addition of nanoparticles and different temperatures. It can be explained by secondary electron emission avalanche (SEEA) and Li’s model.

Integrated modelling of vacuum flashover development: Above‐surface processes and breakdown threshold analyses

AbstractThe flashover in vacuum is a rapid interfacial discharge across the insulator surface when subjected to high applied voltage. Here a theoretical model covering above‐surface processes is introduced. The model calculates the flashover threshold in vacuum, with revised secondary electron emission avalanche theory and improved desorbed neutral transport model. The model serves as the first part of an integrated flashover model, aiming for consistent treatment of both above‐surface and subsurface processes during the entire flashover development. The flashover threshold is obtained by combining the desorbed neutral pressure at given applied voltage and the gas breakdown criterion dictated by the Paschen's law. An analytical formula for threshold estimation containing physical parameters, and a simplified formula consisting of empirical coefficients are introduced, catering for both conceptual understanding and practical application. The derived formulae are validated by experimental data for a variety of insulator materials. The theory generalisation for non‐uniform electric field distribution is further discussed.

Estimation time delay from field emission to secondary electron emission avalanche in vacuum surface flashover

Vacuum surface flashover is the main factor limiting the development of pulsed power system. In this work, a quantitative dynamical model is built to investigate the vacuum surface flashover from field emission to secondary electron emission avalanche (SEEA). The results show that positive charges accumulating on the dielectric surface caused by field emission electrons play a dominant role when the normal electric field on the dielectric surface Edc is small. The growth of the number of positive surface charges exponentially decreases with the distance from the cathode triple junction (CTJ). With the increase in the density of positive surface charges, the growth of positive surface charges mainly depends on the secondary electrons cascade. As a result, the saturation state of Edc will first occur on the dielectric surface at a distance hundreds of micrometers from the CTJ. In addition, the effect of dielectric permittivity on positive surface charges is considered. The density of positive surface charges equals (1+εr) ε0Edc rather than 2ε0Edc. Particle-in-cell simulations are employed to verify the correctness of the theory model, and the agreement of comparisons is favorable. Furthermore, the space charge effect is discussed. When SEEA reaches saturation, electrons can significantly change the spatial distribution of the electric field.

An alternative simulation approach for surface flashover in a vacuum using a 1D2V continuum and kinetic model

Surface flashover across an insulator in a vacuum is a destructive plasma discharge which undermines the behaviors of a range of applications in electrical engineering, particle physics and space engineering, etc. This phenomenon is widely modeled by the particle-in-cell (PIC) simulation, here the continuum and kinetic simulation method is first proposed and implemented as an alternative solution for flashover modeling, aiming for the prevention of unfavorable particle noises in PIC models. A one dimension in space, two dimensions in velocity kinetic simulation model is constructed. Modeling setup, physical assumptions, and simulation algorithm are presented in detail, and a comparison with the well-known secondary electron (SE) emission avalanche analytical expression and existing PIC simulation are made. The obtained kinetic simulation results are consistent with the analytical prediction, and feature noise-free data of surface charge density as well as fluxes of primary and SEs. Discrepancies between the two simulation models and analytical predictions are explained. The code is convenient for updating and to include additional physical processes. The possible implementations of outgassing and plasma species for the final breakdown stage are discussed. The proposed continuum and kinetic approach are expected to inspire future modeling studies for the flashover mechanism and mitigation.

Flashover of insulation materials induced by electrostatic electromagnetic pulse

PurposeThe purpose of this paper is to research the induced flashover laws of different insulation materials under electrostatic electromagnetic pulse, and the induced flashover characteristics of different electrode structures are further explored.Design/methodology/approachAccording to standard IEC 61000–4-2, an experimental system of electrostatic electromagnetic pulse flashover for insulation materials is established. The induction flashover laws of polytetrafluoroethylene, epoxy resin and polymethyl methacrylate surface-mounted finger electrodes under the different intensity of electrostatic electromagnetic pulse are researched. The influence of the finger electrode, needle–needle electrode and needle–plate electrode on insulation flashover was compared. Secondary electron emission avalanche (SEEA) and field superposition theory are used to analyze the experimental results of electrostatic electromagnetic pulse induced flashover.FindingsThe larger the dielectric strength of insulation materials, the more difficult flashover occurs on the surface. The field superposition enhances collision ionization between electrons and gas molecules, which leads to the insulation materials surface induced flashover easily by electrostatic electromagnetic pulse. The sharper the electrode shapes on the insulation materials surface, the stronger the electric field intensity at the cathode triple junction, more initial electrons are excited to form the discharge channel, which easily leads to flashover on the surface of the insulating material.Originality/valueThe proposed field superposition combined with the SEEA method provides a new study perspective and enables a more rational, comprehensive analysis of electrostatic electromagnetic pulse induced flashover of insulation materials. The work of this paper can provide a reference for the safety protection of spacecraft in orbit under a strong electromagnetic field environment, increase the service life of spacecraft and improve the reliability of spacecraft’s safe operation in orbit. It provides a basis for the selection of insulation materials for equipment under the different intensities of the external electromagnetic environment.

Effect of Deposited Charge on Vacuum DC Surface Flashover Under Electron Beam Irradiation

Spacecraft operating environment is rather complex, including high vacuum and energetic electron radiation. Vacuum-insulation interface is usually the weakest link of the insulation system since surface flashover usually occurs at the interface. There are several theories for surface flashover, above which the secondary electron emission avalanche (SEEA) and the electron triggered polarization relaxation (ETPR) are the mainstream. Since researchers have usually assumed that there has been a preexisting positive charge on the insulation surface, when the insulation surface is negatively charged by electron beam irradiation, these theories cannot be directly applied. In this article, the particle tracking method is used to simulate the initial and secondary electron trajectories in the initial phase of surface flashover, and to explain the influence of negative surface charge on surface flashover. The results show that: on the one hand, the negative deposited charge weakens the electric field at the cathode triple junction (CTJ), inhibits the initial electron emission, and hinders the initiation of flashover; on the other hand, the negative deposited charge repels the secondary electrons away from the insulation surface and hinders the multiplication of the secondary electrons and the development of flashover.

Ultralow secondary electron emission and improved vacuum surface insulation of polyimide with scalable nanocomposite coating

Polymers with high surface electric insulation capability are greatly demanded in various electrical devices operating in vacuum ambient. Low secondary electron emission (SEE) is favorable to mitigate vacuum flashover by inhibiting the SEE avalanche across the surface. Although numerous approaches, esp. the surface modifications, promote the flashover strength of the insulator, a facile yet cost-effective modification strategy of a high-quality and scalable flexible insulator remains a formidable challenge. Herein, a facile ion-exchange technique is implemented to fabricate a nanoscale polyimide/chromic oxide (PI/Cr2O3) nanocomposite coating comprising hundreds of organic/inorganic interfaces securely adhered to a flexible PI substrate, which features ultralow secondary electron emission yields (SEEY). The low emissivity is achieved by introducing weakly emissive Cr2O3 nanoparticles as well as interfacial traps within the nanocomposite layer, which outperforms the existing and modified polymers. The PI/Cr2O3 shows a remarkable increase in flashover strength while keeping sufficient mechanical durability. The proposed surface engineering strategy is convenient and scalable, bringing up new insight into industrial applications.

Metal-wire-embedded alumina insulating material using micro- and nanoscale 3D printing for surface flashover mitigation in a vacuum

A micro- and nanoscale 3D printing technique is applied to fabricate a functional insulating material that mitigates surface discharge in a vacuum based on microscopic electron multipactor suppression. The proposed alumina ceramic insulator design consists of surface-embedded thin metal wires that introduce a local gradient of secondary electron emission (SEE) yield, such that the trajectories of multipactor electrons are distorted by accumulated negative surface charge and the SEE avalanche across the insulator surface becomes intermittent. Considerable increases of surface flashover threshold and surface charging reduction are verified by the experiment. Also, additional efforts are made to determine the optimal size and spatial distribution of the metal wire. A convex-shape flashover voltage trace is observed when increasing the width of the wire, suggesting a trade-off between the multipactor mitigation and the insulator strength. The wire’s position between the adjacent cathode triple junction and the middle of the insulator is proved to be favorable for flashover mitigation. The physical details of surface flashover mitigation by the proposed insulator design are revealed by an ab initio particle-in-cell simulation code, corroborating the experiment from a microscopic aspect.

Surface modification of silicone rubber by CF4 radio frequency capacitively coupled plasma for improvement of flashover

The flashover performance of insulating materials plays an important role in the development of high-voltage insulation systems. In this paper, silicone rubber (SIR) is modified by CF4 radio frequency capacitively coupled plasma (CCP) for the improvement of surface insulation performance. The discharge mode and active particles of CCP are diagnosed by the digital single-lens reflex and the spectrometer. Scanning electron microscopy and x-ray photoelectron spectroscopy are used for the surface physicochemical properties of samples, while the surface charge dissipation, charge accumulation measurement, and flashover test are applied for the surface electrical characteristics. Experimental results show that the fluorocarbon groups can be grafted and the surface roughness increases after plasma treatment. Besides, the surface charge dissipation is decelerated and the positive charge accumulation is inhibited obviously for the treated samples. Furthermore, the surface flashover voltage can be increased by 26.67% after 10 min of treatment. It is considered that strong electron affinity of C–F and increased surface roughness can contribute to deepening surface traps, which not only inhibits the development of secondary electron emission avalanche but also alleviates the surface charge accumulation and finally improves the surface flashover voltage of SIR.

Significantly Improved Surface Flashover Characteristics of Epoxy Resin/Al2O3 Nanocomposites in Air, Vacuum and SF6 by Gas-Phase Fluorination

In this work, epoxy resin incorporated with nano-Al2O3 of various concentrations, 0 wt.%, 1 wt.%, 3 wt.% and 5 wt.%, were prepared and subsequently fluorinated for 15 min, 30 min and 60 min at 40°C in a F2/N2 gas mixture (20/80 v/v) with pressure of 0.05 MPa. Fourier-transform infrared spectroscopy was employed for the chemical characterization of epoxy resin/Al2O3 nanocomposites which showed the molecular-chain scission during the gas-phase fluorination. Later, the effect of gas-phase fluorination on DC flashover characteristics of epoxy resin/Al2O3 nanocomposites was analyzed. It was found that gas-phase fluorination of pure epoxy resin can improve its DC flashover voltage in air and sulfur hexafluoride (SF6). In addition, nano-Al2O3 incorporation leads to a slight decrease of the DC flashover strength but it is still higher than that of non-fluorinated epoxy resin. This proves that suppression of charge accumulation can increase the DC flashover voltage of epoxy resin. The vacuum DC flashover voltage of epoxy resin/Al2O3 nanocomposites decreased by 35.8% after 30 min fluorination. However, the vacuum DC flashover voltage of epoxy resin incorporated with 1 wt.% nano-Al2O3 was 17.5% higher than that of unfilled epoxy resin. Based on the secondary electron emission avalanche model of vacuum flashover, the experimental results were analyzed. It was found that the fluorination modifies the surface molecular structure of epoxy resin/Al2O3 nanocomposites, which may weaken its adsorption capacity for gases and make it easier to desorb gases and reduce flashover voltage.

Estimation of surface flashover threshold in a vacuum II: flashover phase transition

Surface discharge in a vacuum occurs under an intense external field, also called a flashover. The flashover threshold over which the surface flashover occurs is of vital importance in the vacuum–solid interface. It is widely assumed that the flashover is initiated by a single surface multipactor and develops as a plasma discharge along a dielectric surface, namely the secondary electron emission avalanche (SEEA). Yet the SEEA model is not versatile for all practical vacuum–solid interfaces and there remain experiment results contradicting the theory predictions without a resolute answer. Here we further expand on previous theories and consider the conventional SEEA model under arbitrary field distributions. The example of a conical insulator is then given to test the validity of the SEEA model under an arbitrary field. It is found that the obtained flashover threshold is only consistent with the experiment at low cone angles where the field near the cathode triple junction is strong, while remarkable discrepancies appear when the anode field is significantly enhanced. The discrepancies can be understood if a different discharge model, i.e. an anode-initiated flashover (AIF) is included. Both particle-in-cell simulation and optical diagnostics are employed to visualize this unique discharge, which are then formalized on theoretical grounds to elucidate the early stage of the AIF. The transition between two flashover phases is then clarified. The plasma–surface interaction and sheath dynamics during the discharge are analyzed theoretically, showing distinct sheath evolutions in two flashover models. Additionally, a new factor reflecting field distortion is introduced to estimate the discharge threshold under an SEEA framework.

Practical design of triple junction for a 90 kV electron gun

High-voltage electron guns can commonly be damaged by surface flashover, which can occur across the insulator surface of the gun as a result of electron emission around the triple junction structure. Using secondary electron emission avalanche (SEEA) theory as a basis, the triple junction in a 90 kV electron gun is optimized in this work to avoid damage from the effects of surface discharges. A metal shielding structure is used to reduce the surface flashover caused by electron emission and ensure that the electron gun provides reliable high voltage performance. The aim of the proposed design method is to reduce the field strength that occurs within the electron gun structure. Simultaneously, it is shown that SEEA theory can provide a reasonable explanation for and a solution to the flashover phenomenon that occurs on the insulator surface. In addition, the metal shielding structure used to address the high voltage vacuum discharge phenomenon proves to be an effective design method. Experiments performed on the electron gun for a 90 kV X-ray tube demonstrate that the proposed design method has a favorable effect on control of the flashover phenomenon.

Tracking Propagation Mechanism on the Surface of Polyvinyl-Chloride-Sheathed Flat Cord based on Electric Field Analysis and Gas Discharge Physics

전기 화재의 주요 원인 중 하나인 트래킹은 전기적 방전에 의한 물리적 현상으로 인식된다. 따라서 트래킹은 전계 해석, 전자생성에 의한 도전성 경로, 기체방전이론을 기반으로 설명되어야 한다. 하지만, 이러한 사항을 반영한 연구 논문은 드물다. 본 논문은 트래킹 진전에서 그들의 영향을 포함한 트래킹 진전 메커니즘을 제안하였다. 그 메커니즘의 제안을 위해, 트래킹 실험, 탄화진전 모델에 대한 전계해석, 연면방전 이론을 적용한 트래킹 진전과정에 대한 설명이 수행되었다. 트래킹 모의실험으로부터, 코로나 방전에서 트래킹 파괴까지 트래킹 진전의 각 단계에서 전류파형이 측정되었다. 전계해석은 탄화의 발생과 진전과정동안 건조대 표면의 전계와 전자생성을 위한 고전계 영역을 파악 하기 위해 수행되었다. 본 논문에서 제안된 트래킹 메커니즘은 코로나 방전에 의한 전자사태, 양이온의 축적, 전자사 태의 확장, 2차 전자사태, 스트리머, 도전성 경로에 의한 트래킹 파괴의 6단계로 구성된다. 트래킹 모의실험에서 측정된 펄스성 전류파형은 제안된 트래킹 메커니즘에 의해 설명될 수 있었다. 본 연구 결과는 화재의 원인인 트래킹을 검출하고, 내트래킹성을 높이는 데 필요한 기술 자료가 될 것이다.Tracking, which is one of the main causes of electrical fires, is perceived as a physical phenomenon of electrical discharge. Hence tracking should be explained based on electric field analysis, conduction path by electron generation, and gas discharge physics. However, few papers have considered these details. This paper proposes a tracking mechanism including their effects on tracking progress. In order to prove this mechanism, a tracking experiment, an electric field analysis for the carbonization evolution model, and an explanation of the tracking process by gas discharge physics were conducted. From the tracking experiment, the current waveforms were measured at each stage of the tracking progress from corona discharge to tracking breakdown. The electric field analysis was carried out in order to determine the electric field on the surface of a dry-band and the high electric field region for electron generation during the generation and progress of carbonization. In this paper, the proposed tracking mechanism consisted of six stages including electron avalanche by corona discharge, accumulation of positive ions, expansion of electron avalanche, secondary electron emission avalanche, streamer, and tracking by conductive path. The pulse current waveforms measured in the tracking experiment can be explained by the proposed tracking mechanism. The results of this study will be used as the technical data to detect tracking phenomenon, which is the cause of electric fire, and to improve the proof tracking index.

Measurement of optical spectrum and mass spectrum in vacuum surface flashover for polymeric materials

The phenomenon of surface flashover in vacuum is a common problem in vacuum insulation systems. Although the theory of secondary electron emission avalanche is widely accepted, the developing process of vacuum surface flashover is not very clear and it needs to be further studied. The surface discharge process was diagnosed by spectral and mass spectrum analysis in this paper. The surface flashover was initiated by a microsecond pulse with a rise time of 500 ns and a full width at half maximum of 8 μs. Optical diagnostic methods were used to obtain the luminous properties of several polymeric materials. The time-domain optical signal was measured by a photomultiplier tube with wavelength range of 300-650 nm. The spectrograph was used to detect the optical emission from the surface discharge. The outgassing characteristics in the flashover were also measured by mass spectrometer connected to the vacuum experiment chamber. The results show that the optical signal appears before flashover and the light intensity reaches its maximum at about 80 ns after the flashover occurs. The optical emission spectrum is mainly in range of 400-800 nm, and C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , H and Cu spectrum lines were detected in polymeric materials. The results of mass spectrum measurement show that the outgassing of polymeric materials in surface flashover includes the desorbed gases and decomposed gases of insulation materials. It is consistent between the results of emission spectrum and mass spectrum.

The Discharge Mechanism Leading to the Tracking Progress in Polyvinyl-Chloride-Sheathed Flat Cord

This paper suggests the mechanism of the discharge phenomenon that leads to tracking progress. For this purpose, a polyvinyl-chloride-sheathed flat cord (PVCSFC), which is widely used as a distribution cord, was employed and an artificial crack was intentionally made on the surface. Tracking was progressed using electrolyte droplets. The mechanism of the discharge phenomenon was suggested from the measurement and analysis of the current waveform. As carbonization progressed during the tracking progress, the frequency of scintillation discharge also significantly increased. The mechanism for scintillation discharge during the tracking progress was based on the change in the electric field of the dry band, initial electron, electron avalanche, photoionization, secondary electron generation (electron detachment, photoemission, and secondary electron emission avalanche), space charge due to positive ions, and formation of conductive channels. This discharge mechanism could explain the physical phenomenon and change in the current waveform that occurs during the tracking progress.

Temperature dependent surface charge and discharge behavior of epoxy/AIN nanocomposites

In this paper, effects of ambient temperature and nanoparticles on surface charge and discharge behavior of epoxy/aluminum nitride (AlN) nanocomposites were investigated. With the rise of ambient temperature, the surface discharge strength of epoxy resin decreases and the conductivity shows significant increase. The charges obtain higher energy, their movement becomes more violent and makes it easier for secondary electron emission avalanche. Meanwhile, the specimen's trap level increases and trap density decreases. 1, 3 and 5 wt% proportions of AlN nanoparticles were added to the epoxy resin to increase the surface discharge strength at different operation temperatures. With the rise of filler content, the trap level, trap density and surface discharge strength increase first and then decrease at 20 °C. The specimen with 5 wt% filler content shows the highest shallow trap density and the one with 1 wt% filler content shows the highest deep trap density at 80 °C. As shallow traps can handle the migration of charges while deep traps may mainly cause electric field distortion, the specimen with 1 wt% filler content shows the highest surface discharge strength at 20 °C while the one with 5 wt% filler content shows the highest at 80 °C. The conclusions can help with finding different formulas to increase epoxy resin's surface discharge strength at different operation temperatures.

Estimation of surface flashover threshold in vacuum: from multipactor to discharge plasma

We propose a novel theoretical formula to estimate the surface flashover threshold in vacuum using the intrinsic properties of dielectric material as well as dielectric-vacuum configuration. The method is based on an above-surface model called secondary electron emission avalanche (SEEA), where flashover development can be divided into multipactor discharge, outgassing and an ionization avalanche which eventually leads to a plasma discharge. The transition from SEE-dominated regime to discharge plasma is supposed to be of significance where gas breakdown takes place within a nonuniform desorbed gas cloud in the vicinity of dielectric surface. Flashover occurs when specific space charge multiplication is achieved, yielding the critical pressure and breakdown voltage. The depiction of previous stages involves the secondary electron emission of dielectric materials, desorption and diffusion of adsorbed gas, ambient temperature, electrode structure, etc. Both particle-in-cell simulation and experiment data can corroborate the obtained theoretical results.

2D particle-in-cell simulation of the entire process of surface flashover on insulator in vacuum

With the introduction of an external circuit model and a gas desorption model, the surface flashover on the plane insulator-vacuum interface perpendicular to parallel electrodes is simulated by a Particle-In-Cell method. It can be seen from simulations that when the secondary electron emission avalanche (SEEA) occurs, the current sharply increases because of the influence of the insulator surface charge on the cathode field emission. With the introduction of the gas desorption model, the current keeps on increasing after SEEA, and then the feedback of the external circuit causes the voltage between the two electrodes to decrease. The cathode emission current decreases, while the anode current keeps growing. With the definition that flashover occurs when the diode voltage drops by more than 20%, we obtained the simulated flashover voltage which agrees with the experimental value with the use of the field enhancement factor β = 145 and the gas molecule desorption coefficient γ=0.25. From the simulation results, we can also see that the time delay of flashover decreases exponentially with voltage. In addition, from the gas desorption model, the gas density on the insulator surface is found to be proportional to the square of the gas desorption rate and linear with time.

Influence of pulse front steepness on vacuum flashover characteristics

Studying flashover characteristics in vacuum environment is extremely significant for designing reliable insulation structures. The waveform of applied voltage excitations greatly affects the flashover process. In this study, the influence of nanosecond pulse front steepness on flashover process in vacuum is investigated. Firstly, flashover experiments with nanosecond pulses are conducted. Nanosecond pulses with different front steepness are generated and used to trigger flashovers on sample surface. The relationship between pulse front steepness and flashover voltage is studied. Meanwhile, a particle-in-cell with Monte Carlo collision (PIC-MCC) two-dimensional self-sustaining discharge model based on secondary electron emission avalanche (SEEA) scheme is established. The distribution of charged particles, electric field and their evolution during flashover process are presented. Furthermore, pulses with various rising steepness are applied to the model. The multiplication and propagation of charged particles in different pulse waveform conditions are studied. In all conditions, two stages during flashover process can be obviously distinguished based on charged particle number evolution which divides the overall flashover delay time into two parts. By analyzing the voltage development in these two time slots, the quasi-linear relationship between pulse front steepness and flashover voltage in nanosecond pulse flashover in vacuum is explained.

Experimental investigation of surface charge accumulation behaviors on PTFE insulator under DC and impulse voltage in vacuum

Surface charge accumulated on insulators plays an important role in flashover process in vacuum, which has not yet been fully understood. In this paper, charging behaviors on insulator surface were experimentally examined under negative DC and impulse voltage. For the case of DC voltage, two charging stages were observed, i.e., the area near cathode was at first negatively charged under lower voltage (stage I) and then followed by a positively charged cathode-anode surface (stage II). Surface charging at stage I is considered to be caused by Schottky injection of homo-charges from electrode into sample surface layer. While at stage II secondary electron emission (SEE) process is responsible to the positively charged anode-cathode surface. However, charging at stage I is quite sensitive to pre-stress process, as well as the electrode-insulator interface conditions. The ongoing injection of electrons from cathode can lead to gradually decreasing in surface charge accumulation as the voltage duration increases. For the case of impulse voltage, Schottky injection of homo-charges has little influence on surface charging as the time is too short for charge injection and migration in surface layer. The SEE process will govern surface charging due to its extremely fast establishment process. A good linear relationship is obtained between saturated surface charge density and applied voltage, which is generally consistent with the numerical calculation result based on secondary electron emission avalanche theory. At last, it is confirmed that the ionization of desorbed gas from insulator surface and subsequent neutralization of electrons with positive surface charge is the main cause to eliminate surface charge in flashover.