Model of a wedge-electrode corona discharge under saturation: Exact solutions

Analytical solutions for the distributions of the electric field potential and electric charge density are derived for the outer region of a steady-state unipolar corona discharge from an ideal wedge-shaped electrode under the conditions of space-charge-limited current. Two situations are considered: a corona is initiated only from the edge of the wedge and from the entire surface of the electrode. In the former case, general solutions are obtained by sewing together exact cylindrically symmetric solutions in the drift space and plane symmetric solutions in space-charge-free regions. In the latter case, the field distribution near the edge turns out to be self-similar, i.e., invariant under extensions in the cross-sectional plane of the wedge, with the center at the top of the wedge. For both models, the dependences of the saturation current per edge’s unit length on the apex angle and applied potential difference are obtained.     

2-D corona field computation in configurations with ionising and non-ionising electrodes

An efficient method is proposed for the computation of the electric field strength and of the space-charge density in configurations of at least three ionising and non-ionising electrodes. The physical model is derived under the assumptions commonly accepted for the study of corona fields. The mathematical model makes use of a conformal mapping that converts the actual boundary-free field zone into a rectangular domain with well-defined boundary conditions. The finite-difference method is then used for solving the differential equations that describe the ionic space-charge and electric field distribution. The computational procedure was employed for studying the simple case of the drift zone of the corona discharge generated between a so-called dual electrode and a grounded plate. The dual electrode consisted of an ionising wire (diameter 0.22 mm) located at 20 mm from a tubular metallic support (diameter 25 mm). The computed current–voltage characteristic and current density distribution at the surface of the collector plate were in good agreement with the experimental data obtained for this combined corona–electrostatics electrode arrangement.     

Study of a positive corona discharge in argon at different pressures

The corona discharge in argon at atmospheric pressure has been studied by means of a 2D model. The reduced characteristic derived from the experimental data has been described by linear regressions for the different pressures and the two studied inter-electrode distances thus confirming the validity of Townsend's approximation also in case of point to plane configuration and argon as process gas. The model validated this hypothesis which has been attributed to the minor influence of space charge in the ionization zone. Its effect is, on the other hand, more significant in the drift zone where the electric field is greatly enhanced, leading, for higher currents, to the formation of a spark gap. Electron and ion distributions allow the influence of structural (electrode configurations and distance) and operative (pressure and discharge current) parameters to be evaluated including the current loss due to diffusion through different confining boundaries.     

Numerical simulation and experimental validation of a direct current air corona discharge under atmospheric pressure

Air corona discharge is one of the critical problems associated with high-voltage equipment. Investigating the corona mechanism plays a key role in enhancing the electrical insulation performance. An improved self-consistent multi-component two-dimensional plasma hybrid model is presented for the simulation of a direct current atmospheric pressure corona discharge in air. The model is based on plasma hydrodynamic and chemical models, and includes 12 species and 26 reactions. In addition, the photoionization effect is introduced into the model. The simulation on a bar-plate electrode configuration with an inter-electrode gap of 5.0 mm is carried out. The discharge voltage-current characteristics and the current density distribution predicted by the hybrid model agree with the experimental measurements. In addition, the dynamics of volume charged species generation, discharge current waveform, current density distribution at an electrode, charge density, electron temperature, and electric field variations are investigated in detail based on the model. The results indicate that the model can contribute valuable insights into the physics of an air plasma discharge.     

Computational study of glow corona discharge in wind: Biased conductor

Corona discharges in flowing gas are of technological significance for a wide range of applications, ranging from plasma reactors to lightning protection systems. Numerous experimental studies of corona discharges in wind have confirmed the strong influence of wind on the corona current. Many of these studies report global electrical characteristics of the gaseous discharge but do not present details of the spatial structure of the potential field and charge distribution. Numerical simulation can help clarify the role of wind on the ion redistribution and the electric field shielding. In this work, we propose a methodology to solve numerically for the drift region of a DC glow corona using the usual approach of collapsing the ionization region to the electrode surface, but allowing for strong inhomogeneities in the electrical and flow setup. Numerical results for a grounded wire in the presence of an ambient electric field and wind are presented. The model predicts that the effect of the wind is to reduce the extension of the corona over the wire and to shift the center of the ion distribution upstream of the flow. In addition, we find that, even though the near-surface ion distribution is strongly affected by the ion injection law used, the current characteristics and the far field solution remain pretty much unaffected.     

Numerical simulation and experimental validation of direct current air corona discharge under atmospheric pressure

Air corona discharge is one of the critical problems associated with high-voltage equipment. Investigating the corona mechanism plays a key role in enhancing the electrical insulation performance. An improved self-consistent multi-component two-dimensional plasma hybrid model is presented for the simulation of a direct current atmospheric pressure corona discharge in air. The model is based on plasma hydrodynamic and chemical models, and includes 12 species and 26 reactions. In addition, the photoionization effect is introduced into the model. The simulation on a bar-plate electrode configuration with an inter-electrode gap of 5.0 mm is carried out. The discharge voltage– current characteristics and the current density distribution predicted by the hybrid model agree with the experimental measurements. In addition, the dynamics of volume charged species generation, discharge current waveform, current density distribution at an electrode, charge density, electron temperature, and electric field variations are investigated in detail based on the model. The results indicate that the model can contribute valuable insights into the physics of an air plasma discharge.     

The correlation between corona current distribution and collection of fine particles in a laboratory-scale electrostatic precipitator

An analysis of the electrostatic gas cleaning fundamental phenomenon shows an essential influence of discharge electrode construction on the gas cleaning process efficiency.In the physical model tests there were used rigid discharge electrodes with corona emitting elements of various geometries. Different constructions of discharge electrode were tested in the aspect of discharge current uniform distribution on collecting electrode surfaces. Measurements of discharge current distribution has been carried out for discharge electrodes with different spike shapes and in different electric field geometry. The research aim was to determine the optimal discharge electrode construction ensuring high collection efficiency of fine particles. Collection efficiency measurements of selected fly ash samples (from coal fired boilers) were carried out on a laboratory testing bench in a horizontal electrostatic precipitator model.     

An empirical model for ionic wind generation by a needle-to-cylinder dc corona discharge

We present the results of an experimental study on ionic wind generation by a needle-to-cylinder dc corona discharge. A strong electrical field in the air generates air flow driven by the motion of ionized gas molecules along electric field lines. We measured the ionic wind velocity and discharge current with respect to various electrode geometries, distances between electrodes, and applied voltages. Our measurements suggest an empirical model for the ionic wind velocity as a function of the geometric factors of the collector electrode and the applied electric potential, which is useful for designing ionic wind cooling systems for small electronics.     

Modelling of corona discharge in cylinder-wire-plate electrode configuration

Numerical computation of the electric field strength and ionic space charge density in electrode systems consisting of ionizing wire and non-ionizing cylinder, connected to the same DC high-voltage supply and facing a grounded plate, is a difficult problem, which is of interest to several electrostatic processes applications. In a previous study a simple numerical method has been proposed to calculate the spatial distributions of electric field and ionic space charge in a case of a continuum and uniform corona discharge originating at the surface of the wire. The aim of the present paper is to improve the physical model of the corona discharge in this particular electrode configuration, by assuming a more realistic law of charge injection on the wire circumference. The computations were carried out for an ionizing wire of radius r=0.1 mm, located at different distances h from a metallic tubular support of radius R=13.4 mm.The initial conditions of the corona discharge took into account the non-uniformity of the charge injection around the ionizing wire electrode. The computational results were compared with those obtained under the assumption of uniform corona discharge. The comparison pointed out that neither the non-uniformity of the electric field nor that of the charge injection can be neglected. They depend on the geometry of the electrode system and affect the distribution of the electric field and of the space charge density in the inter-electrode gap.     

Experimental observation of negative differential characteristic of corona discharge in ultraviolet spectrum

Corona discharge is a self-sustained discharge which appears at electrodes with a small radius curvature in gas insulation. An almost invisible glow occurs just above the inception voltage. Corona phenomenon is mainly used in electro-technological processes to obtain space charge for electrostatic precipitation, separation of different particles, electrostatic liquid or solid coating, neutralization of space charge, etc. All of these processes rely on a strong nonhomogeneous electric field generated by a point – plate electrode system. When the critical value of the applied voltage is reached, the ionization processes near the point electrode start and give rise to the current between two electrodes. If the pointed electrode is positive, it is possible to observe an anomaly of the current – voltage (I-U) characteristic for the point-plate space. It means that while the voltage is raising the current density decreases in a narrow voltage area (2–3 kV). The anomaly was technically named as negative differential conductivity (dI/dU < 0). Unstable current can have a negative influence on electro-technological processes. The anomaly was detected for different shapes and materials of the electrode as well as for various temperatures and distances between electrodes. An oxidation layer, which appears on the metal electrode, also influences the ionization processes near the pointed electrode and causes a decrease of a current. In this paper measuring of the discharge activity in a point – plate electrode system is presented. Ionization of gas atoms and molecules in a high electric field and the following recombination of electrons and positive ions in the corona region can give rise to high-energy photons which produce new electrons in the field of discharge. Corona discharges are detected by DayCor Corona camera which can register UV emission generated by corona in a day light. The experiment was conducted with various shapes of the pointed electrode and distances between the high voltage and the grounded electrode under applied direct voltage with positive and negative polarity.     

Self-consistent structure of a dc discharge with a closed hall current in crossed electric and magnetic fields

A dc glow discharge with a closed Hall current in crossed electric and magnetic fields in helium is investigated. It is shown that the main features of an unmagnetized dc discharge [1] (such as the separation of the discharge into a space charge sheath and a quasineutral plasma, the formation of a cathode fall region and a negative glow, the appearance of a region with a reversed electric field producing a potential well for low-energy electrons and resulting in the formation of a Faraday dark space, and the formation of three pronounced groups of electrons in the electron distribution function) are also retained in a discharge in crossed fields. It is found that the sheath length is almost independent of the magnetic field, while the length of the negative glow region decreases appreciably with increasing magnetic field. The measured electron distribution function agrees well with the nonlocal theory, according to which the current in the Faraday dark space is carried by the intermediate electrons that are not trapped in the potential well and the energies of which are lower than the first excitation energy.     

An analytical method for DC negative corona discharge in a wire-cylinder device at high temperatures

This paper proposes an analytical solution for DC negative corona discharge in a wire-cylinder device based on experimental results in which both the corona and drift regions are considered; this approach aims to provide a theoretical method for analyzing electrostatic precipitation at high temperatures. The inter-electrode space is divided into three zones, namely, the ionization layer, the attachment layer (corona region) and the drift region, to investigate the space charge concentration and the electric field distribution. The boundary of the ionization layer is assumed to be the radius at which the rate of ionization balances that of electron attachment. The radius where the value of E/N equals 110 Td is recommended as the boundary of the attachment layer. It was determined that an increasing temperature leads to a decrease in the largest space charge number density and the largest electric field in the drift region that can be provided by a discharging device. With respect to the device in the present work, when the temperature increases from 350 °C to 850 °C, the largest electric field decreases from ∼9 × 10⁶ V/m to ∼3 × 10⁶ V/m, and the largest charge number density decreases from ∼1.3 × 10¹⁵ m⁻³ to 6.4 × 10¹⁴ m⁻³. The radius of the corona region, the space charge number density and the electric field increase as the applied voltage increases at a given temperature. For example, at a temperature of 550 °C, when the applied voltage increases from 10,500 V to 18,879 V, the radius of the corona region increases from ∼2.9 mm to ∼4.9 mm. It appears to be unreasonable to use a constant value that is calculated from Peek's formula as the electric field at the surface of the cathode under all of the conditions.     

雷云电场作用下长地线表面正极性辉光电晕放电的仿真研究

在雷云电场的缓慢作用下, 一种无流注的正极性辉光电晕在接地物体表面起始, 向周围空间注入大量正极性空间电荷, 从而改变雷电先导对雷击目的物的选择. 本文对雷云电场作用下起始于长地线表面的正极性辉光电晕放电进行了仿真研究; 考虑了正极性离子与其他离子的附着与碰撞作用, 建立了一种精确的二维正极性辉光电晕模型; 并通过在实验室内开展高压电晕放电试验, 测量了不同背景电场下的电晕电流; 与本文所建模型的仿真结果进行对比, 对模型的正确性进行了验证. 基于上述模型, 对正极性辉光电晕在雷云感应作用下的起始发展过程与电晕特性进行了仿真模拟, 得到了该电晕的电晕电流、正离子密度分布规律以及正离子迁移规律. 发现在雷云电场作用下, 电晕放电产生的正离子在迁移初期于垂直于地线的平面内基本呈圆对称状均匀分布, 但随着离子逐渐远离地线其分布不再均匀, 呈拉长的椭圆形分布, 多数离子最终分布于地线上方区域并逐渐向雷云方向迁移; 由于正离子在地线上方迁移区聚集形成的正空间电荷背景对行进电子束具有衰减和消耗作用, 抑制了电子崩的形成, 并降低了电子崩转化为流注的概率, 阻止了新的电子崩对流注的不断注入, 同时正空间电荷背景使气体的碰撞面增大, 增加了与电子的复合概率, 引起大量电子的消耗, 最终抑制了电子崩的形成与流注的发展, 地线表面的上行先导得到抑制.     

A simple model of processes in the drift region of negative corona discharge in a mixture of air with halocarbons

A model for negative glow corona discharge in a coaxial electrode configuration is presented. The main goal of this model is to describe the influence of a more efficiently electron-attaching gas on the distribution of free electron density in the drift region. The calculated distributions of electrons and other ionic components are shown. The model was applied in experiments realized in air + freon mixtures. A qualitative agreement between theoretical and experimental results was achieved.     

Numerical simulation of corona discharge in N2

A numerical study of a negative corona discharge in nitrogen in a point-plane gap using a Monte Carlo method is presented. The simulation provides a detailed structure of avalanches, propagation of successive avalanches and ion distribution can be discerned. The development of electron avalanches is due to ionization and photoionization in the high-field region, while the quenching of the avalanches is due to the low electric field near the plane electrode. Also the accumulation of electrons and positive ions are displayed in detail. The space charge field distortion is studied.     

Three-dimensional analysis of electrohydrodynamic flow in a spiked electrode-plate electrostatic precipitator

A three-dimensional numerical model has been created to evaluate the electrical and electrohydrodynamic characteristics of a single spiked wire-plate electrostatic precipitator. The hybrid Finite Element – Flux Corrected Transport numerical technique is used for solving the Poisson and current continuity equations to estimate the electric potential and ion charge density distributions in the precipitation channel. The fully three-dimensional turbulent airflow distribution is calculated using the commercial FLUENT software assuming a standard k–? turbulence model. A non-uniform corona discharge is assumed, as it is produced along the electrode in the form of a flat tape with some number of spikes. The EHD secondary flow pattern and its interaction with the main airflow in different planes along the precipitation channel are examined for different voltages applied to the corona spiked electrode. The numerical results are compared with experimental data published in the literature.     

Transition region between a nonequilibrium plasma and a negative electrode

A model is developed that describes the transition region between a quasineutral plasma and a planar negative electrode and in which the electron velocity distribution is represented as the sum of two Maxwellian distributions with different temperatures or as the sum of a Maxwellian distribution and distribution corresponding to an electron beam directed toward the electrode. Criteria for the formation of a sheath of positive space charge and a secondary plasma in the transition region are derived. An analysis is made of the dependence of the structure of the transition region on the parameters of the electron distribution, the space charge density distribution in the sheath, and the density of the ion current to the electrode. The criteria obtained are compared with the Bohm criterion.     

Experimental Analysis of a Low Frequency Instability in a Magnetized Discharge Plasma

In the paper we present the results of an investigation of a low frequency (30-100 kHz) instability in a weakly magnetized discharge plasma. The instability is triggered by a disc electrode which terminates the magnetized plasma column and is biased above the plasma potential. Frequency dependence on various parameters, e.g. electrode diameter, electrode bias, neutral gas pressure and plasma density is measured. Space and time dependence of the plasma potential and density in the perturbed region during one period of the electrode current oscillation are measured. During the phase of the current decrease a potential structure moves in axial direction from the edge of the perturbed region towards the electrode. During the phase of current saturation the motion of ions is mostly radial. The observed phenomenon is approximately modeled as a two dimensional potential relaxation instability (PRI).     

Evolution of the ion velocity distribution after sudden turn-on of a periodic electric field: A charge exchange model

An analytical solution to the problem of the ion velocity distribution evolution after turn-on of a periodic electric field is derived. The solution is constructed for the case of resonance charge exchange at a constant collision frequency (charge exchange model). The specific features of the transient process at the early stage of evolution are revealed. The phase shift between the applied field and the ion current at the periodic stage of the process is analyzed. The distribution function exhibits abrupt steps propagating in the velocity space. A method is proposed to study the ion-atom interaction cross section using a periodic electric field. The method is based on analysis of the current toward the electrode with a retarding potential.     

A Model for the Bulk Plasma in an RF Chlorne Discharge

A model has been constructed to describe the electrical characteristics of the central bulk plasma region in a 13.56-MHz parallel-plate discharge in chlorine at pressures of about 1 torr. This region is modeled as a volume-controlled plasma with the electron balance dominated by single-step electron-impact ionization and attachment and with the electron energy distribution function in equilibrium with the local instantaneous electric field. Relationships between the ionization frequency, the attachment frequency, the electron drift velocity, and the electric field are provided by solutions of the Boltzmann equation for mixtures of Cl2 and Cl which result from Cl2 dissociation. From a measured current waveform and Cl2/Cl density ratio, the model generates the local electric-field waveform, the time-varying electron density, and the power density in the central portion of the bulk plasma. The calculated time-averaged power input per unit discharge length compares well with experimentally determined values.