Numerical Simulation of Leakage Current on Conductive Insulator Surface

2019 ◽  
Vol 8 (4) ◽  
pp. 9487-9492
Keyword(s):  
Numerical Simulation ◽  
Electric Field ◽  
Leakage Current ◽  
Method Of Lines ◽  
Electron Attachment ◽  
Negative Ions ◽  
Conduction Current ◽  
Insulator Surface ◽  
Finite Difference Approximations ◽  
Positive Ions

The outdoor insulator is commonly exposed to environmental pollution. The presence of water like raindrops and dew on the contaminant surface can lead to surface degradation due to leakage current. However, the physical process of this phenomenon is not well understood. Hence, in this study we develop a mathematical model of leakage current on the outdoor insulator surface using the Nernst Planck theory which accounts for the charge transport between the electrodes (negative and positive electrode) and charge generation mechanism. Meanwhile the electric field obeys Poisson’s equation. Method of Lines technique is used to solve the model numerically in which it converts the PDE into a system of ODEs by Finite Difference Approximations. The numerical simulation compares reasonably well with the experimental conduction current. The findings from the simulation shows that the conduction current is affected by the electric field distribution and charge concentration. The rise of the conduction current is due to the distribution of positive ion while the dominancy of electron attachment with neutral molecule and recombination with positive ions has caused a significant reduction of electron and increment of negative ions.

scholarly journals Electrical Breakdown in Air and in SF6

1995 ◽  
Vol 48 (3) ◽  
pp. 453 ◽  
Author(s):  
R Morrow ◽  
JJ Lowke
Keyword(s):  
Electric Field ◽  
Electric Field Distribution ◽  
Electrical Breakdown ◽  
Negative Ions ◽  
Continuity Equations ◽  
Positive Ions ◽  
Positive Space Charge ◽  
Attachment Coefficient ◽  
Positive Space ◽  
Positive Point

A theory is presented for the development of streamers from a positive point in atmospheric air. The continuity equations for electrons, positive ions, and negative ions are solved simultaneously with Poisson's equation. For an applied voltage of 20 kV across a 20 mm gap, streamers are predicted to cross the gap in 26 ns, and the calculated streamer velocities are in fair agreement with experiment. When the gap is increased to 50 mm for the same voltage, the streamer is predicted not to reach the cathode. In this case an intense electric field front rapidly propagates about 35 mm into the gap in 200 ns. For a further 9�5 �s the streamer slowly moves into the gap, until the electric field at the head of the streamer collapses, and the streamer front stops moving. Finally, only positive space-charge remains; this moves away from the point, allowing the field near the point to recover, giving rise to a secondary discharge near the anode. The electric field distribution is shown to be quite different from that found previously for SF6; this is explained by the much lower attachment coefficient in air compared with that in SF6. These results show that streamers in air have a far greater range than streamers in SF6. This greater range cannot be explained by comparison of the values of E*, the electric field at which ionisation equals attachment.

scholarly journals Leakage Current Degradation Due to Ion Drift and Diffusion in Tantalum and Niobium Oxide Capacitors

2017 ◽  
Vol 24 (2) ◽  
pp. 255-264 ◽  
Author(s):  
Martin Kuparowitz ◽  
Vlasta Sedlakova ◽  
Lubomir Grmela
Keyword(s):  
High Temperature ◽  
Electric Field ◽  
Leakage Current ◽  
Niobium Oxide ◽  
Ion Concentration ◽  
Homogeneous Distribution ◽  
Insulating Layer ◽  
Ion Drift ◽  
Positive Ions ◽  
And Diffusion

AbstractHigh temperature and high electric field applications in tantalum and niobium capacitors are limited by the mechanism of ion migration and field crystallization in a tantalum or niobium pentoxide insulating layer. The study of leakage current (DCL) variation in time as a result of increasing temperature and electric field might provide information about the physical mechanism of degradation. The experiments were performed on tantalum and niobium oxide capacitors at temperatures of about 125°C and applied voltages ranging up to rated voltages of 35 V and 16 V for tantalum and niobium oxide capacitors, respectively. Homogeneous distribution of oxygen vacancies acting as positive ions within the pentoxide layer was assumed before the experiments. DCL vs. time characteristics at a fixed temperature have several phases. At the beginning of ageing the DCL increases exponentially with time. In this period ions in the insulating layer are being moved in the electric field by drift only. Due to that the concentration of ions near the cathode increases producing a positively charged region near the cathode. The electric field near the cathode increases and the potential barrier between the cathode and insulating layer decreases which results in increasing DCL. However, redistribution of positive ions in the insulator layer leads to creation of a ion concentration gradient which results in a gradual increase of the ion diffusion current in the direction opposite to the ion drift current component. The equilibrium between the two for a given temperature and electric field results in saturation of the leakage current value. DCL vs. time characteristics are described by the exponential stretched law. We found that during the initial part of ageing an exponent n = 1 applies. That corresponds to the ion drift motion only. After long-time application of the electric field at a high temperature the DCL vs. time characteristics are described by the exponential stretched law with an exponent n = 0.5. Here, the equilibrium between the ion drift and diffusion is achieved. The process of leakage current degradation is therefore partially reversible. When the external electric field is lowered, or the samples are shortened, the leakage current for a given voltage decreases with time and the DCL vs. time characteristics are described by the exponential stretched law with an exponent n = 0.5, thus the ion redistribution by diffusion becomes dominant.

Continuum Modeling of Charged Particle Transport: RF Breakdown and Discharges of SF6

1986 ◽  
Vol 68 ◽  
Author(s):  
Brian E. Thompson ◽  
Herbert H. Sawun ◽  
Aaron Owens
Keyword(s):  
Electric Fields ◽  
Electron Attachment ◽  
Negative Ions ◽  
Rate Coefficients ◽  
Rf Discharge ◽  
Continuity Equations ◽  
Positive Ions ◽  
Discharge Model ◽  
Rf Breakdown ◽  
Charged Particle Transport

AbstractContinuity equations for the concentration of electrons, positive ions, and negative ions were constructed and solved to predict rf breakdown voltages and the electrical properties of SF, discharges.These balances for the three types of charged species include terms for convection (electric field-driven fluxes), diffusion, and reactions (ionization, electron attachment, and negative-positive ion recombination).The mobilities, diffusivities, and reaction rate coefficients necessary for the rf discharge model are based on reported measurements and calculations of these parameters in dc electric fields.The electric fields developed in the rf discharge are calculated from Poisson's equation and applied voltage conditions.Predictions based on this model are compared with measured rf breakdown characteristics of SF6.

scholarly journals Electron interaction with copper(II) carboxylate compounds

2018 ◽  
Vol 9 ◽  
pp. 384-398 ◽  
Author(s):  
Michal Lacko ◽  
Peter Papp ◽  
Iwona B Szymańska ◽  
Edward Szłyk ◽  
Štefan Matejčík
Keyword(s):  
Electron Attachment ◽  
Negative Ions ◽  
Electron Collision ◽  
Electron Interaction ◽  
Fragmentation Pattern ◽  
Complex Molecules ◽  
Positive Ions ◽  
Sequential Loss ◽  
Ion Yields ◽  
Resonant Processes

In the present study we have performed electron collision experiments with copper carboxylate complexes: [Cu2(t-BuNH2)2(µ-O2CC2F5)4], [Cu2(s-BuNH2)2(µ-O2CC2F5)4], [Cu2(EtNH2)2(µ-O2CC2F5)4], and [Cu2(µ-O2CC2F5)4]. Mass spectrometry was used to identify the fragmentation pattern of the coordination compounds produced in crossed electron – molecular beam experiments and to measure the dependence of ion yields of positive and negative ions on the electron energy. The dissociation pattern of positive ions contains a sequential loss of both the carboxylate ligands and/or the amine ligands from the complexes. Moreover, the fragmentation of the ligands themselves is visible in the mass spectrum below m/z 140. For the studied complexes the metallated ions containing both ligands, e.g., Cu2(O2CC2F5)(RNH2)+, Cu2(O2CC2F5)3(RNH2)2 + confirm the evaporation of whole complex molecules. A significant production of Cu+ ion was observed only for [Cu2(µ-O2CC2F5)4], a weak yield was detected for [Cu2(EtNH2)2(µ-O2CC2F5)4] as well. The dissociative electron attachment processes leading to formation of negative ions are similar for all investigated molecules as the highest unoccupied molecular orbital of the studied complexes has Cu–N and Cu–O antibonding character. For all complexes, formation of the Cu2(O2CC2F5)4 −• anion is observed together with mononuclear DEA fragments Cu(O2CC2F5)3 −, Cu(O2CC2F5)2 − and Cu(O2CC2F5)−•. All dominant DEA fragments of these complexes are formed through single particle resonant processes close to 0 eV.

scholarly journals The effect of small traces of water vapour on the velocities of ions produced by Röntgen rays in air

1910 ◽  
Vol 84 (569) ◽  
pp. 173-181 ◽  
Keyword(s):  
Electric Field ◽  
Water Vapour ◽  
Lateral Diffusion ◽  
Negative Ions ◽  
Complete Removal ◽  
The Other ◽  
Electric Force ◽  
Dry Air ◽  
Positive Ions ◽  
Low Pressures

Some experiments by Prof. J. S. Townsend on the lateral diffusion of a narrow stream of ions moving in an electric field led to the conclusion that negative ions in perfectly dry air are much smaller than those in air containing a small quantity of moisture. It was consequently to be expected that the complete removal of water vapour would cause an increase in the velocity with which negative ions move under the influence of an electric field of force. At his suggestion the following investigation of the velocities of ions in air at low pressures was undertaken, and it was found that, while the complete removal of water vapour had only a small effect on the velocities of positive ions, yet the same cause increased the velocities of the negative ions by a factor varying between 2 and 30 for the range of pressures and electric forces used in the experiments. The method adopted was to let the ions travel between two gauzes under a known electric force for a time t and then to reverse the field. If v is the velocity of the ions and d is the distance between the gauzes, then ions starting from one gauze will reach the other if t ≮ d / v . If t is gradually decreased, it is possible to find, by means of an electrometer, when ions cease to reach the second gauze; when this happens v = d / t .

Theory of positive columns in electronegative gases

1980 ◽  
Vol 370 (1742) ◽  
pp. 375-387 ◽  
Keyword(s):  
Electron Attachment ◽  
Negative Ions ◽  
State Theory ◽  
Discharge Column ◽  
Electron Collisions ◽  
Charged Species ◽  
Continuity Equations ◽  
Positive Ions ◽  
Axial Concentration ◽  
Very High

A steady state theory of the positive column of a glow discharge in an electronegative gas is presented. Excitation and ionization are assumed to occur by single-electron collisions with neutral molecules. Both electron attachment and detachment are included in the continuity equations, the latter being due to long-lived excited neutral molecules taken to be uniformly distributed in the gas. Fluid-type momentum equations are used to describe the motion of positive and negative ions and of the electrons. By retaining Poisson’s equation throughout the treatment it is possible to impose physically realistic boundary conditions on all three charged species. It is found that the radial distribution of negative ions in the column is substantially different from that of the positive ions and the electrons. This is caused by the inwardly directed drift velocity of the negative ions, which confines them almost completely to the central region of the discharge column. Since the axial concentration of the negative ions relative to that of the electrons depends on the ratio of the coefficients of attachment to detachment, the concentration can reach very high values indeed when the rate of detachment is low.

scholarly journals On the electric charge collected by water drops falling through ionized air in a vertical electric field

1933 ◽  
Vol 142 (846) ◽  
pp. 248-268 ◽  
Keyword(s):  
Electric Field ◽  
Electric Charge ◽  
Water Drop ◽  
Negative Ions ◽  
Selective Absorption ◽  
Net Charge ◽  
Positive Ions ◽  
Vertical Electric Field ◽  
Lower Charge ◽  
Ionized Air

In connection with the theory of thunderclouds and of the electric charge brought down by rain, Wilson has suggested* the following mechanism. Consider an uncharged water drop falling vertically through ionized air. Let there be a vertical electric field, so that ions of one sign are moving down in the same direction as the drop falls, while ions of the other sign are moving up against the drop. The electric field induces equal charges of opposite signs on the upper and lower halves of the drop. Suppose now that the electric field has such an intensity that the velocity of the descending ions is less than the velocity of the falling drop. Under these conditions those descending ions which arc above the drop, cannot overtake the drop and so do not reach it, although attracted by the charge on its upper half. Those descending ions which are below and which the drop overtakes, are first repelled by the lower charge on the drop before being attracted by the upper charge and, since these charges are equal in the neutral drop, it is to be expected that these ions will not reach it. Ions coming up to meet the drop are attracted to the lower charge and give the drop a net charge. This destroys the equality of the induced charges and some of those ions which the drop overtakes are now attracted to it. A limiting condition will be approached in which the net charge is equal to some fraction of the induced charge. This mechanism does not depend on whether the electric field is directed vertically upwards or vertically downwards and for this reason specific mention of the sign of an ion has been avoided. In a particular case, suppose the potential gradient, measured upwards, to be negative, so that positive ions move up and negative ions move down. The charges on the upper and lower halves of the falling drop will then be positive and negative respectively. If the water drop falls more rapidly than the negative ions move down, it will collect a net positive charge, by selective absorption of positive ions at its lower negatively charged surface. Since a drop of 1 mm. radius has a terminal velocity of about 6 metres per second, the electric field must not exceed 400 volts/cm. for ions of mobility 1·5 cm./sec./volt/cm.

scholarly journals Electrosmosis between plane parallel walls produced by high-frequency alternating currents

1937 ◽  
Vol 163 (913) ◽  
pp. 298-317 ◽  
Keyword(s):  
Electric Field ◽  
Solid Surface ◽  
High Frequency ◽  
Negative Ions ◽  
The Body ◽  
Mathematical Treatment ◽  
Constant Field ◽  
Electrostatic Forces ◽  
Plane Parallel ◽  
Positive Ions

The problem of the motion, under the influence of high-frequency alter­nating currents, of fluid between plane parallel walls whose distance apart is very small, appears to be of interest in certain branches of Physical Chemistry. The following paper contains a mathematical treatment of this type of motion under certain specified conditions. We are greatly indebted to Mr. J. J. Bikerman of the Chemistry Department of the University of Manchester for having brought the problem to our notice, and for having given us a great deal of information concerning the physics of the phenomena involved. In general, when two different substances, or phases, have a common surface, there is an electrokinetic potential difference between them. This is produced by an electric double layer of ions in contact with the common surface. Consider the boundary between a solid and an electrolyte, and let us assume the solid to take a negative charge, as is almost invariably the case when the electrolyte is water or a very dilute aqueous solution. The negative layer consists, probably, of ions adsorbed rigidly to the surface. Near the surface, in the fluid, there will be a preponderance of positively charged ions held more or less firmly in position by electrostatic forces. Very close to the “rigid” layer of negative ions the electrostatic forces will be sufficiently great to keep the positive ions rigidly in place. As we leave the solid surface the forces diminish and ultimately a position is reached where diffusion and thermal forces overcome the electrostatic forces. Beyond this surface in the fluid there will still be a preponderance of positive ions, since the electrostatic forces will still be operative, but these ions will be mobile. At points remote from the solid surface there are approximately equal concentrations of positive and negative ions, and the liquid as a whole is electrically neutral. The equilibrium attained when electrostatic and diffusion forces are operating was first calculated by Gouy; the expression given by Gouy for the charge density is used in this paper. On applying an electric field the mobile ions in the layer near the surface begin to move towards one or other of the two electrodes as illustrated diagramatically in fig. 1, and this motion is transmitted to the liquid as a whole through the operation of viscous forces. As the fluid close to the walls contains more positive ions than negative ions greater forces will be called into play near the walls than in the body of the fluid, and, in a constant field, the liquid will move to the cathode. This phenomenon of the movement of a liquid over a fixed surface under the influence of an applied electric field is called “electrosmosis” or “endosmosis”.

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