Field Intensification Factor Research Articles

Influence of the scenario in the calculation of electric field intensification factor Part I: 2D approximation

Nowadays, the so called 'Electric Field Intensification Factor', usually noted as Ki, is evaluated with classical concepts or formulations employed in many applications related with partial and complete electric discharges. There are also engineering applications, such as lightning protection, where usually there is more than one object within the scenario and, evidently, those objects modify the electric field pattern and consequently this Ki, should be corrected considering this influence in order to evaluate properly the real conditions reproduced in the scenario under evaluation. In this paper, some Finite Element Method (FEM) simulations have been done to get a dataset to make a regression thus obtaining an 'environmental correction factor', which will be a function of the dimensions of the main and secondary structures and the distance between them.

Research on the Resonance Properties of E-Type Nano Antenna

Finite Difference Time Domain method(FDTD) is used to study the resonance properties of E-type nano antenna in this paper. According to the result of numerical simulation,the size and location of ledge part made a great influence on the resonance properties of holistic nano antenna while major rectangle part is invariant.The electronic field distribution, enhancement factor and corresponding resonance frequency of E-type nano antennas with invariant major rectangle part and different ledge parts are calculated through FDTD method,comparing with rectangle nano antenna without ledge part, E-type nano antenna has a great promotiom in electronic field enhancement at about 100 times of the excite electronic field intensity while regular rectangle nano antenna can achieve about 30times only.The resonance frequency is relate to the ledge part ,by changing the size and location of ledge part,resonant frequency can be adjusted between 340Thz and 400Thz,at the meantime, the field enhancement almost unchanged. After a glass substrate is added under the E-type nano antenna with constant size,the electronic field intensification factor improved significantly and the electronic field spread over the area around the ledge part rather than the junction of glass and metal.The horizontal position of ledge part has an effect on holistic resonance properties.When the ledge part located in the middle, the electronic field intensification factor of three ledge parts rised to 240 times at the same time,and distinct double resonance peak appeared.When the ledge part moved to the edge, the electronic field enhancement around the ledge parts on the sides weaken and middle ledge part rised to 350 times,double resonance peak disappeared.

The use of ‘Field Intensification Factors’ in calculations for lightning protection of structures

The spatial distribution of the electric field in the vicinity of a prospective strike point on a structure is an important factor in the determination of the likelihood of a lightning strike to that point. Hence, the assessment of the effectiveness of various positions of lightning rods for the protection of structures ideally requires three-dimensional calculations of the electric field, not only for the various trial positions of the lightning rods, but also for various positions of the downward lightning leader. This paper shows that such calculations can be greatly simplified by the use of “field intensification factors”. These factors are calculated for likely lightning attachment points such as corners, edges and lightning rods, but using an imposed electric field which is uniform in the absence of the perturbing structures. It is shown that these factors can be applied in the general case of any lightning downward leader at any arbitrary position, with errors of less than 20% compared with exact calculations made without the use of the approximation. Examples are given of calculated field intensification factors for various shapes and dimensions of typical structures, including composite structures, and protective lightning rods placed on structures. Quantitative relations for the spatial values of the field intensification factor as a function of structure and rod dimensions are obtained, leading to a simple method for the estimation of conditions for corona and upward leader inception. The results are discussed in terms of practical aspects of lightning protection, such as the use of such calculations for the placement of lightning rods in the most appropriate locations on structures.

Anode hotspot temperature estimation in vacuum gaps under 50 Hz alternating excitations

Anode hotspot temperatures for vacuum gaps subjected to 50-Hz AC excitations are computed. The transient heat diffusion equation is solved using a finite difference method. The effects of nonlinear variation of thermal properties with temperature and phase change are studied using the ANSYS 4.4 finite element package. The peak temperatures are estimated by a seminumerical method. The results of a parametric study of the effects of electrode material, field intensification factor, and radius of the spot are presented. The results for stainless steel, copper, and aluminum anodes indicate that the temperature of hot spots can reach the melting point, so they are the main sources of microparticles. The asymmetry of the prebreakdown current waveform about its own peak, which is caused by thermal instability at the anode, is attributed to the nonlinear variation of thermal properties with temperature. The methods discussed can be used to estimate the size of microparticles originating from thermally unstable regions at the anode. >

The effect of mechanical contact on breakdown characteristics in vacuum

Using copper-chromium electrodes, an experiment was conducted to clarify the reduction of insulation strength by mechanical contact in vacuum. The experiment consisted of prebreakdown current measurements and SEM (secondary electron microanalyzer) observation of the electrode surface. Experimental results revealed that the field intensification factor obtained from the prebreakdown current was increased by mechanical contact. SEM observation showed that mechanical contact caused microprotrusions to be generated. This phenomenon suggests that a reduction of insulation strength by mechanical contact is caused by field emission from a roughened surface. If mechanical contact is made, dielectric breakdown occurs when the field strength of microprotrusions on the cathode surface reaches a critical value (1.0 to 1.7*10/sup 8/ V/cm).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Area effect on electric breakdown of copper and stainless steel electrodes in vacuum

The breakdown field strength E/sub b/(= alpha Vb/d) of gaps made with pure copper and stainless steel depends on the effective area S/sub eff/. It can be expressed by the single experimental equation E/sub b/=K/sub 1/S/sub eff//sup -n/, where K/sub 1/ is a constant, n is about 0.24, S/sub eff/ is the electrode area subjected to more than 90% of maximum field strength, alpha is the shape factor, d is the gap length, and V/sub b/ is the breakdown voltage. The field intensification factor beta /sub l/ obtained through the measurement of prebreakdown current can be expressed by a single experimental equation beta /sub l/=K/sub 2/S/sub eff/n, where K/sub 2/ is a constant. This means that the area of effect of E/sub b/ is represented by the area effect of beta /sub l/ and that the vacuum breakdown may be initiated by field emission.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Limiting Values of Critical Electric Stress, and the Design Prediction of EHV/UHV SF6 Insulation Breakdown

An analysis of SF6 Paschen curves in the EHV/UHV range has been made. It is observed that the limiting value of critical electric stress is not the stress at which the apparent ionization and attachment coefficients are equal, that is, it is not the limiting value found for lower voltage treatments. Paschen departures, concluded to be a genuine phenomenon, are found to occur as an hyperbolic function of gap spacing. The Paschen curve, including departures, yields two new values of limiting critical stress. From those values, an equation is developed which may be used to predict insulation breakdown in uniform field configurations. Using a field intensification factor, the equation is adapted to the important engineering configuration of coaxial cylinders. The resultant equation gives good correlation with the breakdown behavior found by several groups using differing electrode geometries. Prediction of breakdown voltage is more accurate than that obtained by the widely used law of similarity. The breakdown equation is in a form suitable for use in prediction of EHV/UHV SF6 breakdown in engineering insulation design situations.

The semiconductor field-emission photocathode

The recently developed large-area field-emission photocathode is described. It consists of a finely spaced array of point emitters fabricated by etching of p-type silicon or other semiconductor. Uniform emission over areas of 6-7 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> have been obtained. For Si, the spectral response extends from 0.4 to 1.1 µm. Quantum yields of 25 percent at 0.86 µm have been measured, which is about five times the value reported for the extended S-20 photocathode and comparable to the best III-V photoemitters. Calculations indicate that quantum yields of up to 40 percent at 0.86 µm and 28 percent at 0.9 µm are attainable with the present photocathode structures. For low dark current densities, photocathode cooling to temperatures approaching 77 K must be employed at present. The dark current is shown to be dominated by surface-generated electrons in the space-chargeregion of the emitters. Effects of phosphorus gettering and annealing treatments on dark current are discussed, and the spatial frequency response of the device is determined. The results of a computer study show that the field intensification factor of p-semiconductor field emitters behaves quite differently from that of metallic emitters.

Prebreakdown currents and breakdown voltages in vacuum at cryogenic temperatures

These investigations were conducted to measure the prebreakdown current and breakdown voltage between aluminium, copper, stainless steel, niobium and gold electrodes in vacuum and uniform fields at room, liquid nitrogen and liquid helium temperatures. The range of electrode spacings for the current measurements was 0·1-4 mm and for the breakdown voltages was 0·1-1·8 mm. The results showed that the current decreased with decreasing electrode spacing and decreasing cathode temperature. They also showed that the breakdown voltage increased with increasing electrode spacing and decreasing cathode temperature. It was shown that the prebreakdown currents obeyed a cold-cathode emission law analytically similar to the Fowler-Nordheim relation and that the changes in values could be explained by changes in the field intensification factor and emitting area. The breakdown voltages indicated that the same mechanism prevailed at all spacings and temperatures and suggested that breakdown was initiated by the cold-cathode emission currents causing an instability at either the anode or the cathode.

Prebreakdown currents in ultrahigh-vacuum gaps between aluminium electrodes

Measurements of prebreakdown currents have been made for highly polished plane parallel aluminium electrodes in an ultrahigh vacuum (10−9 torr), as a function of electrode separation, in the range 0.076–2.8 mm. The prebreakdown currents are found to be consistent with the Fowler-Nordheim field-emission theory. The field-in tensification factor is calculated at each gap separation. For gap separations larger than 0.89 mm, a large increase in the prebreakdown current, at a particular applied voltage (ignition), is observed. The ratio of the current increase, depending on electrode separation, is observed to be in the range 10–160. The ignition voltage is determined as a function of gap separation and found to increase with increasing gap separation. It is suggested that the ignition can only occur at a given gap separation, when the prerequisite values of a prebreakdown current, combined with an applied voltage, are simultaneously present. At short gap separations (≪0.76 mm), the ignition phenomenon is absent. It is shown that this is because the condition for the required current value cannot be satisfied at the required ignition voltage.

Change in Field Intensification Factor β of an Electrode Projection (Whisker) at Short Gap Lengths

The field intensification factor, β, was found theoretically to be a function of gap length, projection height, and projection tip radius. The electrode projection was approximated by a grounded plane and separate grounded sphere, the opposing electrode by a charged plane. The results may be used to find the height and tip radius of a projection in a small gap by measuring β as a function of gap length.

A theoretical study of field emission initiated vacuum breakdown

Calculation of the breakdown field due to field emission from cathode protrusions of conical and cylindrical shape has been used in an attempt to explain the various anomalies in recent vacuum breakdown experiments. The onset of melting is taken to be the ultimate breakdown point and the effects of electron back-scattering, space charge, electron penetration at the anode and the Nottingham effect are amongst the important processes considered. The results indicate that the breakdown fields for either cathode or anode primary melting are similar in value. The main parameters affecting whether one or the other mechanism is dominant are the field intensification factor and the geometric shape of the emitter. Results are given for copper, aluminium and tungsten electrodes in the gap range 10-3-10.0 cm.

Interelectrode currents in vacuum for small gaps

Some measurements on small values of pre-breakdown current between metal electrodes for small gaps are reported. These provide more detail on the “bend” in the field emission graphs. The results are interpreted as supporting modest values for the field intensification factor and conflict with an increase in this factor with increased electrode spacing.

The production of positive ions by field ionization at the surface of a thin wire

Wires of platinum and tungsten 4-10 μm in diameter were used. They were placed along the axis of a coaxial cylinder. When the wire was charged positively with respect to the cylinder and any of the gases ethylene, water, oxygen, nitrogen, nitrous oxide, ammonia, carbon monoxide and hydrogen was present, a current was observed, with a voltage between wire and cylinder less than 20 kv. The current was directly proportional to gas pressure except with water and ammonia. It appeared to be due to field ionization at the surface of the wire. Currents exceeding 10-7 A were obtained with wires 2 cm long. Field ionization was also brought about with a thin wire between parallel plates. With the plates apparatus and with the cylinder apparatus, a fraction of the ions produced could be extracted through a slit cut in one plate, or in the cylinder. The electric field at the wire surface was not great enough, for a smooth surface, to produce field ionization. It is proposed that a considerable local intensification of field occurs because of surface roughness. The field intensification factor for a 10 μm diameter platinum wire was investigated by measuring the field emission of electrons from the wire, first as a function of field at constant temperature and secondly as a function of temperature at constant field. The temperature variation of field emission from 650-1375° k agreed very well with the theory given by Good and Muller (1956). Corrections for thermionic emission at the higher temperatures from the flat parts of the surface were made with a method which used the Schottky equation. The field intensification factor found in this way was 70. Such a value explains the occurrence of field ionization.