Characteristic Parameters of the Anode Spot

In most of the works, the anode spot has been shown to be present whenever an electric arc occurs in the wake of an operating contactor, causing a slight contraction of the arc column. The role played by the anode is that of an electron collector, and it has now been acknowledged that the metal surface subjected to electron bombardment is unique with a circular shape. Starting from these hypotheses and using the laws of conservation at the level of the anode spot area, a theoretical model was set up enabling the following parameters to be stated for currents of average intensity (< 2000 A). ra Spot radius. Ta Mean temperature. Ga Erosion speed. Pa Mean pressure. Jea? Current total density. Jea Density of the emitted electron current. The system consisted of a set of six nonlinear equations; however, a numerical solution enabled the values of the six parameters to be stated for a given arc current I. Concerning copper or silver contacts, the results reported will be compared to experimental and theoretical works from other authors. The model proved valid through our own experiments, which showed the evolution of a metal surface subjected to an anode spot. In particular, mention will be made of the redeposition effect which enables the contactors to perform several million operations.     

On fractal properties of small-scale ionospheric irregularities

We consider the problem of relating the local structure of small-scale ionospheric turbulence to the measured frequency-spectrum indices and fractal dimensions of amplitude records of the signals received on the Earth during remote sensing of the ionosphere onboard the satellites. It is shown that knowledge of these parameters permits one to determine the true values of the local-spectrum indices of the electron-density fluctuations for isotropic small-scale turbulence of the ionosphere both under natural conditions and during its modification by high-power short-wave radiation as well as to specify fractal dimensions of space filled by small-scale irregularities of the turbulent structures in the ionosphere. We show the necessity of detailed experimental studies of the fractal properties of small-scale ionospheric irregularities of both natural and artificial origin by using a multifractal analysis in combination with the synchronous correlation processing of received signals during remote sensing of the ionosphere. This will give important information on the local structure of small-scale ionospheric turbulence inaccessible for studies within the framework of the classical method of radio scintillation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 4, pp. 300–308, April 2007.     

Fractal aggregates evolution of methyl red in liquid crystal

The spontaneous formation of dendritic aggregates is observed in a two-dimensional confined layered system consisting of a film composed of liquid crystal, dye and solvent cast above a polymer substrate. The observed aggregates are promoted by phase separation processes induced by dye diffusion and solvent evaporation. The growth properties of the aggregates are studied through the temporal evolution of their topological properties (surface, perimeter, fractal dimension). The fractal dimension of the completely formed structures, when they are coexistent with different types of structures, is consistent with theoretical and experimental values obtained for Diffusion-Limited Aggregates. Under different experimental conditions (temperature and local dye concentration) the structure forms without interactions with other kinds of structures, and its equilibrium fractal dimension is smaller. The fractal dimension is thus not a universal property of the observed structures, but rather depends on the experimental conditions.     

Investigations of the ignition of arc spots on cold cathodes in anoble gas atmosphere

To investigate the ignition of arc spots on cold cathodes under defined conditions, a special experimental setup was developed. An arc ignited between horn electrodes in a pure argon gas atmosphere is blown magnetically against a third so called commutation electrode, which is negatively biased against the arc plasma. The ignition of arc spots on this cathode was investigated by electrical measurements and high-speed photography. The arc traces of short current pulses were examined by in situ optical microscopy of the cathode surface. Two different modes of arc-spot ignition were observed: an initiation by a diffuse glow discharge, which may pass into a constricted arc spot, and an immediate formation of a constricted arc spot. The two modes of arc-spot ignition at atmospheric pressure were attributed to different surface structures, which are characterized by broad or narrow distributions of local ion current density enhancement factors. Ion current density enhancement may raise the field strength and temperature on the tips of microprotrusions so far that they emit electrons. A sufficiently high density of small emission sites produces locally such a high average current density that a plasma channel and an arc spot on the cathode surface arc formed. With lower pressure, the influence of the surface structure is reduced and pushed back by Townsend-γ emission     

Spontaneous extinguishing of a vacuum arc in terms of the ectonmodel

Based on the ecton model, a statistical method for studying the processes in the cathode spot of a vacuum arc has been proposed. It has been demonstrated that the spontaneous extinguishing of a DC arc and the effect of “current chopping” inherent in an AC arc are due to the cellular structure of a cathode spot and by the finite lifetime of an ecton. The principal characteristics that are responsible for the stability of the arc operation are the current per cell and the efficiency of the recovery mechanism. The average operative time of the discharge is longer for the materials showing lower currents per cell. The influence of the conditions of arc operation, such as the parameters of the external electric circuit, the cathode surface condition, the presence (or absence) of an external electric field, etc., is reduced in the main to a change in the efficiency of the recovery mechanism     

Direct observation of cathode spot grouping using nanostructured electrode

Clear footprint of an arc spot, which is formed after arc spot runs on a fiberform nanostructured tungsten, reveals the detailed structure and motion of arc spot in a magnetic field. Fine inner structure of an arc trail is observed, exhibiting that many sub-arc spots existed inside the arc spot, with forming a group. The sub-arc spots move randomly but they globally move to some direction, which is affected by the axial and parallel magnetic field with respect to the specimen. The trails are analyzed by using box-counting method and fractality of the arc trails in magnetic field is discussed. It is shown that the nanostructured metal can clearly record the footprint of the arcs, similar as the man's footprints in the snow, and be a powerful tool for basic arc experiments.     

Heat transfer and cold cathode erosion in electric arc heaters

A simple thermophysical model is proposed for cold electrode erosion in electric arc heaters. The model regards erosion as characterized by an effective enthalpy of electrode material ablation, resulting in heat unbalance between heat supply and heat removal by conduction. Replacing the arc spot by a moving surface heat source, the space-time evolution of the electrode surface temperature is studied in coordinates coupled to the source. Applying heat diffusion equations, we show that the erosion problem can be represented by a system of three simple equations. An experimental coaxial setup, with a magnetically driven arc, has been used for the erosion measurements in copper electrodes. Special thermal experiments were carried out for measuring needed arc spot parameters. A comparison of the model with our own and other experimental data demonstrates a reasonable agreement. The present model reveals the relative significance of the different parameters in the erosion process, and permits us to predict the erosion behavior in cold electrode electric arc heaters in a wide range of parameters     

Structure and parameters of vacuum arc cathode spots

The effect of such parameters of cathode materials as the heat of atom evaporation, atomic weight, work function of electrons on the structure of cathode spots of a vacuum arc, conditions of charged particle generation, and, most important, the F-emission of electrons, is considered. Determining the interrelation of cathode parameters and processes in a vacuum arc cathode spot helps develop conditions for a vacuum arc to effectively modify the surfaces of materials.     

On aberrations in saw‐tooth refractive X‐ray lenses and on their removal

The X‐ray lens, which is composed of opposing canted saw‐tooth structures, originally assembled from cut‐out pieces from long‐playing records, is understood by recognizing that an incident plane X‐ray wave will traverse a varying number of triangular prisms in them. The refraction will deflect any beam towards the prism tips and the variation of the deflection angle, which grows linearly with the number of traversed prisms, can result in X‐ray focusing. The structure offers focusing flexibility by simply changing the taper angle. This report will discuss the aberrations arising in the saw‐tooth structure in its simplest form with identical prisms. It is found that the saw‐tooth structures in low‐Z materials with focal length below 1 m provide less flux density in the focal spot than stacks of one‐dimensionally focusing refractive lenses with identical transmission function. This is due to excessive aberrations in the regular structure, which are absent in stacks of concave lenses, and which limit the focusing to spot sizes of just submicrometre dimensions, as measured experimentally for some lenses. It will be shown that this limitation can be overcome by appropriately modifying the prism shape. Then the image size could be reduced by about an order of magnitude to the diffraction limit with competitive numbers even below 0.1 µm. Microfabrication techniques are identified as the appropriate means for producing the structures.     

Structure, internal friction, and Young’s modulus of fractal carbon deposits

We have observed that carbon deposits obtained by atomizing graphite in an electric arc in an atmosphere of argon and helium exhibit porosity and possess fractal structure. The results of measurements of the internal friction Q ⁻¹ and the effective Young’s modulus E as a function of temperature are presented. Data on the resistivity, density, and microhardness of the carbon deposits are presented. A possible mechanism for formation of fractal structures in carbon deposits is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 584–586 (March 1998)     

Application of vacuum arc cathode spot model to graphite cathode

A model of near-electrode processes is applied here to describe the behavior of cathode spots on graphite cathode in vacuum arc. The physical model is based on a kinetic treatment of cathode evaporation, electron emission from the cathode, and plasma production. The model consists of physical assumptions and a system of equations that are formulated in the paper. Spot parameters, such as cathode erosion rate, cathode potential drop, cathode surface temperature, current density, electric field, and plasma density, temperature, and velocity in the near-electrode region are calculated numerically. The calculation includes the dependence of spot parameters on spot current and spot lifetime. The variation of spot parameters as a function of spot lifetime are very strong at lifetimes shorter than 10 μs. The calculations indicate that Joule heating in the cathode body is significant, and may exceed cathode heating by the ion heat flux. Calculated spot parameters are compared with the corresponding experimental data for relatively low arc currents (<100 A) and their agreement is discussed     

Some features of the fractal structure of the developed small-scale ionospheric turbulence

We present the results of the first studies of the fractal structure of the developed small-scale ionospheric turbulence (SSIT) during special experiments on radio-raying of the midlatitude ionosphere by signals from orbital satellites in 2005–2006. It is established that under conditions of developed turbulence, typical values of the fractal dimension of the space occupied by natural SSIT inhomogeneities are, as a rule, close to the topological dimension of their embedding space, and the true values of the spectral index of isotropic SSIT only slightly differ from the corresponding generally accepted nominal values in the embedding space. Nevertheless, even small differences in the mentioned parameters detected in the experiment witness a sharply nonuniform distribution of the local fractal structures of the developed SSIT in space. We propose a stochastic model of the nonstationary process for fast amplitude fluctuations of signals during their propagation in the ionosphere with nonuniform spatial distribution of small-scale electron-density fluctuations. Eventually, namely this nonuniform distribution of small-scale electron-density fluctuations leads to the specific multifractal structure of the amplitude records of received signals. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 287–294, April 2008.     

Unipolarbögen

Unipolar arcs have achieved considerable importance as a plentiful source of contaminations in tokamak plasmas. A definition of unipolar and plasma induced discharges is given, and the main properties of the space charge sheath between plasma and wall as well as the existence conditions of unipolar arcs (necessary voltage drop, current balance) are considered. From a simple model that includes the superposition of two completely different plasmas — the tokamak plasma and the cathode spot plasma of the arc — the radial dependencies of the current densities and voltages between plasma and wall and of the plasma parameters are derived. It is shown, that — in typical cases — the anode region is a ring-shaped area situated at distances from the arc cathode spot r > b with 0.3 cm ? b ? 1 cm, and that the density decrease of the arc plasma n ～ r^?μ necessitates an exponent 2 ? μ ? 3 because of the current balance condition (arc current = backflow current). Moreover some thermodynamic aspects (unipolar arcs as a kind of dissipative structures), the ignition problem, the effects of magnetic fields, the problems of diagnostics and the possibilities of simulations are shortly discussed.     

The Arc Cathode Regime: An Approach from Basic Laws

The question is examined whether or not the existence of a cathode mechanism with high power density may be predicted from general physical laws, as well as the order of magnitude of the main cathode parameters of such a discharge. The answer is yes, though – because of many feedbacks and simplifications – the numerical values calculated in this way are not more than crude estimations. Essentially two conditions have to be fulfilled: The first is the dominance of collective electron emission processes, the second is the dominance of Joule heating combined with the limit of stationarity. Both conditions result in similar values of the cathode parameters. In this low-current region (about 10…100 A) the existence of a high-current density cathode mechanism (order of magnitude: 10⁸ A/cm²) is proved, with consequences for all the other parameters, in rough agreement with the results of measurements in arc cathode spots. Thus the typical arc spot regime may be founded theoretically by these argumentations.     

带状真空电弧磁过滤器等离子体分布特性及制备类金刚石膜研究

采用大尺寸矩形石墨靶作为真空阴极电弧源, 研制了带状真空电弧磁过滤器. 使用法拉第杯和朗缪尔探针对90 ℃弯曲磁过滤器中的带状等离子体出口所在平面的15个区域的离子能量和密度进行了测试; 用该带状真空电弧磁过滤器制备了类金刚石膜(diamond-like carbon, DLC); 对相应位置上的类金刚石膜进行了Raman分析和膜厚测量. 结果表明: 磁过滤器出口所在平面的15个划分区域中离子能量分布接近麦克斯韦分布, 离子能量分布与类金刚石膜的结构具有明显的对应特征, 离子密度分布与DLC膜膜厚分布相互之间具有相关性.     

Properties of Anchored Cathode Spots of a Dc Mercury Vacuum Arc

Ensembles of anchored cathode spots of a dc mercury vacuum arc have been studied by fast framing and streak photography. From these photographs, several statistical properties of the cathode spots have been determined: distribution functions for their diameters, velocities, and displacements, as well as spot shape and average values for the spot current and its density. The measurements showed that the anchored cathode spots were quasi-stationary. No indications of a microstructure within the individual cathode spots were found at an optical resolution of 0.37 ?m. Strong evidence is presented that the dc cathode spot parameter values reported here are typical for a clean mercury surface, and that those reported in the earlier literature are typical for impurity-covered surfaces.     

Measurement of Aggregate Fractal Dimensions Using Static Light Scattering

Aggregates formed from colloidal particles will vary in shape according to the aggregation regime prevalent. Compact structures are formed when the aggregation is slow, whilst loose tenuous structures are formed when rapid (or diffusion limited) aggregation prevails. These structures can be fractal in nature, that is, there is a relationship between porosity and the number of primary particles making up the aggregate, and is described by the fractal dimension, d_F. Fractal dimensions of hematite aggregates have been measured experimentally using the static light scattering technique. Fractal dimensions varied with aggregation regimes; for the rapid aggregation regime, d_F was found to be 2.8, whilst for conditions in which aggregation was slow (retardation forces prevail), d_F's of 2.3 were measured. For conditions which lead to aggregation in which both diffusion and retardation forces play a part, structures with fractal dimensions such that 2.3 < d_F < 2.8 were found. The effects of adsorbed fulvic acid, a naturally occuring organic acid, on the kinetics of hematite aggregation and on the resulting structure of hematite aggregates were also investigated. The study of aggregate structure shows that the fractal dimensions of hematite aggregates which are partially coated with fulvic acid molecules are higher than those obtained with no adsorbed fulvic acid. The scattering exponents obtained from static light scattering experiments of these aggregates range from 2.83 ± 0.08 to 3.42 ± 0.1. The scattering exponents of greater than 3 indicate that the scattering is the result of objects that contains pores which are bounded by surfaces with a fractal structure, and can be related only to surface fractal dimension. The high fractal dimensions are due to restructuring within the aggregates, which only occured at low coverage by the organic acid.     

微米量级表面结构形貌特性对二次电子发射抑制的优化

抑制二次电子倍增效应是提高空间大功率微波器件和粒子加速器等设备性能的重要课题,而使用表面处理降低材料的二次电子发射系数是抑制二次电子倍增的有效手段.为优化寻找抑制效果最好的表面形貌,本文采用蒙特卡罗方法模拟了各种微米量级不同表面形貌的二次电子发射特性,研究占空比、深宽比、结构形状及排列方式等的影响.模拟结果表明,正方形、圆形、三角形凸起和凹陷结构的二次电子发射系数随占空比和深宽比的增大而减小,但存在饱和值;凸起结构的排列方式对二次电子发射系数的影响不大,但是凸起结构形状却对二次电子发射系数的影响较大,其中三角形的抑制效果最佳.对凹陷结构而言,不同形状的抑制效果差别不大;同时,占空比和深宽比相同时,凸起结构较凹陷结构抑制效果更佳.究其原因,核心在于垂直侧壁的“遮挡效应”,凹陷结构遮挡效应的大小与“陷阱”垂直高度有关,而凸起结构遮挡效应的大小和凸起部分的斜方向投影大小有关.     

Strategies for Evaluating Boundary Fractal Dimensions by computer aided image analysis

For many profiles the values of the boundary fractals deduced by different exploration techniques are identical but the presence of deep fissures of convoluted structure can perturb the information gathered by the exploration technique. Data for different boundaries generated by different exploration techniques are used to illustrate the physical significance of the deduced fractal dimensions as evaluated using the different techniques. Heuristic programs for teaching an automated instrument to distinguish between different regions of ruggedness around a profile and to prevent “fractal rabbits” from appearing in the data are outlined. It is shown how the logic for removing fractal rabbits from the experimental data will also generate data on the presence of sharp edges on the profile. The possible occurrence of pseudo-texture fractal dimensions from projection occlusion is discussed.     

Mapping physical problems on fractals onto boundary value problems within continuum framework

In this Letter, we emphasize that methods of fractal homogenization should take into account a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal attributes can be quantified by a set of dimension numbers. Accordingly, physical problems on fractals can be mapped onto the boundary values problems in the fractional-dimensional space with metric induced by the fractal topology. The solutions of these problems represent analytical envelopes of non-analytical functions defined on the fractal. Some examples are briefly discussed. The interplay between effects of fractal connectivity, loop structure, and mass distributions on electromagnetic fields in fractal media is highlighted. The effects of fractal connectivity, geodesic metric, and loop structure are outlined.