The diffuse, or spotless, mode of current transfer has been observed on cathodes of vacuum arcs under conditions where the average cathode temperature was high enough, about 2000 K. It has been known for many years that none of the known mechanisms of current transfer to cathodes of vacuum arcs and, in particular, of the electron emission is capable of producing the current densities of the order of 105 - 106 Am-2 deduced from the experiment. A fresh attempt to clarify this question is made in this work. Cathodes made of chromium are considered, on which the most of the experiments have been performed. It is shown that an account of the difference between values of thermionic and photoelectric work functions given in the reference literature allows one to significantly reduce the deviation between the theory and the experiment. Unfortunately, data on thermionic work function available in the literature refer to the cathode surface temperatures below 1400 K, which is significantly smaller than measured temperatures of the chromium cathodes of vacuum arcs operating in the spotless mode. Therefore, further experimental data are needed in order to clarify this effect.

Este trabalho Ø dedicado modelaªo da interacªo plasma-cÆtodo em descargas de arco em vÆcuo e em descargas de arco unipolares. Pela primeira vez foi desenvolvido um modelo numØrico detalhado de manchas catdicas solitÆrias em descargas de arco em vÆcuo. O modelo leva em conta todos os mecanismosrelevantesdosfenmenosfsicosdemanchascatdicas: obombardeamento dasuperfciedocÆtodoporiıesprovenientesdeumplasma prØ-existente; avaporizaªo do material do cÆtodo na mancha, a ionizaªo deste material vaporizado e a interacªo do plasma produzido com o cÆtodo; desenvolvimento do efeito de Joule no interior do cÆtodo; fusªo do material do cÆtodo e movimento do metal fundido sob o efeito da pressªo exercida pelo plasma e da fora de Lorentz; a deformaªo da superfcie fundida do cÆtodo; a formaªo de crateras e jactos de metal fundido; a ejecªo de gotas. Os resultados da modelaªo permitem identicar as diferentes fases da vida de uma mancha solitÆria. A emissªo de electrıes da superfcie do cÆtodo e o transporte de calor por convecªo sªo os mecanismos dominantes de arrefecimento na mancha catdica, limitando deste modo a temperatura mÆxima possvel no cÆtodo. A formaªo de crateras na superfcie do cÆtodo ocorre sem explosıes, seguida da formaªo de um jacto de metal fundido e da ejecªo de uma gota. Os resultados da modelaªo sªo concordantes com estimativas efectuadas para diferentes mecanismos de erosªo do cÆtodo, com base nos dados experimentais relativos erosªo em cÆtodos de cobre de descargas de arco em vÆcuo. A fase inicial de uma descarga de arco unipolar em condiıes relevantes para a fusªo nuclear em reactores tokamak foi investigada no mbito do modelo detalhado de manchas catdicas solitÆrias em descargas de arco em vÆcuo. Mais concretamente, a interacªo de um uxo intenso de energia com uma placa de tungstØnio imersa num plasma de hØlio e a correspondente transferŒncia de corrente foi estudada em condiıes baseadas em experiŒncias laboratoriais. Uma vez que o arco Ø de natureza unipolar, a transferŒncia de corrente fora da mancha Ø tida em consideraªo no modelo utilizado e a variaªo da diferena de potencial entre o plasma e a placa Ø avaliada a partir da condiªo de corrente total nula transferida para a placa a cada instante. Os resultados da modelaªo revelam a formaªo de uma cratera, mas sem a formaªo de um jacto de metal fundido ou a ejecªo de uma gota. A modelaªo Ø realizada para diferentes condiıes e demonstra-se que Ø necessÆrio ter em consideraªo a limitaªo da corrente terminica de electrıes pela banha de carga de espao.

This work is concerned with devising a method of evaluation of electron emission in the framework of the Murphy-Good theory, which would be as simple and computationally efficient as possible while being accurate in the full range of conditions of validity of the theory. The method relies on Pad e approximants. A comparative study of electron emission from cathodes of arcs in ambient gas and vacuum arcs is performed with the use of this method. Electron emission from cathodes of arcs in ambient gas is of thermionic nature even for extremely high gas pressures characteristic of projection and automotive arc lamps and is adequately described by the Richardson-Schottky formula. The electron emission from vaporizing (hot) cathodes of vacuum arcs is of thermo-field nature and is adequately described by the Hantzsche fit formula. Since no analytical formulas are uniformly valid for field to thermo-field to thermionic emission, a numerical evaluation of the Murphy-Good formalism is inevitable in cases where a unified description of the full range of conditions is needed, as is the general case of plasma-cathode interaction in vacuum arcs, and the technique proposed in this work may be the method of choice to this end.

Este trabalho È dedicado ‡ modelizaÁ„o da igniÁ„o de descargas autÛnomas de baixa corrente, e de caraterÌsticas tens„o-corrente mÈdias de descargas de coroa. Foi desenvolvida uma abordagem para simulaÁ„o de descargas quasi-estacion·rias de baixa corrente, sendo aplic·vel para descargas DC e tambÈm de baixa frequÍncia. Esta abordagem colmata a lacuna entre os mÈtodos modernos de modelizaÁ„o numÈrica e as abordagens de engenharia, e foi implementada como parte de um modelo numÈrico que simule as descargas referidas em ar de alta press„o. O modelo inclui equaÁıes de conservaÁ„o e transporte de espÈcies carregadas e a equaÁ„o de Poisson. Utiliza-se um modelo cinÈtico ímÌnimoíde processos quÌmicos no plasma, em descargas de baixa corrente em ar de alta press„o, que tem em conta os eletrıes, uma espÈcie eÖcaz de iıes positivos, e os iıes negativos s O

Three approaches to describing the separation of charges in near-cathode regions of highpressure arc discharges are compared. The first approach employs a single set of equations, including the Poisson equation, in the whole interelectrode gap. The second approach employs a fully non-equilibrium description of the quasi-neutral bulk plasma, complemented with a newly developed description of the space-charge sheaths. The third, and the simplest, approach exploits the fact that significant power is deposited by the arc power supply into the near-cathode plasma layer, which allows one to simulate the plasma–cathode interaction to the first approximation independently of processes in the bulk plasma. It is found that results given by the different models are generally in good agreement, and in some cases the agreement is even surprisingly good. It follows that the predicted integral characteristics of the plasma–cathode interaction are not strongly affected by details of the model provided that the basic physics is right.

Self-organized patterns of cathodic spots have been observed in microdischarges operated in xenon, but not in other gases. However, modelling has indicated that it is, in principle, possible to observe the patterns of spots in discharges operated in other gases provided that experimental conditions, in particular pressure, are right. In this work, self-organized patterns of cathodic spots are for the first time observed in dc glow microdischarges operated in a gas other than xenon: krypton. The experiments have been guided by the modelling. According to both the experiment and the modelling, patterns in krypton are similar to those found earlier in xenon, however occur at higher pressures.

Stability of stationary spots on cathodes of arcs in vacuum and ambient gas has been investigated by means of simulation of development in time of perturbations imposed over steady-state solutions. Two cases of loading conditions have been considered, namely, spots operating at fixed current (the case typical of small-scale experiments) and spots operating at fixed voltage (the case typical of high-power circuit breakers). Results are reported on spots on large copper cathodes of vacuum arcs and on spots on tungsten cathodes of high-pressure argon arcs. It is shown, in particular, that if the ballast resistance in a small-scale laboratory experiment with a high-current arc is insufficient, potential consequence may be a thermal explosion of a spot, if the arc burns in vacuum, and massive melting of the cathode surface, if the arc burns in ambient gas. This conclusion conforms to trends observed in the experiment.

The nonlinear surface heating model of plasma-cathode interaction in high-pressure arcs is extended to take into account the Joule effect inside the cathode body. Calculation results are given for different modes of current transfer to tungsten cathodes of different configurations in argon plasmas of atmospheric or higher pressures. Special attention is paid to analysis of energy balances of the cathode and the near-cathode plasma layer. In all the cases, the variation of potential inside the cathode is much smaller than the near-cathode voltage drop. However, this variation can be comparable to the volt equivalent of the energy flux from the plasma to the cathode and then the Joule effect is essential. Such is the case of the diffuse and mixed modes on rod cathodes at high currents, where the Joule heating causes a dramatic change of thermal and electrical regimes of the cathode. The Joule heating has virtually no effect over characteristics of spots on rod and infinite planar cathodes.

A novel non-equilibrium model has been developed to describe the interplay of heat and mass transfer and electric and magnetic fields in a DC electric arc. A complete diffusion treatment of particle fluxes, a generalized form of Ohm’s law, and numerical matching of the arc plasma with the space-charge sheaths adjacent to the electrodes are applied to analyze in detail the plasma parameters and the phenomena occurring in the plasma column and the near-electrode regions of a DC arc generated in atmospheric pressure argon for current levels from 20 A up to 200 A. Results comprising electric field and potential, current density, heating of the electrodes, and effects of thermal and chemical non-equilibrium are presented and discussed. The current–voltage characteristic obtained is in fair agreement with known experimental data. It indicates a minimum for arc current of about 80 A. For all current levels, a field reversal in front of the anode accompanied by a voltage drop of (0.7–2.6) V is observed. Another field reversal is observed near the cathode for arc currents below 80 A.

A self-consistent space-resolved numerical model of cathode spots in vacuum arcs is realized on the computational platform COMSOL Multiphysics. The model is applied to the investigation of stationary spots on planar cathodes made of copper or composite CuCr material with large ( 20 µm) chromium grains. The modeling results reveal a well defined spot with a structure, which is in agreement with the general theory of stationary cathode arc spots and similar to that of spots on cathodes of arcs in ambient gas. In the case of CuCr contacts with large chromium grains, spots with currents of the order of tens of amperes on copper coexist with spots on chromium with currents of the order of one or few amperes. The main effect of change of the cathode material from copper to chromium is a reduction of thermal conductivity of the cathode material, which causes a reduction of the radius of the spot and a corresponding reduction of the spot current.