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- Detailed numerical simulation of cathode spots in vacuum arcs: Interplay of different mechanisms and ejection of dropletsPublication . Kaufmann, H. T. C.; Cunha, M. D.; Benilov, M. S.; Hartmann, W.; Wenzel, N.A model of cathode spots in high-current vacuum arcs is developed with account of all the poten tially relevant mechanisms: the bombardment of the cathode surface by ions coming from a pre existing plasma cloud; vaporization of the cathode material in the spot, its ionization, and the inter action of the produced plasma with the cathode; the Joule heat generation in the cathode body; melting of the cathode material and motion of the melt under the effect of the plasma pressure and the Lorentz force and related phenomena. After the spot has been ignited by the action of the cloud (which takes a few nanoseconds), the metal in the spot is melted and accelerated toward the periph ery of the spot, with the main driving force being the pressure due to incident ions. Electron emis sion cooling and convective heat transfer are dominant mechanisms of cooling in the spot, limiting the maximum temperature of the cathode to approximately 4700–4800 K. A crater is formed on the cathode surface in this way. After the plasma cloud has been extinguished, a liquid-metal jet is formed and a droplet is ejected. No explosions have been observed. The modeling results conform to estimates of different mechanisms of cathode erosion derived from the experimental data on the net and ion erosion of copper cathodes.
- Bifurcation points in the theory of axially symmetric arc cathodesPublication . Benilov, M. S.; Cunha, M. D.Steady-state current transfer from arc plasmas to axially symmetric cathodes is treated in the framework of the model of nonlinear surface heating. An approach is developed to calculate the bifurcation points at which three-dimensional spot-mode solutions branch off from solutions describing the diffuse mode and axially symmetric spot modes. In particular, the first bifurcation point positioned on the diffuse-mode solution has been calculated, and thus its stability limit, i.e., the current below which the diffuse mode becomes unstable. Calculation results are given for the case of a tungsten cathode in the form of a circular cylinder in high pressure plasmas. The effect produced on the stability limit by variations of control parameters ~cathode dimensions, work function of the cathode material, plasma-producing gas, and its pressure! is studied and found to conform to trends observed experimentally. The stability limit is found to be much more sensitive to variations of control parameters than characteristics of the diffuse mode are, the strongest effect being pro duced by variations of cathode dimensions and of the work function of the cathode material. This finding conforms to the fact that the diffuse-spot transition is difficult to reproduce in the experiment.
- Formation of stationary and transient spots on thermionic cathodes and its preventionPublication . Almeida, Pedro G. C.; Benilov, M. S.; Cunha, M. D.Spots on cathodes of high-pressure arc discharges induced by a rapid increase in the arc current are studied numerically and experimentally. Appearance of stationary and transient spots is analysed in the context of the general pattern of steady-state modes of current transfer to thermionic cathodes and their stability. Transient spots are studied in experiments with COST-529 standard lamps. Modelling and experimental results are in reasonable agreement. A method to prevent formation of transient spots on cathodes of high-pressure arc discharges by means of short negative rectangular current pulses is proposed and validated both numerically and experimentally. Experimental indications are found that the main mechanism of blackening of burners of HID lamps that accompanies appearance of transient cathode spots is evaporation of the cathode material and not sputtering.
- Modelação da interacção entre um plasma de arco de alta pressão e cátodos refractáriosPublication . Cunha, Mário DionísioNesta dissertação apresento um estudo detalhado de vários aspectos da interacção entre um plasma de arco de alta pressão e cátodos refractários. Um modelo da camada de plasma junto ao cátodo num plasma sujeito a uma pressão da ordem de uma ou várias atmosferas é reconsiderado com base em recentes resultados teóricos. A física da camada de plasma junto ao cátodo é analisada para valores da queda de tensão na camada de plasma junto ao cátodo até 50V, de acordo com recentes resultados experimentais que mostram que a queda de tensão na camada de plasma junto ao cátodo numa descarga de arco de alta pressão pode atingir valores tão elevados. São identificados os mecanismos que originam a não monotonia da dependência da densidade de fluxo de energia (proveniente do plasma para a superfície do cátodo) em relação à temperatura da superfície do cátodo, para um valor fixo da queda de tensão junto ao cátodo. Uma descrição fechada da interacção plasma-cátodo é obtida por meio da resolução numérica do problema não linear com condições de fronteira para a distribuição da temperatura no interior do corpo do cátodo. São apresentados resultados da modelação numérica da descarga difusa nas condições de funcionamento de uma lâmpada de descarga experimental, sendo bom o acordo entre os resultados numéricos e os dados experimentais. Manchas solitárias num cátodo plano infinito e modos difuso e mancha axialmente simétricos em cátodos finitos de descargas de arco de alta pressão são estudados num grande intervalo de corrente. São analisados aspectos gerais e apresentados resultados numéricos referentes a cátodos de tungsténio planos e de forma cilíndrica a operar num plasma de argon à pressão atmosférica para correntes de arco até 100 kA. Émostrado, em particular, que a temperatura da superfície do cátodo no interior de uma mancha solitária varia relativamente pouco, podendo ser estimada com uma precisão de cerca de 200 − 300K sem ser necesário resolver a equação da condução térmica no corpo do cátodo. O comportamento assimptótico das soluções para um cátodo finito no caso limite de altas correntes é encontrado e confirmado pelos resultados numéricos. É confirmado um padrão geral das características tensão-corrente de vários modos de transferência de corrente em cátodos finitos sugerido previamente com base numa análise de bifurcações. É estudada a transição de modos mancha num cátodo finito no limite de cátodos de grandes dimensões para o modo mancha solitária num cátodo plano infinito. É estabelecido que o modo mancha solitária representa uma forma limite do modo mancha de alta tensão num cátodo finito. É considerada a questão da distinção entre modo difuso e modo mancha num cátodo finito. É desenvolvida uma abordagem para o cálculo de pontos de bifurcação nos quais soluções mancha tridimensionais bifurcam-se a partir de soluções que descrevem o modo difuso e modos mancha axialmente simétricos. Em particular, é calculado o primeiro ponto de bifurcação posicionado na solução que descreve o modo difuso e, por conseguinte, o seu limite de estabilidade, isto é, a corrente abaixo da qual o modo difuso torna-se instável. São apresentados os resultados da modelação numérica efectuada para o caso de um cátodo de tungsténio de forma cilíndrica a operar num plasma de alta pressão. É estudado o efeito produzido no limite de estabilidade pelas variações dos parâmetros de controle (dimensões do cátodo, função de trabalho do material do cátodo, tipo e pressão do gás que produz o plasma). Foi encontrado que o comportamento do limite de estabilidade sujeito a estas variações está em conformidade com as tendências observadas experimentalmente. Foi encontrado que o limite de estabilidade é muito mais sensível às variações dos parâmetros de controle do que as características tensão-corrente do modo difuso, sendo o efeito mais forte produzido pelas variações das dimensões do cátodo e da função de trabalho do material do cátodo. Este resultado está em conformidade com o facto experimental de que a transição difuso-mancha é de difícil reprodução.
- Numerical investigation of the stability of stationary solutions in the theory of cathode spots in arcs in vacuum and ambient gasPublication . Benilov, M. S.; Cunha, M. D.; Hartmann, W.; Wenzel, N.The stability of stationary spots on cathodes of arcs in vacuum and ambient gas is investigated by means of the simulation of the temporal evolution of perturbations imposed over steady-state solutions. Two cases of loading conditions are considered, namely, spots operating at a fixed current (the case typical of small-scale experiments) and spots operating at a 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 small-scale laboratory experiments with a high-current arc is insufficient, the 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.
- Simulating changes in shape of thermionic cathodes during operation of high-pressure arc dischargesPublication . Cunha, M. D.; Kaufmann, H. T. C.; Santos, D. F. N.; Benilov, M. S.A numerical model of current transfer to thermionic cathodes of high-pressure arc discharges is developed with account of deviations from local thermodynamic equilibrium occurring near the cathode surface, in particular, of the near-cathode space-charge sheath, melting of the cathode, and motion of the molten metal under the effect of the plasma pressure, the Lorentz force, gravity, and surface tension. Modelling results are reported for a tungsten cathode of an atmospheric-pressure argon arc and the computed changes in the shape of the cathode closely resemble those observed in the experiment. The modelling has shown that the time scale of change of the cathode shape during arc operation is very sensitive to the temperature attained by the cathode. The fact that the computed time scales conform to those observed in the experiment indicate that the model of non-equilibrium near-cathode layers in high pressure arc discharges, employed in this work, predicts the cathode temperature for a given arc current with adequate accuracy. In contrast, modelling based on the assumption of local thermodynamic equilibrium in the whole arc plasma computation domain up to the cathode surface could hardly produce a similar agreement.
- Stability of stationary solutions in the theory of cathode spots in arcs in vacuum and ambient gasPublication . Benilov, M. S.; Cunha, M. D.; Hartmann, W.; Wenzel, N.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.
- Effect of protrusions on cathodic-arc-attachment mode in high-pressure arc dischargesPublication . Benilov, M. S.; Cunha, Mário D.; Faria, Maria J.It is shown via computer simulations that a protru sion on a thermionic arc cathode may dramatically change the pattern of steady-state modes of current transfer. This happens through a bifurcation of a special type occurring at certain geom etry of the cathode and may play a role in operation of electrodes of compact high-intensity discharge lamps.
- Three-wave interaction in two-component quadratic nonlinear latticesPublication . V. V. Konotop, V. V.; Cunha, M. D.; Christiansen, P. L.; Clausen, C. BalslevWe investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that energy conversion and pulse propagation known from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other.
- The Feynman integrand for the perturbed harmonic oscillator as a Hida distributionPublication . Cunha, Mário; Drumond, Custódia; Leukert, Peter; Silva, José Luís; Westerkamp, WernerWe rwiew some basic notions and results of White Noise Analysis that are used in the con struction of the Feynman integrand as a generalized White Noise functional. We show that the Feyn man integrand for the harmonic oscillator in an external potential is a Hida distri