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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.
- Revisiting theoretical description of the retrograde motion of cathode spots of vacuum arcsPublication . Benilov, Mikhail S.; Kaufmann, Helena T. C.; Hartmann, Werner; Benilova, Larissa G.A fresh attempt to develop a self-consistent descrip tion of the retrograde motion of cathode spots on volatile cathodes is undertaken. Three potential mechanisms of effect of transversal magnetic field on the distribution of parameters in the spot are studied: the effect of magnetic field on hydrodynamics processes in the spot, in particular, on the formation of liquid-metal jet and the droplet detachment, and the effect of transversal magnetic field over the motion of ions and emitted electrons in the near-cathode space-charge sheath. It is found that for typical conditions of cathode spots in vacuum arcs the effect of magnetic field over the formation of liquid-metal jet and the droplet detachment is negligible; the motion of the ions in the near-cathode space-charge sheath is not disturbed; and the motion of the emitted electrons is disturbed only marginally. Thus, the above-mentioned potential mechanisms are hardly relevant and the first-principle understanding is still missing. A phenomenological description of the retrograde motion is developed as an alternative. The description employs general considerations without relying on specific assumptions and the (only) unknown parameter can be determined from comparison with 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.
- Computing DC discharges in a wide range of currents with COMSOL MultiPhysics: time-dependent solvers vs. stationary solversPublication . Almeida, P. G. C.; Benilov, M. S.; Bieniek, M. S.; Cunha, M. D.; Gomes, J. G. L.; Kaufmann, H. T. CostaThe benefits of the usage of stationary over time-dependent solvers of COMSOL Multiphysics in the modelling of DC discharges are explored and demonstrated using as examples glow and high pressure arc discharges; in particular, it is investigated whether time-dependent solvers can be used for a systematic computation of different modes of these discharges. It has been found that most modes of both glow and high-pressure arc discharges cannot be computed in the whole range of their existence by a time-dependent solver. Further, time-dependent solvers are unsuitable for a computation of all the states belonging to the retrograde sections of the current-voltage characteristics of the modes, so the discharge manifests hysteresis, which, in principle, can be observed in the experiment.
- Numerical simulation of the initial stage of unipolar arcing in fusion-relevant conditionsPublication . Kaufmann, H. T. C.; Silva, C.; Benilov, M. S.A model for the initial phase of unipolar arcing has been developed with account of an external energy source which triggers the arcing, the vaporization of the atoms from the heated surface, the ions and electrons produced by ionization of the vapor, the electron emission from the metal surface, and melt motion and surface deformation. Current transfer outside the arc attachment is taken into account and the potential difference between the plasma and the metal surface (the plate) is evaluated from the condition that the net current transferred to the plate is zero at each moment. The model is used for simulation of the interaction of an external energy load (laser beam) with a tungsten plate immersed in a helium background plasma. The results revealed the formation of a crater, but no jet formation or droplet detachment. If the plate is large (R = 100 mm), the peak temperature attained is 5200 K, and the plate potential remains below the plasma potential. If the plate is small (R = 10 mm), a peak temperature of 7500 K is reached, the potential of the plate surpasses the plasma potential, circulation of the melt at the pool periphery occurs, and the erosion (which is mainly due to the vaporization of the metal atoms in the spot) reaches the value of 37 μg.
- Detailed numerical simulation of cathode spots in high-current vacuum arcsPublication . Kaufmann, H. T. C.; Cunha, M. D.; Benilov, M. S.; Hartmann, W.; Wenzel, N.A detailed numerical model of cathode spots in high-current vacuum arcs is given. The model provides a complete description of all phases of life of an individual spot taking into account the presence of metal vapor left over from a previous explosion, the interaction of the vaporized plasma from the cathode spot with the cathode surface, and Joule heat generation in the cathode body. Melting and motion of molten metal due to Lorentz force are also accounted for, together with surface tension effects and the pressure exerted by the plasma over the cathode surface. First results are presented and analyzed for copper cathodes with a protrusion and planar cathodes. Emphasis is given to the investigation of the effect of the vaporized plasma and of hydrodynamic processes. No thermal runaway is observed.
- Advanced modeling of plasma-cathode interaction in vaccum and unipolar arcsPublication . Kaufmann, Helena Teresa da Costa; Benilov, Mikhail S.; Cunha, Mário DionísioEste 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.
- Detailed numerical simulation of cathode spots in vacuum arcs—IPublication . Cunha, Mário D.; Kaufmann, Helena T. C.; Benilov, Mikhail S.; Hartmann, Werner; Wenzel, NorbertA model of cathode spots in high-current vacuum arcs is developed, with account of the plasma cloud left over from a previously existing spot, all mechanisms of current transfer to the cathode surface, including the contribution of the plasma produced by ionization of the metal vapor emitted in the spot, and the Joule heat generation in the cathode body. The simulation results allow one to clearly identify the different phases of life of an individual spot: the ignition, the expansion over the cathode surface, and the thermal explosion. The expansion phase is associated with a nearly constant maximum temperature of the cathode, which occurs at the surface and is approximately 4700–4800 K. Thermal explosion is a result of thermal instabil ity (runaway), which develops below the cathode surface when the Joule heating comes into play. The development of the spot is interrupted if the plasma cloud has been extinguished: the spot is destroyed by heat removal into the bulk of the cathode due to thermal conduction. Therefore, different scenarios are possible depending on the time of action of the cloud: the spot may be quenched before having been formed or during the expansion phase, or even at the initial stage of thermal explosion.