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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.
- 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.
- 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.
- Modelling interaction of multispecies plasmas with thermionic cathodesPublication . Benilov, M. S.; Cunha, M. D.; Naidis, G. V.The model of the near-cathode plasma, developed previously for the case of a single-species plasma-producing gas, is generalized for the case of multiple plasma-producing species. Results are presented of calculation of a diffuse mode of current transfer to tungsten cathodes in a mercury plasma with an addition of sodium. It is found that the presence of 1% of sodium results in a considerable expansion of the range of stability of the diffuse mode.
- Phenomenological approach to simulation of propagation of spots over cathodes of high-power vacuum circuit breakersPublication . Cunha, M. D.; Wenzel, N.; Benilov, M. S.; Hartmann, W.A phenomenological description of an ensemble of a large number of spots on negative contacts of high-power vacuum circuit breakers is developed by means of generalization of the concept of random walk of a single cathode spot in low-current vacuum arcs. The model is formulated in terms of a convection-diffusion equation governing the evolution of the number of spots per unit area, taking into account the variation of the number of spots with the arc current and the “retrograde repulsion” between spots. The approach is applied to description of the distribution of cathode spots during the initial expansion process after arc ignition in conditions of two independent experiments simulating high-power switches. A reasonably good agreement between the theory and the experiment is found. The developed model can be used as a module of global numerical models of the interruption process in high-power vacuum circuit breakers.
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