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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.
- 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.
- 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.
- 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.
- 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.
- Modeling cathode spots in vacuum arcs burning on multi-component contactsPublication . Benilov, M. S.; Benilova, L. G.; Cunha, M. D.; Hartmann, W.; Lawall, A.; Wenzel, N.A self-consistent space-resolved numerical model of cathode spots in vacuum arcs is developed on the basis of the COMSOL Multiphysics software. The model is applied to cathode spots on copper-chromium (CuCr) contacts of vacuum interrupters. In the limiting case of large grains, the main effect of change in cathode material from Cu to Cr is the reduction of thermal conductivity of the cathode material, which causes a reduction of spot radius and spot current. Hence, the model indicates that spots with currents of the order of tens of amperes on Cu coexist with spots on Cr with currents between one and two amperes. The parameters of spots on small Cr grains of the order of 10 µm size are rather close to those of spots on pure Cu, whereas the parameters for spots on medium-size Cr grains of around 20 µm are quite different from those of spots on both pure Cu and pure Cr. The power flux is directed from the cathode into the plasma, i.e., it is the cathode that heats the plasma – and not the other way round. What maintains the spot is a substantial Joule heating inside the cathode bulk. About 70 percent of the heat is generated in the grain and 30 percent in the surrounding copper. One may hypothesize that such grains are highly unstable, leading to explosive-like behavior with a consequent additional loss of cathode material, and a severe limitation in spot lifetime.
- Simulation of thermal instability in non-uniformities on the surface of cathodes of vacuum arcsPublication . Cunha, M. D.; Benilov, M. S.; Hartmann, W.; Wenzel, N.Instability stemming from the strong dependence of electron emission current on the local surface temperature plays an important role in current transfer to hot cathodes of arc discharges. In the case of vacuum arcs, this instability may lead to micro explosions on cathode surface even if the surface is planar. This work is concerned with numerical simulation of effect produced by surface non-uniformities. It is found that the effect is non-trivial: the presence of surface non-uniformities can not only accelerate the development of the instability, which is what one would expect intuitively, but also slow it down and even suppress.