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.
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