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Model of the formation of an elementary crater on the cucr cathode of a vacuum interrupters

Semiempirical hydrodynamical model has been developed to describe the formation of a microcrater and liquid-metal jets in vacuum arc on CuCr cathode with chrome particles that are both, larger or smaller than microcrater within the two-dimensional axisymmetric problem formulation. This model includes Navier-Stokes equations for viscous incompressible liquid with free surface, thermal conductivity equation that considers heat convection and Joule heating, and continuity equation for calculation of current density distribution in the cathode. It was shown that the diameter of elementary crater in homogeneous Cr cathode is equal to 3-7 μm when the time of current flow through cathode binding area is equal to 20-60 ns within current range of elementary cell of cathode spot that is 1.5-7 A. Due to relatively low thermal conductivity of chrome the effect of Cr particle size on crater parameters is significant only if their size comparable with crater diameter. If particle size is larger than the diameter of molten area at least by 0.5 μm, space-time characteristics of crater formation process are identical to that of the Cr homogenous cathode. If initial size of chrome particle is smaller than the radius of forming crater, the chrome is pressed out of the crater.