Mathematical model of the short arc phenomena at the initial stage

A mathematical model is presented describing transient phenomena accompanied by a vacuum short arc at the initial stage of contact opening. It enables one to describe the evolution of transient short anode dominated arc, which appears just after the rupture of molten bridge, into diffusive cathode dominated arc. The model of an vacuum arc includes equations for the cathode region (sheath, ionization zone, cathode surface and bulk), arc column and anode region. The heat flux components entering and leaving electrode surfaces owing to ion bombardment, electron emission, inverse electron flux and radiation from the arc, melting, evaporation and heat conduction are taken into account. The peculiarity of this model is the radial dependence of unknowns values and anode spot extension with due regard to both arc column expansion and increasing of conic arc base during contact opening. The model enables one to find the temperature and electrical fields, heat flux components, electron, ion, and inverse back-diffusion components of current density in dependence on current, opening velocity, contact gap, and properties of contact materials. It was found also that the duration of transient anode dominated arc depends on the parameters of liquid bridge. Transition of transient anode arc into diffusive cathode arc is formulated. The results of the calculations for the copper and molybdenum contacts are given for the current range from 100 A to 500 A and opening velocities from 0.5 m/sec to 20 m/sec.