The present modeling deals with the physical description of the high-current (>10 kA) constricted vacuum arc, driven by a transverse magnetic field (TMF), as found in vacuum circuit breakers applying TMF arc control. The MHD approach together with detailed heat transfer and evaporation equations for the electrodes are used to describe the arc behavior selfconsistently, restricting to two dimensions (2D). A newly developed model describes the cathode attachment of the constricted arc in form of a large laterally extended foot point, instead of the regular cathode spots. This model leads to the characterization of the physical quantities of the arc plasma and describes the arc motion as step-wise due to the different velocities of the current attachment areas of cathode and anode.
II. PHYSICAL MODELA. Plasma zone:The present conditions allow the application of the MHD approach [1], based on the continuity equations of mass, momentum and energy, in combination with Maxwell's equations and the generalized Ohm's law. These equations are described in [2], and are similar to that of [3]. As usual, the plasma is regarded as quasineutral and consists of interpenetrating fluids of heavy species (ions and neutrals) and of electrons. The mass equation considers the rate equations for Cu, Cu+, Cu++ and Cu++, and it includes the process of ion production and loss by electron impact and recombination due to three body collisions. The fluids of heavy species and electrons have temperatures T and Te, convection velocities u and ue, and pressures p and Pe, respectively.