We present results of the numerical simulation of a constricted vacuum arc at high current (> 10 kA) driven by a magnetic field in a three-dimensional (3d) geometry. Such arcs are found in vacuum interrupters using the transverse magnetic field (TMF) arc control method. The model takes into account in a consistent way the electric current, the magnetic field generated by it, as well as the flow of material and heat in the plasma and in the electrodes. Especially for the two arc foot points, that is, the interfaces of the hot plasma column with the cathode and the anode, the material and heat flows are calculated from a microscopic description of the processes in the sheath. The simulation is able to describe a self-sustained constricted arc moving under the influence of the magnetic field generated by its current including the heating of the electrodes and the formation of new arc roots. Results can be compared with those of simulations made in the past, which are based on the same model, but are using a two-dimensional (2d) geometry only. First results show that the basic findings of the two-dimensional simulations can be confirmed. Systematic studies are, however, not yet practical as the computational effort is high.
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