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This paper deals with the numerical simulation of constricted high-current vacuum arcs (> 15 kA), driven by a transverse magnetic field. The magnetohydrodynamic approach and the radiative transfer equation in the P1 approximation, together with detailed treatment of heat transfer and evaporation at the electrodes, are used to describe the arc behavior self-consistently in a 2-D geometry. The model developed describes the cathode attachment of the constricted arc as a large laterally extended foot point, instead of as regular cathode spots. This model leads to the characterization of the physical quantities of the arc plasma and describes the arc motion. A stepwise movement of the arc results due to different instantaneous velocities of the current attachment areas at the cathode and the anode.