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This paper deals with the numerical simulation of the constricted high-current vacuum arc (>15 kA), driven by a transverse magnetic field (TMF). The magnetohydrodynamic approach, radiative transfer in P1 approximations, together with the detailed heat transfer and evaporation equations for the electrodes, is used to describe the arc behavior self-consistently in 2D geometry. A model developed describes the cathode attachment of the constricted arc, as a large laterally extended foot point, instead of 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 anode.