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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), as found in vacuum circuit breakers applying the TMF arc control. The magnetohydrodynamic approach, together with the detailed heat transfer and evaporation equations for the electrodes, is used to describe the arc behavior self-consistently, restricted to 2-D. A newly developed model describes the cathode attachment of the constricted arc, as a large laterally extended foot points, instead of regular cathode spots. The arc maintains itself when the electrode temperatures are higher than 3400 K on the cathode and 2900 K on the anode. 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. Index Terms--Cathode connection, heat transfer, magnetohydrodynamic (MHD), moving arc, numerical simulations, transverse magnetic field (TMF) vacuum interrupter, vacuum arc.