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This paper presents an analysis on the statics and dynamics of a current carrying plasma channel under the influence of an applied magnetic field and under very general flow conditions. Based on this analysis a stability criterion for a discharge channel which emanates from a crater of a low-pressure arc cathode attachment wil be derived. As a consequence of this stability theory one may explain arc spot motion by a kink instability of the discharge channel causing the channel to bend more and more and eventually contacting the cathode surface at a nearby site thereby creating a new emitting spot. By means of this criterion, the dissipation mechanisms during a spot lifetime are determined for pure copper and molybdenum cathodes under the assumption of least possible voltage requirement.