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In an arc plasma generator in air at atmospheric pressure, stabilized by a magnetic field and a vortex flowing gas, with a copper tubular cathode cavity, based on the analysis of forces acting on the cathode region, the shape of the arc column, the direction of the arc current density J near the cathode surface, the position of the cathode spot and its 'jumping' process are studied. The cathode spot's movement over the cathode surface is the result of a repetitious process of birth of new spots and disappearance of old spots provoked by the magnetic field and the gas flow. The spot lifetime is estimated at around (3-4)*10-4 s. Moreover, following this study, the position of the plane (Z=Zc) in which the arc cathode spot rotates is determined as a function of arc current I, components of the magnetic field Br and BZ, flowing gas velocities UZ and Utheta , the velocity of the arc cathode spot rotation Vtheta arc and the radius of the arc cathode spot a0. The results of this study are in satisfactory agreement with experimental determinations. In this analysis cylindrical coordinates r, theta and Z are used with the symmetrical axis of the cathode tube oriented in the Z direction.

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