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In an arc without external magnetic field the current carrying region is identical with the conducting plasma column. This is no longer generally true if the arc is in an axial magnetic field and if the electrode radius is much smaller than the plasma radius. Radial current components then produce a rotational motion of the plasma and an azimuthal Hall current, and hence electromotive forces which try to suppress the current perpendicular to the magnetic field. In a plasma with finite viscosity the rotation is determined by the Navier-Stokes equation, which is solved here for a homogeneous plasma simultaneously with generalized Ohm's law. The results show that the plasma rotation is always an essential, and often the dominant, mechanism for guiding the arc current parallel to the magnetic field lines.

Zur Begrenzung der radialen Ausdehnung des Lichtbogenstromes durch ein axiales Magnetfeld: I. Problemstellung, Bogenmodell und typische Resultate