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A partial differential equation for the electric potential in an arc with an applied axial magnetic field is derived by using Ohm's law and the equations ∇·j=0 and ∇XE=0. To clarify the physics the potential equation is solved for two simple cases where the plasma is assumed to be homogeneous. The solutions reveal that the Hall parameter ω e  τ e  and the arc length strongly influence the potential distribution. The dependence of the potential on the axial and radial temperature profiles is studied numerically by relaxation methods.

Zur Theorie der Verteilungen von Potential, elektrischer Feldstärke und Stromdichte in einem Lichtbogen endlicher Länge im starken axialen Magnetfeld