The energy balance is used to derive a partial differential eqution for the heat flux potential in a rotational symmetric arc column of finite length. This equation is combined with a corresponding equation for the electric potential in order to calculate the distributions of temperature and electric potential for an arc discharge in a strong axial magnetic field. Because the coupling of the two equations is very complicated, all investigations have to be made numerically. The influence of mass flow is studied by taking into account drastically simplified distributions of the azimuthal and radial flow velocities.
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