The numerical solution of the energy balance of a cylindrically symmetric hydrogen arc immersed in an axial, strong, homogeneous magnetic field led to the current-voltage-characteristic and the radial temperature distribution. Three types of arc models were used, each with different assumptions on radiation losses. The results show that, by the reduction of the thermal conductivity perpendicular to the magnetic field for a fully ionized plasma, the necessary electrical power is diminished for temperatures along the axis higher than about 2·104°K. For example, an arc with 1 cm radius in a hydrogen atmosphere of 5 · 104 dyne/cm2, in an external magnetic field of 20 kGauss, a temperature along the axis of 105°K requires about 3,5 kW per cm arc length. Of this, radiation losses account for about 0,5 kW per cm. However, without a superimposed magnetic field the electrical power is about 200 kW per cm.