The formation of a steady helical instability in a wall-stabilized hydrogen arc at low currents is investigated experimentally. To determine the onset-point of the instability theoretically the basic equations of electrodynamics and the balance of mass, momentum and energy are solved in the limiting case of vanishing growth-rate of the instability, taking into account the dissipative terms as well as the temperature dependence of the density. It turns out that the destabilizing J X B-forces, which try to deflect the arc by a convective heat-transfer, are balanced by the thermal stabilization of the tube-wall as well as by the unsym metrical energy-production in the curved arc. Onset-point and pitch of the helix result from the theory in full agreement with the measurements.
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Jürgen Mentel (1971) studied this question.