The Solution Structure of the Elenbaas–Heller Equation for Inductively Coupled Plasmas and Wall Stabilized Arcs

A numerical bifurcation analysis is presented for inductively coupled plasmas and wall-stabilized arcs for argon and hydrogen. Because of the non-linear transport and radiative properties, both problems admit multiple solutions, up to three for argon and up to four for hydrogen. The multiplicity structure primarily dependents on the non-linear, and, especially, the non-monotonic relationship between thermal conductivity and temperature. As a result of the non-monotonicity, a multipoint energy equilibrium between joule heating (heat generation) and heat dissipation by conduction and radiation exists, giving rise to the multiplicity that is a characteristic feature of both radiating and non-radiating arcs. Despite the relatively simple one-dimensional model employed, the agreement with the experimental data is good.