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

Rizos N. Krikkis ()
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Rizos N. Krikkis: Institute of Thermal Research, 2 Kanigos Str., PO Box 106 77 Athens, Greece

J, 2026, vol. 9, issue 3, 1-19

Abstract: 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.

Keywords: inductively coupled plasma; wall-stabilized arc; thermal plasma; Elenbaas–Heller equation; multiplicity (search for similar items in EconPapers)
JEL-codes: I1 I10 I12 I13 I14 I18 I19 (search for similar items in EconPapers)
Date: 2026
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