Modeling of electric arcs: A study of the non-convective case with strong coupling

In this paper, we investigate a mathematical model for electric arcs. The model is based on the equations of magnetohydrodynamics, where the flow and heat transfer in a plasma is coupled to electrodynamics. Our approach neglects convection and yields a reaction-diffusion model that includes only the core phenomena of electric arcs: Ohmic heating and nonlinear electric conductivity. The equations exhibit interesting mathematical properties like non-unique steady states and instabilities that can be linked to electric arc properties. Additionally, a 3D axisymmetric simulation of the creation and extinction of an electric arc is presented based on a strongly coupled numerical algorithm for the non-convective model. The approach is especially suited for high-current arcs where strong coupling becomes necessary.