Magnetic field approaches in dc thermal plasma modelling

Abstract

The self-induced magnetic field has an important role in thermal plasma configurations generated by electric arcs as it generates velocity through Lorentz forces. In the models a good representation of the magnetic field is thus necessary. Several approaches exist to calculate the self-induced magnetic field such as the Maxwell–Ampere formulation, the vector potential approach combined with different kinds of boundary conditions or the Biot & Savart (B&S) formulation. The calculation of the self-induced magnetic field is alone a difficult problem and only few papers of the thermal plasma community speak on this subject. In this study different approaches with different boundary conditions are applied on two geometries to compare the methods and their limitations. The calculation time is also one of the criteria for the choice of the method and a compromise must be found between method precision and computation time. The study shows the importance of the current carrying path representation in the electrode on the deduced magnetic field. The best compromise consists of using the B&S formulation on the walls and/or edges of the calculation domain to determine the boundary conditions and to solve the vector potential in a 2D system. This approach provides results identical to those obtained using the B&S formulation over the entire domain but with a considerable decrease in calculation time.