A Simple Theory for Cathode Jets in Plasma Arcs

International audienceIn this paper, we propose a simple and practical method for the modeling of the local and total magnetic force generated at the cathode. We prove that, if the current density profile obeys the same distribution along the axial-direction, the axial force depends only on the total current and the ratio of the arc spot radius to the radius of the arc column. We also provide an estimate for that the radial force. The power generated by Joules heating is also inserted as a term source in the energy balance equation. The use of source terms is very attractive for large scale industrial applications as it prevents from solving Maxwell's equations that require fine meshing in the arc region and imprecise boundary conditions. It also helps to circumvent the extra complications in computation that are related to the cathode and anode falls. In the case of a mono-phase or 3-phase arc, if steady-state simulations are desired, a time-average is calculated