Two-dimensional analysis of free burning arcs in argon

The authors present a theoretical model of a free burning argon arc. Equations describing the conservation of mass, momentum and energy are solved together with Ohm's law and Maxwell's equation for the magnetic field in a cylindrical coordinate system. The material properties used in these solutions are derived theoretically, using the assumption of local thermodynamic equilibrium (LTE). Calculations are made for an axisymmetric, laminar arc burning between a rod electrode and a plane electrode. Comparisons between predicted and measured temperatures and velocities show good agreement for 100 A, 200 A and 400 A arcs in argon for a pre-specified current density of 10⁸ A m^-2 at the rod electrode and a plasma pressure of 1 atm. They describe the consequences of variations in the current density at the rod electrode and in the net radiation losses. They also discuss the importance of energy transfer due to the electron convection current and analyse in detail the various components which contribute to the momentum and energy conservation.