A 1-D model of the interaction between an electric arc and a solid refractory cathode has been developed. This model is based on the equilibrium of the charged particle fluxes in the cathode layer by considering current density conservation, and balance of energy at the sheath/presheath and at the sheath/cathode surface interfaces forming a closed system of equations. It allows the sheath and presheath to be described and the main physical quantities to be obtained by only using current density as input parameter. The calculations were performed for atmospheric argon discharge and a tungsten refractory cathode. The results obtained, such as the cathode sheath voltage drop and the power flux transmitted to the cathode, are compared with those of the literature, and good agreement is observed. Moreover, our model can be used for a range of current densities (1 × 10 4 -5 × 10 8 A · m −2 ) accurately describing attachment at low current. The heat flux deduced reaches a maximum of 6 × 10 7 W · m −2 at equilibrium between ionic heating and thermionic cooling. The thermionic electron emission current density is dominant for current densities higher than 5 × 10 6 A · m −2 .

A theory based on the literature works is developed to define a self-consistent model of the arc–cathode interaction in thermal plasma domain. The proposed model, applied in this paper in a two-dimensional coordinate system includes a physical description of the arc–cathode interaction, the cathode bulk, the sheath, the pre-sheath and the local thermodynamic equilibrium plasma column.This model allows assuming the electric current conservation through a two-temperature treatment of the sheath and pre-sheath regions. This model has been applied in a free burning arc configuration in an argon gas with a cylindrical tungsten cathode and current intensity equal to 200 A. The orders of magnitude of the current density and of the heat flux are, respectively, 106 A m−2 and 107 W m−2.Three parametric studies are performed: on the ionization layer length, on the value of the secondary emission coefficient and on the formulation of the electrical conductivity in the pre-sheath. The size of the ionization layer and the chosen value of the secondary emission coefficient have a significant influence on the properties of the discharge.

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