In arc welding the quality of the weld is strongly influenced by the thermal history of the workpiece which is itself governed by the electric arc heat source. The models for predicting weld properties thus need a good evaluation of the distribution of the heat input from thearc to the workpiece. To have a predictive model of arc heat source it is necessary to take into account the cathode and its coupling with the plasma. The coupling allows to calculate the temperature and current density distributions along the cathode surface rather than prescribing them. This thesis focuses on the arc-cathode coupling for a plasma assumed to be in local thermal equilibrium. A self-consistent coupling boundary model for high-intensity electric arc on a refractory cathode (thoriated tungsten) was developed accounting for the physics of the sub-layers of the cathode layer and the non-uniformity of the cathode surface physical state. The cathode layer model accounts for the non-equilibria in the cathode layer. It was tested in one-dimensional calculations and then extended to a cathode-plasma coupling boundary condition for gas tungsten arc implemented in OpenFOAM. Different modelling assumptions commonly used for developing the model were questioned and investigated. It was checked that the secondary electron emission is negligible compared to the effect of emitted electrons and ions. It was verified that it is justified to neglect the space charge of emitted electron when calculating the cathode surface electric field. It was verified that Richardson-Dushman electron emission law supplemented with Schottky correction is used within its domain of validity in GTA applications even for low work function emitters. It was shown that the radiative absorption of the cathode surface is not negligible compared to the radiative emission. The cathode layer model was also further developed to take into account the in homogeneity of the cathode material. It was shown that the cathode in homogeneityhas a significant effect on the size of the arc attachment and consequently on the cathode surface and the plasma temperature. Good agreement was obtained with the measured cathode surface and plasma temperatures without imposing any adjustable parameters. The results showed that the proposed model, which is only based on physical principles, is ableto predict the trends observed experimentally.