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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 times 104-5 times 108 A ldr m-2) accurately describing attachment at low current. The heat flux deduced reaches a maximum of 6 times 107 W ldr m-2 at equilibrium between ionic heating and thermionic cooling. The thermionic electron emission current density is dominant for current densities higher than 5 times 106 A ldr m-2.