A one‐dimensional analysis of the anode boundary layer of an atmospheric pressure, high intensity argon arc reveals substantial deviations from local thermodynamic equilibrium (LTE) in this layer. The temperature of the heavy species approaches the temperature of the anode in the immediate vicinity of the anode surface, whereas the electron temperature remains sufficiently high to ensure the required electrical conductivity. Temperature and density gradients in the anode boundary layer contribute substantially to the electric current flow so that the potential drop across the boundary layer becomes negative. The main voltage drop, which is in the order of 1 V, is essentially confined to the sheath at the bottom of the boundary layer overlying the anode surface. The thickness of this sheath is several orders of magnitude smaller than the anode boundary layer and the potential drop in the sheath is also negative. Therefore, the anode fall becomes negative for the entire parameter range covered in this paper, in contrast to the results of previous theories. This finding affects the anode energy balance as well as the interpretation of indirect (calorimetric) anode fall measurements which is important for the design of arc gas heaters.