The atmospheric pressure carbon arc in inert gases such as helium is an important method for the production of nanomaterials. It has recently been shown that the formation of the carbon deposit on the cathode from gaseous carbon plays a crucial role in the operation of the arc, reaching the high temperatures necessary for thermionic emission to take place even with low melting point cathodes. Based on observed ablation and deposition rates, we explore the implications of deposit formation on the energy balance at the cathode surface, and show how the operation of the arc is self-organised process. Our results suggest that the can arc operate in two different regimes, one of which has an important contribution from latent heat to the cathode energy balance. This regime is characterised by the enhanced ablation rate, which may be favourable for high yield synthesis of nanomaterials. The second regime has a small and approximately constant ablation rate with a negligible contribution from latent heat.