Maxwell’s Construction for Non-linear Heat Structures and Determination of Radius of Arc Spots on Cathodes

The temperature distribution in a half-space (the cathode bulk) heated by an energy flux coming from the adjacent media (plasma) is considered for the case when the dependence of the energy flux density on the local surface temperature is localized in a narrow temperature range. A condition is derived of co-existence of a region that collects the energy flux with a surrounding energy flux-free region (Maxwell’s construction). This condition allows one to calculate the radii of current spots on arc cathodes.