Time of appearance of optical breakdown in air near the surface of a solid

An estimate is obtained of the time of appearance of optical breakdown in air near a rough surface of a solid. The various stages of breakdown are considered: heating of surface irregularities to the evaporation temperature, equilibrium heating of the vapor to the ignition temperature, and transformation of local spherical breakdown regions into a homogeneous planar breakdown in air. An analysis is made of the variance of the time of appearance of breakdown as a function of the degree of roughness of the surface.