On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes

The initial radiation fields, Poynting vector, and total electromagnetic power that a vertical return stroke radiates into the upper half space have been computed when the speed of the stroke, ν, is a significant fraction of the speed of light, c , assuming that at large distances and early times the source is an infinitesimal dipole. The initial current is also assumed to satisfy the transmission‐line model with a constant v and to be perpendicular to an infinite, perfectly conducting ground. The effect of a large ν is to increase the radiation fields by a factor of (1 ‐ β 2 cos 2 θ) −1 , where β = ν/c and θ is measured from the vertical, and the Poynting vector by a factor of (1 ‐ β 2 cos 2 θ) −2 . This increase is just a few percent or less at small β, but when β = 0.67, the fields are about 80% larger at small θ and 50% larger at θ = 30°, and the power that is radiated is increased by 26%. When β = 0.5 and the peak current is 30 kA, typical values for negative first strokes, the peak power that is radiated into the upper hemisphere is 1.0 × 10 10 W.