On the transmission line model for lightning return stroke representation

The widely used transmission-line (TL) model of lightning return stroke in a vertical channel is most rigorously represented by a vertical phased array of current sources that produce a spherical transverse electromagnetic (TEM) wave in the case of return-stroke speed v equal to the speed of light c. If the radius of the lightning channel were equal to zero, the equivalent representation could be obtained by applying a hypothetical infinitesimal source of pure spherical TEM wave at the bottom of the channel. A non-zero-radius vertical wire above ground excited by a practical source at its bottom end cannot support unattenuated current waves, and the associated electromagnetic field structure is non-TEM.