An electrodynamic description of lightning return strokes and dart leaders: Guided wave propagation along conducting cylindrical channels

The return-stroke breakdown pulse and the dart leader are treated as electric waves guided by conducting lightning channels; such waves are launched when current is injected into a conducting channel (producing the dart leader) or when charge on a channel begins to drain to Earth (producing the return stroke). The guided waves are self-consistent solutions to the full set of Maxwell's equations, obeying physical boundary conditions for cylindrical channels. These waves are shown (1) to move with velocities substantially slower than c along the channel, (2) to push current inside the lightning channel, (3) to move charge and voltage along the channel, and (4) to transport energy along and into the channel via Poynting flux. The velocity of a guided wave is a function of only three parameters: the channel radius rch, the channel temperature T, and the risetime Δt of the wave front. These velocities are found to fall in the range of velocities of return strokes and of dart leaders. The wave amplitude is fixed by fixing one parameter in addition to rch, T, and Δt; thus four parameters fully determine the velocity of the wave, the voltage of the wave, the current of the wave, the electric field of the wave, the linear charge density of the wave, the power carried by the wave, and the power delivered by the wave into the channel. For an example return stroke those predicted quantities are in agreement with experimental observations and for an example dart leader those predicted quantities are consistent with the limited measurements. The dart leader and the return stroke are caused by the same type of guided electromagnetic waves: the difference in velocity is owed mostly to the difference in channel temperature. In the case of the dart leader the waves deliver Poynting flux along the outside of the channel down from a thundercloud generator to the downward-propagating wave front. At the wave front of the dart leader the delivered energy goes into heating the channel and into storage in the form of E2/8π around the newly charged channel. In the case of the return stroke the Poynting flux is localized to the vicinity of the wave front where stored energy E2/8π is delivered radially inward onto the channel to heat the channel in the propagating front. The net result of a dart leader and return stroke is that charge is moved from the cloud to the ground and that energy is moved from the cloud onto the channel.

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