Time-domain solution to Maxwell´s equations for a lightning dart leader and subsequent return stroke leader and subsequent return stroke

In this study we present an analytic solution to Maxwell´s Equations for the lightning leader followed by a novel return stroke model. We model the leader as a downward propagating boxcar function of uniform charge density and constant velocity, and the subsequent return stroke is modeled as an upward propagating boxcar with a time dependent velocity. Charge conservation is applied to ensure self-consistency of the driving current and charge sources, and physical observations are used to support model development. The resulting transient electric and magnetic fields are presented at various distances and delay times and compared with measured waveforms and previously published models.