Radiation field and current of the lightning stepped leader

Abstract

Expressions are derived relating the stepped leader radiation field to the leader current and current propagation velocity. These expressions are also applicable to the return stroke. The waveforms of the stepped leader radiation field measured by Pierce, Appleton, and Chapman can be reproduced by the sum of the effects of two current waves: (1) a slow current wave with a current width at half-maximum of about 14 μsec and a propagation time of about 12 μsec, which produces the wings of the radiation field curve, and (2) a fast current wave with a current width at half-maximum of 4 to 5 μsec and a propagation time of about 1 μsec, which produces the positive and negative peaks of the radiation field. The fast current is associated with the luminous leader step; the slow current is most reasonably associated either with the leader step or with the leader channel above the step. The peak current for the typical stepped leader waveform described by Pierce is calculated to be between about 800 amps and 5 ka; the maximum rate of change of current between about 0.25 and 1.5 ka/μsec. Alternatively, the maximum rate of change of leader current is derived from Hodges's data on the ratio of peak leader radiation field to peak return stroke radiation field. For a modal type α stepped leader the maximum rate of change of current is found to be about 2 ka/μsec; for a modal type β leader, about 10 ka/μsec. The currents calculated to flow in the stepped leader provide a charge transfer of between about 2×10−3 and 10−2 coul per leader step, an insufficient amount of charge to account for the 10−3 coul/m found on a typical fully developed stepped leader. Relatively steady currents must therefore flow in the leader channel to account for the charge transfer. Since the significant light output from a stepped leader has considerably shorter time duration than the significant current, it is probable that the photographed luminosity of the leader is due to the electrical breakdown at the propagating current fronts, rather than to the larger currents that subsequently flow.