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Textbooks rarely give time−domain solutions to antenna problems. For the case of a finite linear antenna along which a fixed current waveform propagates, we present analytical time−domain solutions for the electric and magnetic radiation (far) fields. We also give computer solutions for the total (near and far) fields. The current waveform used as an example in the computer calculations approximates that of a lightning return−stroke, a common geophysical example of the type of radiation source under consideration.

[1] X-ray and electric field measurements were made during five nearby negative natural lightning strikes in north central Florida during the summer of 2004. The observed X-ray emission typically was detected $1 ms before the first return stroke, during the stepped-leader phase, and had energies extending up to a few hundred keV. The X rays were produced in discrete, intense bursts emitted in coincidence with the formation of the leader steps, demonstrating unambiguously that the source of lightning X rays is closely related to the stepping process. The X-ray emission from lightning stepped leaders is found to be remarkably similar to that from lightning dart leaders, suggesting that these different types of leaders share a common mechanism. The reported observations have important implications for understanding how runaway breakdown occurs and how lightning leaders propagate. Citation: Dwyer, J. R., et al. (2005), X-ray bursts associated with leader steps in cloud-to-ground lightning,

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We compare five lightning return stroke current models that exhibit a simple relationship between the current at the return stroke channel-base and the current along the return stroke channel, namely the Bruce-Golde (BG) model, the transmission line (TL) model, the Master, Uman, Lin, and Standler (MULS) model, the Traveling Current Source (TCS) model, and the Modified Transmission Line (MTL) model, by assuming a common current wave shape at the channel base and then calculating the channel currents and charges and the resultant electric and magnetic fields. There are basically two characteristics that distinguish the models, namely, (1) the treatment of the return stroke wave front and (2) the spatial and temporal distribution of charge removed from the leader channel. The simpler BG model can be used as an excellent approximation to the TCS model. The latter reduces to the former when the current injected downward by the traveling current source has an infinite speed. The MULS model is equivalent to the MTL model when the MULS uniform current is assumed to be zero. The BG and TCS models produce sharper initial field peaks than do the TL, MTL, and MULS models. The ratio of the peak field derivative to the peak current derivative is near the ratio of the peak field to the peak current for the MULS and MTL models and is equal for the TL model, whereas for the BG and TCS models the ratio of the peak derivatives is about twice the ratio of the peak field to peak current. The TL model is unrealistic for long-time field calculations due to the fact that no net charge is removed from the channel. The other four models produce overall fields which are reasonable approximations to measured fields from natural lightning even though, for the assumed channel-base current, the BG and TCS models do not reproduce the observed distant-field zero crossing and the MTL and MULS models do not reproduce the magnetic "hump" observed after the initial field peak at close range. None of the models can reproduce the fine structure observed in the measured fields. 1. 20,395 20,396 NuccI ET AL ' LIGHTNING RETURN STROKE CURRENT MODELS D = 200 km D = •OO km FiB. 2. (a) Typical vertical electric field intensity (leEr column) and horizontal maBnctic flux density (riBht column) Ear first (solid line) and subsequent (dashed line) return strokes and distances oE 1, 2, 5, 10, 15, 50, and 200 kin. The EollowinB characteristic Ecaturcs oE the wave Earms arc identified •or electric field, initial peak, ramp startinB time, romp, and l?0-•s value and zero crossinBs; Ear maBnctic field, initial peak, hump, halE-value. Adopted from Li• • al. [1929].were not correlated by stroke. Willett et al. [1989], in an extension of the previously described experiment, presented simultaneous measurements of channel-base current, current derivative, return stroke speed, electric field at 5 km, and electric field derivative at 5 km. Some data of the type described by Willett et al. [1989], provided by the Centre d'Etudes Nucleaires de Grenoble (CENG), the Centre Na- 13...

We analyzed in detail the electric field variations preceding the first return strokes of 80 cloud‐to‐ground lightning flashes in nine different storms observed at the NASA Kennedy Space Center during the summers of 1976 and 1977. The electric field variations are best characterized as having two sections: preliminary variations and stepped leader. The stepped‐leader electric‐field change begins during a transition period of a few milliseconds duration marked by characteristic bipolar pulses. The durations of stepped leaders lie most frequently in the range 6–20 milliseconds. We infer from our measurements and critical review of the previous literature that there is only one type of stepped leader, not the two types, α and β, often referred to in the literature.