Antenna models of lightning return-stroke: an integral approach based on the method of moments

Abstract

In this chapter, we have presented the antenna theory-based electromagnetic models of the lightning return stroke where the lightning return-stroke channel (RSC) is considered as a monopole wire antenna above a conducting ground. We have also described the time- and frequency-domain solutions of the governing electric field integral equation (EFIE), utilizing the method of moments. The EFIE is used to determine the current distribution along the channel from which remote electromagnetic fields are readily computed.In the original antenna theory (AT) model in the time domain, the lightning RSC is represented by a lossy vertical monopole antenna, which is fed at its lower end by a voltage source. The voltage waveform is specified on the basis of the assumed input current of the antenna and the antenna resistance per unit length. There are only two adjustable parameters in this model, namely, the wave propagation speed for a nonresistive channel and the value of the distributed channel resistance. Once these two parameters are specified, the spatial and temporal distributions of the current along the channel are found by solving the governing EFIE, using the method of moments. The time-domain AT model has been compared with other lightning return-stroke models in terms of current and line charge density distributions along the channel, and the predicted remote electromagnetic fields. The primary features of the time-domain AT model are as follows: (1) the current amplitude decreases and current rise time increases as the current wave propagates along the channel, in agreement with optical observations, (2) the current wave propagates along the channel at a speed lower than the speed of light due to corona effects and ohmic losses in the channel, and (3) the model-predicted electric and magnetic fields are reasonably consistent with typically measured fields.