On Practical Implementation of Electromagnetic Models of Lightning Return-Strokes

In electromagnetic models, the return-stroke channel is represented as an antenna excited at its base by either a voltage or a current source. To adjust the speed of the current pulse propagating in the channel to available optical observations, different representations for the return-stroke channel have been proposed in the literature using different techniques to artificially reduce the propagation speed of the current pulse to values consistent with observations. In this paper, we present an analysis of the available electromagnetic models in terms of their practical implementation. Criteria used for the analysis are the ease of implementation of the models, the numerical accuracy and the needed computer resources, as well as their ability to reproduce a desired value for the speed of the return stroke current pulse. Using the CST-MWS software, which is based on the time-domain finite-integration technique, different electromagnetic models were analyzed, namely (A) a wire embedded in a fictitious half-space dielectric medium (other than air), (B) a wire embedded in a fictitious coating with permittivity (epsilon(r)) and permeability (mu(r)), and (C) a wire in free-space loaded by distributed series inductance and resistance. It is shown that, by adjusting the parameters of each model, it is possible to reproduce a desired value for the speed of the current pulse. For each of the considered models, we determined the values for the adjustable parameters that allow obtaining the desired value of the return speed. Model A is the least expensive in terms of computing resources. However, it requires two simulation runs to obtain the electromagnetic fields. A variant of Model B that includes a fictitious dielectric/ferromagnetic coating is found to be more efficient to control the current speed along the channel than using only a dielectric coating. On the other hand, this model requires an increased number of mesh cells, resulting in higher memory and computational time. The presence of an inhomogeneous medium generates, in addition, unphysical fluctuations on the resulting current distributions. These fluctuations, which strongly depend on the size of the coating as well as on its electric and magnetic properties, can be attenuated by considering conductive losses in the coating. Considering the efficiency in terms of the required computer resources and ease of implementation, we recommend the use of Model C (wire loaded by distributed inductance and resistance).