Lightning electromagnetic radiation over a stratified conducting ground: Formulation and numerical evaluation of the electromagnetic fields

Abstract

[1] The formulation describing the electromagnetic field radiated by a lightning return stroke over a two-layered conducting ground is presented in this paper. The derivation of the Green's functions required to solve the problem is first discussed in detail, and the expressions for the lightning electromagnetic fields are determined. Afterward, an efficient method for the numerical evaluation of the electromagnetic field is proposed. The proposed method is based on a suitable modification of a previously developed model for the evaluation of the fields in the presence of a lossy but homogeneous soil. Particular attention is devoted to the soil reflection coefficient properties, both from a physical and from a mathematical point of view. In part 2 of the paper, the developed approach and numerical algorithms will be used to evaluate the effect of the soil stratification on the radiated fields and to perform the validity assessment of simplified approaches proposed in the literature.

High-Efficient Evaluation of the Lightning Electromagnetic Radiation Over a Horizontally Multilayered Conducting Ground With a New Complex Integration Path

“…If the MTLE model is applied for the channel current, the formula of the E r (r, z) can be summarized as follows [13]: …”

“…By following the same derivation of pioneer work of Wait's [18], a whole set of expression of electromagnetic field components of a lightning channel, expressed in the form of GSI, is presented in [13]. It seems that there is a minuscule chance to simplify these GSIs to have a closed form, due to the complication of the integrand.…”

“…In [9] and [13], the integration is conducted along the real axis, which makes the Bessel function in the integrand become highly oscillatory and decay slowly for a large horizontal distance, and the situation is getting worse with an increasing horizontal distance. If the integration path is not along the real axis, the characteristic of the integrand of the GSIs will be completely different.…”

“…The detailed formulations of the electromagnetic field produced by a lightning channel with the modified transmission line model with exponential decay (MTLE) stroke model [22] can be found in [13], which serves as a starting point in this paper. The expressions for a multilayered ground can be found in Wait's book [18] thoroughly.…”

“…In [13], an algorithm, based on a suitable modification of the previously developed approach for a lossy homogeneous soil, was well presented. To truncate the GSI, an upper bound in the integral tail for each frequency was derived and evaluated in an analytical way with the incomplete gamma function.…”