Campos Eletromagnéticos produzidos por descargas atmosféricas: uma abordagem analítica no domínio do tempo.

Abstract

This work develops a set of time-domain analytical equations which allows the calculation of the electromagnetic fields produced by lightning discharges. A revision of the treatment of this subject in the technical literature is presented, from the pioneering studies carried out in the beginning of the last century up to the most recent publications. In the following, the characteristics of a lightning discharge are described, highlighting the parameters used in the "engineering models" developed for the calculation of the fields and induced voltages. This description includes the basic assumptions and techniques used along the text, including a discussion on its implications in the calculation of the electromagnetic fields. The calculation is carried out initially considering perfectly conducting earth, leading to equations that are very important for the calculation of the fields for finitely conducting earth. Considering perfectly conducting earth, expressions for the vertical electric field, radial electric field and azimuthal magnetic field are developed. After that, the work addresses the effect of finitely conducting earth, leading to analytical expressions for the radial electric field at the earth surface, which is generated by the azimuthal magnetic field and by the flow of current through the earth. The equations are developed for stimuli in the shape of step, being lately expanded analytically for stimuli in the shape of trapezium. The application of the expressions for arbitrary stimuli is carried out numerically through the Duhamel Integral. Along the text, the main expressions are verified by comparing their results with results obtained from other techniques, like numeric integration, Sommerfeld Integrals or finite-difference in time-domain (FDTD). The last chapter is dedicated to present the measurement of the radial electric field at the earth surface, using rocket-triggered lightning (RTL), and the experimental results are compared with the results obtained from the expressions developed in this work.