Steady‐state analysis of electromagnetic field by vertical electrical dipole over lossy ground

Abstract

AbstractThe lightning discharge effect is shown by a model in which a lightning current climbs to a lightning cloud from the ground. The electromagnetic field induced at the observation point is the integration of the contribution due to an infinitesimal vertical dipole placed on the discharge path integrated along the path from the ground surface to the height of the cloud. When the conductivity of the ground is taken into account, the expression of the electromagnetic field due to the infinitesimal electric dipole contains a term given by a complicated infinite integral called the Sommerfeld integral that includes the Bessel function. For a wave source with an isolated waveform lasting for a short period of time such as the lightning discharge current, the frequency components exist over a broad range. Hence, in the analysis of the transient electromagnetic field by the lightning discharge, the frequency changes significantly with the source location. As a result, the behavior of the integrand in the Sommerfeld integral changes significantly. This paper treats a case in which the wave source varies sinusoidally so that the transient analysis is anticipated and a useful result is obtained for the steady state. To this end, the analysis of the electromagnetic field induced by a vertical electric dipole on the lossy ground is described with special attention given to the numerical processing of the Sommerfeld integral.