Comparison of Electromagnetic Models of Lightning Return Strokes Using Current and Voltage Sources

Electromagnetic models based on antenna theory have been recently applied in lightning studies. Their practical use is facilitated by existing thin-wire antenna numerical codes that utilize localized voltage sources. Such voltage sources have to be tuned to provide the lightning channel-base current for which experimental data are available. This involves some preparatory steps, such as the determination of the input impedance of the antenna (in the frequency domain) and Fourier and inverse Fourier transforms. These steps may involve methodological and computational errors. In this paper, we present initial results of an effort to introduce an alternative current source model formulation that will enable a direct specification of the channelbase current in electromagnetic models of lightning. INTRODUCTION One of the classes of models applied recently in lightning studies is the so-called electromagnetic models [Rakov and Uman, 1998]. They are usually based on thin-wire antenna approximation and involve a numerical solution of Maxwell’s equations using the method of moments [Harrington, 1993] to find the current distribution along the lightning channel, from which electromagnetic fields can be computed. Moini et al. [2000] and Kordi et al. [2002] applied the time-domain approach utilizing the Thin-Wire Time-Domain code (TWTD) [e.g., van Blaricum, 1972], and Baba and Ishii [2001, 2003] applied the frequency-domain approach utilizing the Numerical Electromagnetic Code (NEC-2) [Burke, 1980]. One potential problem in application of existing antenna computer codes in lightning studies is related to the use of a localized voltage source model. Since lightning is usually characterized by measured or analytically specified currents at the channel base, the natural choice in modeling would be a current instead of voltage source. However, current sources are usually not provided in the existing antenna codes. This short paper explores the possibility of using current sources in electromagnetic models of lightning. We will confine our analysis to the frequency domain approach and the implementation to one well-known thin-wire, momentmethod antenna code by Richmond [1974]. MODELING OF SOURCES IN ANTENNA THEORY As an example Fig. 1 illustrates two alternative possibilities for energizing the antenna by a voltage and a current source and their possible field representations. Jordan and Balmain [1968] discusses other different source model representations. The impressed electric field E0 (Fig. 1a) and Dirac delta current source J0 (Fig. 1b) are equivalent to localized voltage and current sources, respectively, applied across an infinitesimally narrow gap (delta gap sources). (a) (b) E = -V / z 0 0 ∆ V0 I0 J z x y 0 δ δ ( ) ( )