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Abstract. A new approach based on antenna theory is presented to describe the lighming returnstroke process. The lightning channel is approximated by a straight and vertical monopole antenna with distributed resistance (a so-called lossy antenna) above a perfectly conducting ground. The antenna is fed at its lower end by a voltage source such that the antenna input current, which represents the lighming return-stroke current at the lightning channel base, can be specified. An electric field integral equation (EFIE) in the time domain is employed to describe the electromagnetic behavior of this !ossy monopole antenna. The numerical solution of EFIE by the method of moments (MOM) provides the time-space distribution of the current and line charge density along the antenna. This new antenna-theory (or electromagnetic) model with specified current at the channel base requires only two adjustable parameters: the return-stroke propagation speed for a nonresistive channel and the channel resistance per unit length, each assumed to be constant (independent of time and height). The new model is compared to four of the most commonly used "engineering" return-stroke models in terms of the temporal-spatial distribution of channel current, the line charge density distribution, and the predicted electromagnetic fields at different distances. A reasonably good agreement is found with the modified transmission line model with linear current decay with height (MTLL) and with the Diendorfer-Uman (DU) model.

[1] The interaction of lightning with the 553-m high CN Tower in Toronto is modeled using the antenna theory model. A simple lossless wire structure is used to represent the tower. The return-stroke channel is modeled as a lossy vertical antenna attached to the tower top. The lossy antenna and the wire structure representing the tower are assumed to be fed at their junction point by a voltage source. The voltage waveform of this source is selected so that the source current resembles a typical lightning current waveform not influenced by the presence of the tall strike object. An electric field integral equation in the time domain is employed to calculate the lightning return stroke current distribution along the CN Tower and along the lightning channel. The equation is solved numerically using the method of moments. The lightning current flowing in the tower at the 474-m level above ground, predicted by the antenna theory (AT) model, compares favorably with the measurements conducted at the CN Tower. Once the temporal and spatial distributions of the current along the tower and along the lightning channel are determined, the corresponding remote electromagnetic fields are computed. Waveshapes of modelpredicted electric and magnetic fields at a distance of 2 km from the tower are in good agreement with measurements. The contribution of the tower to the electric and magnetic fields at 2 km is about four to five times the contribution of the lightning channel.

Modal analysis is widely approached in the classic theory of power systems modelling. This technique is also applied to model multiconductor transmission lines and their self and mutual electrical parameters. However, this methodology has some particularities and inaccuracies for specific applications, which are not clearly described in the technical literature. This study provides a brief review on modal decoupling applied in transmission line digital models and thereafter a novel and simplified computational routine is proposed to overcome the possible errors embedded by the modal decoupling in the simulation/ modelling computational algorithm.

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[1] Electric fields on the ground 500 m, 5 km, and 50 km from the lightning channel base computed using the transmission line (TL) and antenna theory (AT) return-stroke models for a typical subsequent stroke current at the channel base and a return-stroke speed equal to the speed of light (v = c) are compared. The AT model gives a total electric field peak that is about 10% lower than the field peak predicted by the TL model. Optical measurements of the return-stroke speed within the bottom 100 m of the lightning channel are reviewed and found to be not supporting the assumption of v = c.