Vhf Radiation Beam Pattern of Return Strokes

Return stroke current pulse can propagate as fast as at a significant fraction of the speed of light c. Such a fast-moving pulse is expected to radiate differently than the conventional RF emitters. In this report, we will carry out a theoretic analysis for the high-speed effect on the radiation beam pattern. The theoretic analysis is based on relativistic considerations, and it differs from previously reported, classical electrodynamic-based analyses. We then investigate the FORTE observations of return strokes. FORTE obtained VHF radiation signals from tens of thousands of return strokes over the contiguous United States in the summers of 1998 and 1999. About 10% of the return strokes were initiated with a very narrow (< 100 ns), intense, and highly linearly polarized radiation pulse. Statistic examinations of these pulses indicate that they form a beam pattern that tilts upward, in agreement with the model predication for a propagating current pulse at speed of ~0.6c. INTRODUCTION Electromagnetic radiation produced by a fast-propagating current pulse will defer from a dipole radiation, especially in the aspect of beam pattern. Le Vine and Willett [1992] studied these effects with a conventional EM approach in which careful quasi-static time-space geometries were examined for the effective pileup or corruption of the radiation field. They have further tested their theoretic models against ground-based, multiplestation electric field change observations. Thottappillil et al., [1998] also investigated the propagation effects based on conventional geometric approaches, and came up with similar results. The FORTE satellite provides, for the first time, systematic VHF lightning observations from the up-half space. This unique capability would allow us to examine more directly the VHF radiation beam pattern of the observed return strokes. In this paper, we will revisit the propagation effects on the radiation field with a different, more concise approach. We will also analyze the FORTE observations of return strokes to reveal the possible beam patterns, and will compare the observed results with the theoretic models. THEORETIC ANALYSIS Figure 1 shows the problem under consideration, in which a current pulse propagates upward along the lightning channel and its produced radiation field is measured at point P(x, y, z). The instantaneous vector potential due to the current segment (dz′) is Here, dz’ is assumed to move along with the current pulse at speed v. The retar of (x, y, z), so that any differential operation on (x, y, z) in the stationary frame This leads to In the (x, y, z) coordinates, t is uniform and ∇t = 0, but viewing from stationary nonlinear compressions of the space and time, so that from Equation 1 we have Rearranging the above equation, we have ( ) , ẑ z d ) z ( r t , z i ) r , t ( A d ′ ′ ′ ′ = π μ