On Return-Stroke Currents and Remote Electromagnetic Fields Associated with Lightning Strikes to Tall Structures. Part I: Computational Models

In this paper, analytical expressions relating far fields and currents associated with lightning strikes to tall towers are derived. The derived equations are general and can be used with any engineering model. It is shown that the far field can be decomposed into three terms, namely (1) contribution of the main return stroke pulse along the lightning channel, (2) contribution of the multiple-reflection process along the elevated strike object, including the contribution of upward propagating pulses transmitted into the channel, and (3) contribution of the so-called ‘‘turn-on’’ terms, associated with the current discontinuity at the return stroke wavefront. This discontinuity is associated with neglecting reflections at the upward moving front. It is also shown that only the first term is model-dependent and that the far field–current relationship does not significantly depend on the adopted engineering model. It is therefore possible to use the analytical equation relating the current peak and the associated distant electric or magnetic fields, derived by Bermudez et al. (2005) for the transmission line (TL) model, for any engineering model extended to include a tall strike object. It is also shown that the peak amplitude of the electromagnetic field radiated by a lightning strike to a tall structure is relatively insensitive both to the value of the return stroke speed and the top reflection coefficient. These results and findings of this paper emphasize the key differences between return strokes initiated at ground level (or from short strike objects) and those striking tall towers: (1) The electromagnetic field from lightning strikes to tall towers is largely determined by the tower and only to a lesser extent by the channel, (2) electromagnetic fields associated with tall strike objects are less model-sensitive than those corresponding to a strike to ground; in particular, the early time response of the field is nearly model-independent, and (3) unlike ground-initiated strikes, for which the far field peak is strongly dependent on the return stroke speed (proportional according to the TL model), far field peaks associated with strikes to tall strike objects are little sensitive to the return stroke speed. This is a particularly interesting result when lightning currents are measured directly on instrumented towers to calibrate the performance of lightning location systems, since in most practical cases the value of the return stroke speed is unknown. Note that points (2) and (3) can be considered as corollaries of point (1).