Lightning Electromagnetic Fields: Modeling and Measurements

All lightning processes, in both cloud and cloud-toground discharges, are associated with the motion of charges an& as a result, produce electromagnetic fields. Only one (presumably the most important from an EMC point of view) process, the return stroke in cloud-toground lightn& is considered in this review. There are basically four levels of sophistication in the mathematical modeling of the lightning return stroke. (1) The first, and most mathematically sophisticated level, typically involves the solution of three gas dynamic equations representing the conservation of mass, of momenand of energy, coupled to two equations of state, with the input parameter being channel current versus time, and the initial conditions imposed on the solution being the initial channel temperature the initial channel radius, and the initial channel pressure or mass density. Such “physical” models are primarily concerned with the radial evolution of a short segment of lightning channel and its associated shock wave (primary model outputs include temperature, pressure, and mass density as a function of radial coordinate and time). (2) The second level of sophistication is represented by electromagnetic models that are based on a lossy, thin-wire antenna approximation to the lightning channel. These models involve a numerical sol&on of Maxwell's equations. (3) The third level of sophistication is represented by distributed-circuit models that describe the lightning discharge as a transient process on a vertical transmission line characterized by resistance (R), inductance (I,), and capacitance (C) all per unit length. The line is usually assumed to be uniformly charged (by the preceding leader) to a specified potential and then closed at the ground end with a specified earth resistance to initiate the return stroke. There have been attempts to incorporate a “physical” model into a distributed-circuit model, the forma being used to find R as a function of time. (4) The fourth level of sophistication is represented by “e@neeaing” models that specify a spatial and temporal distribution of the channel current (or the channel charge density) based on such observed lightning return-stroke characteristics as current at the channel base, upward-propagating f?ont speed, and luminosity profile.