An improved return stroke model with specified channel‐base current

Abstract

An improved return stroke model that is both physically oriented and has a relatively straightforward mathematical basis is proposed. The current at the channel base is specified, and a time‐dependent discharging of the charge stored on the leader channel determines the channel current as a function of height and time. The discharging process is separated into (1) the exponential discharge of the leader head and leader core with a relatively short time constant, less than 1 μs, which we call the “breakdown” time constant, and (2) the exponential discharge of the charge stored around the leader core with a longer time constant, of the order of microseconds. If a typical measured channel‐base current is assumed and if the discharge time constants are properly chosen, electric and magnetic field wave shapes calculated with the model exhibit all the significant characteristics of measured fields. From a comparison of calculated and measured field wave shapes, we find a ratio of the breakdown time constant to the channel‐base current rise time between 1 and 5. Comparison of typical characteristics of field wave shapes from natural and from artificially initiated (triggered) lightning indicates a faster discharging process for triggered lightning. Depending on the breakdown time constant, the return stroke speed determined using the well‐known formula for the transmission‐line model, with inputs being the peak electric field and peak current from the present model, are in the range from about 50 percent to 90 percent of the return stroke speed assumed in the present model. The corresponding transmission‐line model speeds determined from the peak derivatives of the electric field and current are in the range from about 140 percent to 160 percent of the assumed return stroke speed. These results supply some indication of why transmission‐line model speeds determined from the ratio of measured peak current and field derivatives in triggered lightning are greater than the speeds determined from the ratio of measured peak currents and fields. For a given channel‐base current, the initial peak electric field and field derivative derived from the model increases as the height above ground of the strike point increases. The new model can therefore explain the differences in the data obtained from the triggered lightning studies at Kennedy Space Center in 1985 and in 1987 as being due to the different height of the triggering structures in those two years. If natural lightning strikes an elevated object, the increase of the initial electric field and field derivative can result in an additional substantial error in determining the peak current and peak current derivative from the transmission‐line model.