A leader-return-stroke consistent macroscopic model for calculations of return stroke current and its optical and electromagnetic emissions

Abstract

A downward lightning flash usually starts with a downward leader and an upward connecting leader followed by an upward return stroke. It is the preceding leader that governs the following return stroke property. Besides, the return stroke property evolves with height and time. These two aspects, however, are not well addressed in most existing return stroke models. In this paper, we present a leader-return stroke consistent model based on the time domain electric field integral equation, which is a growth and modification of Kumar's macroscopic model. The model is further extended to simulate the optical and electromagnetic emissions of a return stroke by introducing a set of equations relating the return stroke current and conductance to the optical and electromagnetic emissions. With a presumed leader initiation potential, the model can then simulate the temporal and spatial evolution of the current, charge transfer, channel size, and conductance of the return stroke, furthermore the optical and electromagnetic emissions. The model is tested with different leader initiation potentials ranging from −10 to −140 MV, resulting in different return stroke current peaks ranging from 2.6 to 209 kA with different return stroke speed peaks ranging from 0.2 to 0.8 speed of light and different optical power peaks ranging from 4.76 to 248 MW/m. The larger of the leader initiation potential, the larger of the return stroke current and speed. Both the return stroke current and speed attenuate exponentially as it propagates upward. All these results are qualitatively consistent with those reported in the literature.