On the use of lumped sources in lightning return stroke models

[1] We consider the use of lumped voltage and current sources in engineering lightning return stroke models with emphasis on those including a tall strike object. If the model is to be used for computing remote electric and magnetic fields, we suggest a representation of the lightning channel as a transmission line energized by a lumped voltage source, with the voltage magnitude being expressed in terms of the lightning short-circuit current and equivalent impedance of the lightning channel. Such a representation assures appropriate boundary conditions (reflection and transmission coefficients) at the channel attachment point and is equivalent to a distributed-shuntcurrent-source representation of the lightning channel. This is in contrast with the use of series ideal current source which presents infinitely large impedance to current waves reflected from the ground and/or from discontinuities in the lightning channel, such as the moving return stroke front or branches, and therefore is inadequate when such reflections are involved. If the model is to be used only for injecting lightning current into a grounded object or system, a Norton equivalent circuit (an ideal current source in parallel with the equivalent impedance of the lightning channel) is sufficient to represent the lightning discharge.