Behaviour of the Rise and Fall Characteristics of the Channel Discharge Function for the Generalized Lightning Traveling Current Source Return Stroke Model

The channel discharge function in the generalized lightning travelling current source return stroke model (GTCS) in a complex and time domain is analyzed. Heidler's form of the channel-base current function is accepted. The expression of the initial channel charge distribution function is proposed. First, using this form of the charge distribution function it is shown that the previously established return stroke models, the Bruce-Golde (BG), the Traveling Current Source - (TCS), the Diendorfer-Uman (DU) and the Thottappillil-Uman (TU) models can be derived as the special cases of the GTCS. Second, if the general case is treated, i.e., the values of the parameters in the initial channel charge distribution function are arbitrary (independent of the channel-base current parameters), certain limits of their values can be deduced regarding the general properties of the channel discharge function in the GTCS. Third, for this case the simple analytical forms of the channel discharge function in the time domain for a few microseconds of the discharge (discharge risetime) at the observed channel altitude are derived. Since the risetime of the channel discharge function defines the magnitude and the risetime of the radiated lightning electromagnetic pulse (LEMP) it turns out that the measuring of the LEMP at various distances can provide the values of the function parameters. This will be the “key” for the further examination of the gaseous-dynamic processes in the channel during the return stroke phase.