Time Domain Modelling of First Return Stroke of Lightning

The four most important factors that govern the return stroke evolution can be identified as: (i) electric field due to charge distributed along the channel, (ii) transient enhancement of conductance by several orders at the bridging regime (iii) the non-linear increase in channel conductance at the propagating current front and (iv) the associated dynamic electromagnetic field which support the evolution of current along the channel. For a more realistic modelling of the lightning return stroke, the present work attempts to consider these aspects in suitable manner. The charge simulation method is employed for evaluating the quasi-static field due to (i). For the dynamic field, the problem involves conduction along a thin structure with open boundary on one side. Further, in order to efficiently represent a vertically extended grounded strike object, as well as, channel of quite arbitrary geometry, boundary based approach is believed to be the ideal choice. Considering these, a time-dependent electric field integral equation (TD-EFIE) along with a sub-sectional collocation form of the method of moments (MoM) is chosen for the numerical field evaluation. The dynamic variation of conductance in the channel other than the bridging zone is modelled by a first order arc equation. For the bridging zone, arc equation which explicitly portray in some sense, accumulation of energy is considered. Accordingly, formulations given by Barannik, Popovic and Toepler were scrutinized for their suitability. After some preliminary simulation studies, a self contained model for the first return stoke of a lightning flash is presented. The stability of the model is verified by running the program for longer durations with different cloud base potentials and cloud base heights. Simulation results are in agreement with the field data on current and velocity decay rate for the first one kilometer height. Also, the relation between the charge density at channel tip and the return stroke current peak favorably compares with the literature.