Abstract
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.
Highlights
Lightning is known to be a luminous, high current, natural electric discharge produced in the atmosphere, of length extending up to kilometers
The paper is organized in the following manner; a brief review of the existing lightning return stroke models along with their suitability and limitations will be presented (Section 2), which is followed by time domain electromagnetic modelling (Section 3), simulation results (Section 4) and conclusion (Section 5)
Distributed circuit model [4,5,6,7] suffers from serious inherent limitations. It assumes Transverse Electro-Magnetic (TEM) mode of propagation of return stroke current wave which is difficult to accept as (i) there is a large component of electric field in the direction of propagation all along the wavefront and most importantly at the bridging zone, (ii) for TEM mode there should be atleast two conductors with total charge at any wavefront section equal to zero [8] and further, in general, the separation distance between them should be very small compared to the associated wavelengths
Summary
Lightning is known to be a luminous, high current, natural electric discharge produced in the atmosphere, of length extending up to kilometers. Due to the large magnitude and rate of rise of current associated with the return stroke phase of a lightning discharge, it is basically responsible for most of the lightning induced damages and has gained maximum prominence. For the electromagnetic aspects of lightning discharges, it would be adequate to reliably emulate the return stroke current evolution along with. Any realistic model for the return stroke current evolution should necessarily incorporate the above mentioned aspects. This forms the basic goal of this research work. The paper is organized in the following manner; a brief review of the existing lightning return stroke models along with their suitability and limitations will be presented (Section 2), which is followed by time domain electromagnetic modelling (Section 3), simulation results (Section 4) and conclusion (Section 5)
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