Abstract
Cloud-to-ground lightning discharges in 2D and 3D domains were simulated using a stochastic dielectric breakdown model. The dependency between fractal dimension of the discharge patterns and the power of the local electric field η was critically evaluated. An exponential decrease in fractal dimension was observed as η increases. Fractal dimension of simulated 3D discharge patterns and 2D images of lightning discharges were compared by taking projections of simulated patterns. Discharge patterns similar to actual lightning were obtained when η ≈ 5.2. Influence of ground objects on simulated lightning discharges was also studied by introducing additional boundary conditions to the ground plane. It was observed that pointed structures on the ground have a higher probability of attracting simulated lightning discharges. An extension was introduced to dielectric breakdown model to simulate the development of upward connecting positive leader discharges that occur during the decent of a downward moving negative leader. It was found that the height of the stepped leader tip above the ground (at the time when the upward connecting leader initiation occurs) is dependent on the initial breakdown voltage threshold. The height of the point of interception was found to decrease exponentially as the breakdown threshold is increased. DOI: http://dx.doi.org/10.4038/sljp.v13i2.5433 Sri Lankan Journal of Physics, Vol. 13 ( 2 ) ( 2012 ) 09 - 25
Highlights
Electrical discharges that occur during the breakdown of all gaseous, liquid and solid dielectrics are recognized as having a strong tendency to develop into complex branched structures
Stochastic dielectric breakdown model was applied to both 2D and 3D domains to simulate lightning discharges
Appearance and fractal dimension of discharge patterns are strongly dependent on the model parameter η
Summary
Electrical discharges that occur during the breakdown of all gaseous, liquid and solid dielectrics are recognized as having a strong tendency to develop into complex branched structures. Various categories of discharges such as lightning, surface discharges, and treeing in polymers occur as trajectories of luminous filaments, which often branch into intricate patterns. There are fundamental differences between discharge mechanisms of those various discharge types, global structure of the branched tree-like patterns often shows a close structural similarity within a large variety of discharge types[1]. N. Perera et al /Sri Lankan Journal of Physics, Vol 13(2), (2012) 9-25 10
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