The Magnetic Field Induced by a Lightning Strikes Indirect Effect Double Exponential Current Waveform

Problem statement: Develop a new formula which describes the magnetic field induced by a lightning strike\u27s indirect effect double exponential current waveform. Approach: A novel approach for developing a closed-form solution for the magnetic field from the indirect effect double exponential current waveform will be presented. In the literature, models typically employ the pulse waveform to derive the corresponding electromagnetic fields. However, given the Department of Defense (DoD) has incorporated the double exponential current waveform as part of their Electromagnetic Environmental Effects Requirements For Systems , we felt it important to develop a solution for the magnetic field which utilized this waveform. In order to facilitate the integration required for deriving the field, Taylor series expansion was used for all variable dependent exponential terms. In many publications, the dipole and monopole techniques have been used when solving for the magnetic field. However, for this study the dipole technique was deemed the preferred method for evaluating the field. A derivation of the magnetic field will be presented along with a graphical illustration of the field\u27s distribution over time. Results: The equation presented utilized Taylor series to augment the integration required to solve for the magnetic field. Conclusion: A new method for deriving the magnetic field induced by a lightning strike\u27s indirect effect double exponential has been presented. By approximating the variable dependent exponential terms, we were able to minimize the complexity of the mathematics required to solve for the magnetic field in closed-form

How Lightning Tortuosity Affects the Electromagnetic Fields by Augmenting Their Effective Distance

A novel approach for developing the electromagnetic fields from a lightning return stroke which follows a tortuous path will be presented. The proposed model is unique in that it recognizes that the symmetrical tortuosity of lightning directly impacts the observable distance r, which in turn, alters the resulting electromagnetic fields. In the literature, lightning return stroke models typically employ the assumption that the cloud-to-ground path is straight. Although this assumption yields fairly consistent results across an array of varying approaches, it does not account for lightning\u27s natural physical appearance. Furthermore, straight-line models only account for the cloud-to-ground discharges and do not address branching and/or cloud-to-cloud discharges which are far more common. In reality, the steps which make up the lightning channel\u27s initial descent are staggered or tortuous with respect to each other. Given this fact, the upward traveling current wavefront which follows this prescribed path will exhibit the same characteristics. In doing so, each current segment, which forms along its respective step, induces electromagnetic fields with angular aggregates that propagate outward from their origin. This, in turn, will generate spatial points where there are fields of higher and lower intensities. The results presented in this paper will show how the effective observable distance due to symmetrical tortuosity alters the resulting electromagnetic fields. Furthermore, it will be shown that as the observable distance r is increased, results from the proposed model closely resemble the straight-line model which strongly suggests that symmetrical tortuosity is only influential at relatively close distances