The change in electric potential due to lightning
ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 5, pp. 887-901.

The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The expression for the lightning induced electric potential change is derived both for the continuous equations, and for a spatially discretized formulation of the continuous equations. The results for the continuous equations are based on the properties of the eigenvalues and eigenfunctions of the following generalized eigenproblem: Find uH 0 1 (Ω), u0, and λ such that u,v =λu,v Ω for all vH 0 1 (Ω), where Ω n is a bounded domain (a box containing the thunderstorm), is a subdomain (the lightning channel), and ·,· Ω is the inner product u,v Ω = Ω u·vdx.

DOI: 10.1051/m2an:2008026
Classification: 35J25, 35Q60, 35A20, 35P10
Keywords: lightning, electric potential, Ampere's law, Maxwell's equations, laplacian, generalized eigenproblem, double layer potential, complete eigenbasis
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     title = {The change in electric potential due to lightning},
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Hager, William W.; Aslan, Beyza Caliskan. The change in electric potential due to lightning. ESAIM: Modélisation mathématique et analyse numérique, Volume 42 (2008) no. 5, pp. 887-901. doi : 10.1051/m2an:2008026. http://www.numdam.org/articles/10.1051/m2an:2008026/

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