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 , , and such that for all , where is a bounded domain (a box containing the thunderstorm), is a subdomain (the lightning channel), and is the inner product
Keywords: lightning, electric potential, Ampere's law, Maxwell's equations, laplacian, generalized eigenproblem, double layer potential, complete eigenbasis
@article{M2AN_2008__42_5_887_0, author = {Hager, William W. and Aslan, Beyza Caliskan}, title = {The change in electric potential due to lightning}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {887--901}, publisher = {EDP-Sciences}, volume = {42}, number = {5}, year = {2008}, doi = {10.1051/m2an:2008026}, mrnumber = {2454626}, zbl = {1152.35027}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2008026/} }
TY - JOUR AU - Hager, William W. AU - Aslan, Beyza Caliskan TI - The change in electric potential due to lightning JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 887 EP - 901 VL - 42 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008026/ DO - 10.1051/m2an:2008026 LA - en ID - M2AN_2008__42_5_887_0 ER -
%0 Journal Article %A Hager, William W. %A Aslan, Beyza Caliskan %T The change in electric potential due to lightning %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 887-901 %V 42 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008026/ %R 10.1051/m2an:2008026 %G en %F M2AN_2008__42_5_887_0
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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