Volume 42, Number 5, September-October 2008
|Page(s)||887 - 901|
|Published online||04 July 2008|
The change in electric potential due to lightning
Department of Mathematics, University of Florida, PO Box 118105, 32611-8105 Gainesville,
Florida, USA. firstname.lastname@example.org; http://www.math.ufl.edu/~hager
2 Department of Mathematics and Statistics, University of North Florida, 32224 Jacksonville, Florida, USA. email@example.com; http://www.unf.edu/coas/math-stat/ aslan
Revised: 16 March 2008
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
Mathematics Subject Classification: 35J25 / 35Q60 / 35A20 / 35P10
Key words: Lightning / electric potential / Ampere's law / Maxwell's equations / Laplacian / generalized eigenproblem / double layer potential / complete eigenbasis.
© EDP Sciences, SMAI, 2008
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