The change in electric potential due to lightning

¹ Department of Mathematics, University of Florida, PO Box 118105, 32611-8105 Gainesville, Florida, USA. hager@math.ufl.edu; http://www.math.ufl.edu/~hager
² Department of Mathematics and Statistics, University of North Florida, 32224 Jacksonville, Florida, USA. aslan@unf.edu; http://www.unf.edu/coas/math-stat/ aslan

Received: 28 September 2007
Revised: 16 March 2008

Abstract

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