Author(s): F. Delfino, R. Procopio & M. Rossi
We present a new method for evaluating the electromagnetic field created by a
lightning discharge under the assumption of a finite conductivity ground.
case the expressions for the vertical and radial components of the electric field
and for the azimuthal component of the magnetic one involve the so-called
Sommerfeld integrals, which require a huge computational effort due to their
characteristics of slow convergence.
From a mathematical standpoint the
Sommerfeld’s integrals are improper integrals (i.e.
over a semi-infinite domain
The presence in the integrand of the highly oscillating Bessel
function and of an integrable singularity are the main causes of numerical
The proposed algorithm allows the extraction of the singularity and
performs part of the integral analytically.
Consequently, a standard quadrature
formula can be applied to the remaining term.
The method has been developed in
the frequency domain and, for the evaluation of each field component, about
1000 Sommerfeld integrals are necessary, each of them requiring about six
seconds of CPU time on a Pentium IV, 1.6 GHz PC.
This method has been numerically tested in the simulation of a straight
vertical lightning channel electromagnetic field, assuming typical values for the
In particular, the field has been evaluated at different
distances from the channel in order to point out the distance ranges where
conductivity effects cannot be neglected.
All the simulations have been carried
out assuming, for the channel base current, the well-known Heidler’s function
and for the spatial-temporal distribution of the lightning current along the return
stroke channel (i.e.
the current return-stroke model) the classical MTLE
wave propagation, lightning electromagnetic field, Sommerfeld
integrals, numerical techniques.
Size: 481 kb
Paper DOI: 10.2495/BE050571
the Full Article
This article is part of the WIT OpenView scheme and you can download the full text Adobe PDF article for FREE by clicking the 'Openview' icon below.
this page to a colleague.
This paper can be found in the following bookBoundary Elements XXVII: Incorporating Electrical Engineering and Electromagnetics Buy