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Title: Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations

Journal Article · · Journal of Geophysical Research: Atmospheres
 [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

The fundamental electromagnetic equations used by lightning researchers were introduced in a seminal paper by Uman, McLain, and Krider in 1975. However, these equations were derived for an infinitely thin, one-dimensional source current, and not for a general three-dimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a three-dimensional, time-dependent current density distribution based on Jefimenko's original electric and magnetic equations. To do this, we derive the Jefimenko electric field equation into a new form that depends only on the time-dependent current density similar to that of Uman, McLain, and Krider, rather than on both the charge and current densities in its original form. The original Jefimenko magnetic field equation depends only on current, so no further derivation is needed. We show that the equations of Uman, McLain, and Krider can be readily obtained from the generalized equations if a one-dimensional source current is considered. For the purpose of practical applications, we discuss computational implementation of the new equations and present electric field calculations for a three-dimensional, conical-shape discharge.

Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOD; USDOE
Grant/Contract Number:
AC52-06NA25396
OSTI ID:
1406201
Report Number(s):
LA--UR-15-26674
Journal Information:
Journal of Geophysical Research: Atmospheres, Journal Name: Journal of Geophysical Research: Atmospheres Journal Issue: 7 Vol. 121; ISSN 2169-897X
Publisher:
American Geophysical UnionCopyright Statement
Country of Publication:
United States
Language:
English

References (4)

The initiation of lightning by runaway air breakdown journal January 2005
A Hierarchy of Explicit Low-Dispersion FDTD Methods for Electrically Large Problems journal December 2012
Time‐dependent generalizations of the Biot–Savart and Coulomb laws journal February 1991
The relation between expressions for time-dependent electromagnetic fields given by Jefimenko and by Panofsky and Phillips journal November 1997

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