Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations
Abstract
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, onedimensional source current, and not for a general threedimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a threedimensional, timedependent 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 timedependent 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 onedimensional 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 threedimensional, conicalshape discharge.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOD; USDOE
 OSTI Identifier:
 1406201
 Report Number(s):
 LAUR1526674
Journal ID: ISSN 2169897X; TRN: US1703030
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Geophysical Research: Atmospheres
 Additional Journal Information:
 Journal Volume: 121; Journal Issue: 7; Journal ID: ISSN 2169897X
 Publisher:
 American Geophysical Union
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Classical electromagnetism
Citation Formats
Shao, XuanMin. Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations. United States: N. p., 2016.
Web. https://doi.org/10.1002/2015JD024717.
Shao, XuanMin. Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations. United States. https://doi.org/10.1002/2015JD024717
Shao, XuanMin. Tue .
"Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations". United States. https://doi.org/10.1002/2015JD024717. https://www.osti.gov/servlets/purl/1406201.
@article{osti_1406201,
title = {Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations},
author = {Shao, XuanMin},
abstractNote = {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, onedimensional source current, and not for a general threedimensional current distribution. In this paper, we introduce a corresponding pair of generalized equations that are determined from a threedimensional, timedependent 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 timedependent 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 onedimensional 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 threedimensional, conicalshape discharge.},
doi = {10.1002/2015JD024717},
journal = {Journal of Geophysical Research: Atmospheres},
number = 7,
volume = 121,
place = {United States},
year = {2016},
month = {4}
}
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 McDonald, Kirk T.
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Time‐dependent generalizations of the Biot–Savart and Coulomb laws
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 Griffiths, David J.; Heald, Mark A.
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