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Title: 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, 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.

Authors:
 [1]
  1. 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):
LA-UR-15-26674
Journal ID: ISSN 2169-897X; TRN: US1703030
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Geophysical Research: Atmospheres
Additional Journal Information:
Journal Volume: 121; Journal Issue: 7; Journal ID: ISSN 2169-897X
Publisher:
American Geophysical Union
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Classical electromagnetism

Citation Formats

Shao, Xuan-Min. 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, Xuan-Min. Generalization of the lightning electromagnetic equations of Uman, McLain, and Krider based on Jefimenko equations. United States. https://doi.org/10.1002/2015JD024717
Shao, Xuan-Min. 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, Xuan-Min},
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, 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.},
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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Works referenced in this record:

The initiation of lightning by runaway air breakdown
journal, January 2005


The relation between expressions for time-dependent electromagnetic fields given by Jefimenko and by Panofsky and Phillips
journal, November 1997

  • McDonald, Kirk T.
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Time‐dependent generalizations of the Biot–Savart and Coulomb laws
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