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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 12, 2016
- Source ID
- 10.1002/2015jd024717
Entities
People
- Xuan‐Min Shao
Organizations
- Defense Threat Reduction Agency
- Los Alamos National Laboratory