Uman Equations, Jefimenko Equations, and Lightning Electromagnetics

Abstract:

Uman et al. [1975] introduced a pair of electromagnetic field equations for a one-dimensional time-varying source current and these equations are widely used to study lightning discharge processes in the lightning community. It is somehow not well recognized by the lightning community that Jefimenko [1966] introduced a pair of electromagnetic equations that are related to general time-varying, three-dimensional current and charge density. Jefimenko [2004] has further proved that his equations are equivalent to the Maxwell equations but showed that they are more advantageous regarding the causality from the sources to the resultant fields. Although more general, it is not straightforward to apply the original Jefimeko equations to lightning electromagnetics since the fields depend not only on current but also on charge density, and each term in the equations is not solely related to the more conventional radiation, induction or the static fields. In this presentation, we derive the original Jefimenko equations one step further to show that they can be related solely to the source current, and we group the terms according to the more conventional radiation, induction and static components. The new forms of the Jefimenko equations are in agreement with Uman’s equations if a one-dimensional source current is considered. However, the new Jefimenko equations are three dimensional in nature and are expressed in general vectors and vector operators and therefore can be easily applied to lightning electromagnetic calculations for a more realistic, 3-d lightning current distributions.

Uman, M. A., D. K. McLain, and E. P. Krider (1975), Am. J. Phys., 43, 33-38.

Jefimenko, O. D. (1966), Electricity and Magnetism, Appleton-Century-Crofts, New York.

Jefimenko, O. D. (2004), Eur. J. Phys., 25, 287-296.