Asymptotic expansions for transient electromagnetic fields

Abstract

Asymptotic expansions may be derived for transient electromagnetic (EM) fields. The expansions are valid when [Formula: see text] is less than about 0.1. Here l, σ, [Formula: see text], and t are the respective lengths, conductivities, permeabilities of free space and time. Cases for which asymptotic expansions are presented include (1) layered grounds, (2) axisymmetric structure, and (3) two‐dimensional (2-D) structures. In all cases the transient voltage eventually approaches that of the host medium alone, the ratio of anomalous response to the half‐space response being proportional to [Formula: see text]. Here v is equal to 0.5 for layered structures and 1.0 for 2-D or 3-D structures.