This report assembles models for the response of a wire interacting with a conducting ground to an electromagnetic pulse excitation. The cases of an infinite wire above the ground as well as resting on the ground and buried beneath the ground are treated. The focus is on the characteristics and propagation of the transmission line mode. Approximations are used to simplify the description and formulas are obtained for the current. The semi-infinite case, where the short circuit current can be nearly twice that of the infinite line, is also examined.3
An improved asymptotic series for an integral representing transient current on an infinite cylindrical antenna caused by a step voltage source, applied at the gap, is given. A generating function for obtaining the general coefficient is derived. The method is applicable to types of integrals whose integrands consist of a product of a slowly varying function and a rapidly varying function. A simple accurate formula obtained before, by the averaging method, is shown to be the leading term of this infinite series. The averaging used in evaluating integrals is shown to improve the accuracy of the leading term.
The recently developed asymptotic theory of wave propagation is extended to slightly inhomogeneous and slowly varying anisotropic media which exhibit both spatial and temporal dispersion. A particular form of the constitutive relation is first introduced. Asymptotic solutions are then obtained by assuming a series solution ``ansatz'' into Maxwell's equations and the constitutive relation. The eikonal equation and the transport equation are obtained, by a procedure similar to that of Lewis, for lossless media, in which a Hermitian operator is involved. The modified transport equations obtained from other forms of the constitutive relation are given. They are interpreted as generalized Poynting theorems for appropriate physical situations. Finally, as a by-product of this work the space-time conductivity tensor of anisotropic plasmas σ(r, t), which is the 4-dimensional Fourier-Laplace transform of σ̃(k,ω), is found to be very simple.
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