Consolidated approach to two-body electromagnetic scattering

Abstract

In this paper we present a new consolidated approach to the problem of determining the electromagnetic field resulting from a finite electric current source outside two electrically different media. This approach rests on properties of generalized functions and the solution of a given problem depends essentially only on the gradients of the characteristic functions of the various regions. In particular we study the scattered fields from a flat earth, from a two-layered earth, from an earth consisting of two different adjacent electrical media (the "mixed-path" problem), and from a rough surface. We show that each of these problems can be modeled and solved from one set of equations; in each case we carry the analysis to a stage where it agrees with that presented by the authors in specific detailed papers that treat each problem separately. As such the solutions can be shown to agree with classical approaches. The technique used here contains a minimum of sophisticated analysis and has the following properties: The source field is arbitrary, the resulting equations directly relate the unknown electric and known source field intensities without the use of intermediate Hertz potentials, and the boundary conditions evolve directly from the formulation as auxiliary equations.

The First-Order High Frequency Radar Ocean Surface Cross Section for an Antenna on a Floating Platform

“…Beginning with the first-order electric field equation for scatter from a time-invariant rough surface derived in [3]- [5], the displacement of the transmitting and receiving antenna has been added in the analysis and the results adjusted to incorporate the time-varying surface (in this case, that of the ocean). The cross section follows in the usual way, and using an actual barge motion, model results are simulated for a variety of sea states and radar operating frequencies.…”

“…For the purpose of the ensuing analysis involving a barge-mounted source, we define a small displacement from the origin by Given that , so that and , (1) may be written as (3) where (4) By analogy to (1), in (3) also includes all orders of scatter, but now the source is not fixed. As before, a Neumann series solution may be effected to give a first order field analogous to that in (2) as (5) In simplifying (5), it is noted that in plane polar coordinates (see Fig. 1), Defining and applying the gradient indicated in (5), while ignoring the variation and making the observation that, for large is slowly varying, gives…”

“…The background to this analysis is found initially in [3] and also appears in the open literature in [4], [5]. In [3], [4], the powers of the surface slope which are greater than unity (for a single scatter) are neglected.…”

On the Development of a High-Frequency Radar Cross Section Model for Mixed Path Ionosphere–Ocean Propagation

“…In [8], ionospheric and auroral clutter models for HF surface wave and over-the-horizon (sky-wave) radar systems were developed using a geometric optics approach, but the mixed path mode was not considered. Walsh et al [9] and [10] laid a theoretical foundation for the analysis of radio waves scattering from the sea surface, and this has been used to derive the HF radar ocean surface cross sections for a variety of deployment configurations [11]- [17]. In this paper, this analysis has been extended to develop an analytical model to assess the relative importance of the ionospheric clutter associated with the mixed path mode.…”

An analytical model for HF radar ionospheric clutter

“…The ionosphere reflection coefficient used in the analysis is assumed to be a stochastic process with an associated spectral density function to account for phase variations along the surface associated with non-uniformity of the signal path. Techniques for rough surface scatter developed previously [3], [4] are used to analyze the backscattered mixed signal from the ocean surface.…”