Natural-mode representation of transient scattered fields

Augmented electric‐ and magnetic‐field integral equations

“…Many of the results contained in this paper were first presented at the 1980 International URSI Symposium on Electromagnetic Waves and in the associated report [ Yaghjian, 1980[ Yaghjian, , 1981 that these spurious homogeneous solutions exist in the exterior region is to note that the homogeneous solutions to (1) are the same for both the interior and exterior problems, and that the homogeneous interior and exterior operators of (2) are effectively adjoints of each other [Muller, 1969;Marin, 1973]--adjoint linear operators for an even determined set of equations having identical real eigenvalues, i.e., resonant frequencies.) Although Maxwell's equations and boundary conditions are used to derive (1) and (2), it must be concluded that (1) and (2) when applied in the exterior region are not equivalent to Maxwell's equations plus boundary conditions.…”

A simple way of solving transient thin‐wire problems

“…In this paper, a technique based on the naturalmode method [Marin, 1973] is used to obtain approximate analytical expressions for the time history of the current induced on a thin wire when it is excited either by an incident step-function plane wave or by a slice generator whose output voltage Copyright ¸ 1976 by the American Geophysical Union. is a step function in time.…”

“…The induced surface current density j on a conducting body satisfies the integro-differential equa- is the free-space Green's function, E inc is the incident electric field, n is the outward unit normal to the surface S of the scattering body, and the time dependence exp (st) is understood. It is known that the singularities in the complex frequency (s) plane of the surface currents induced on a finite sized, perfectly conducting body can be identified either as the singularities of the incident field or as poles [Marin, 1973] Some comments are in order here concerning (6). First, the expression (6) is valid provided there is no degeneracy, i.e., for each s, there is only one linearly independent current distribution j, that satisfies (2).…”

“…First, the expression (6) is valid provided there is no degeneracy, i.e., for each s, there is only one linearly independent current distribution j, that satisfies (2). The case of degeneracy can easily be incorporated into the series representation (6) of the induced current in the same way as degeneracy was incorporated into the corresponding expression in Marin, [ 1973]. However, it is left out here since degeneracy does not seem to occur in the case of a thin wire.…”

“…fact that •Y' is symmetric) and the assumption that •Y'-• has only simple poles (which has been substantiated in all cases investigated numerically) make it possible to obtain the following forced solution of (1)by using the Mittag-Leffler theorem [seeMarin, 1973]' …”