Thomas H. Shumpert

Scattering by a thin wire parallel to a ground plane using the singularity expansion method

A thin wire parallel to a ground plane is analyzed using moment methods to find the complex natural resonant frequencies and modal current distributions. The resonant frequencies are found as functions of the wire radius and distance above the ground. The complex frequencies appear to be divisible into two classes: 1) those associated with the resonant length of the dipole and 2) those associated with interactions of the dipole and its image. For large dipole radii, the two classes interact and some anomalies, which appear, are investigated. The time domain response to a step-function plane wave is computed using the singularity expansion method and the results compare favorably with the Fourier transform solution.

Backscatter RCS for TE and TM excitations of dielectric-filled cavity-backed apertures in two-dimensional bodies

Transverse electric (TE) and transverse magnetic (TM) scattering from dielectric-filled, cavity-backed apertures in two-dimensional bodies are treated using the method of moments technique to solve a set of combined-field integral equations for the equivalent induced electric and magnetic currents on the exterior of the scattering body and on the associated aperture. Results are presented for the backscatter radar cross section (RCS) versus the electrical size of the scatterer for two different dielectric-filled cavity-backed geometries. The first geometry is a circular cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the cylinder is dielectric filled and is also of circular cross section. The two cylinders (external and internal) are of different radii and their respective longitudinal axes are parallel but not collocated. The second is a square cylinder of infinite length which has an infinite length slot aperture along one side. The cavity inside the square cylinder is dielectric-filled and is also of square cross section. >

Trajectories of the singularities of a thin wire scatterer parallel to lossy ground

A Pocklington-type integro-differential equation is formulated for the current induced on a cylindrical scatterer near a finitely conducting ground. The Fresnel reflection coefficient for vertical polarization is employed to scale ground-reflected scattered radiation produced by the induced currents. This formulation is reduced to a system of algebraic matrix equations suitable for numerical evaluation through application of the method of moments. The singularity expansion method (SEM) is used to obtain the natural frequencies of the scatterer. Trajectories of these singularities (i.e., natural frequencies) are presented as a function of scatterer height-to-length ratio, ground conductivity, and relative permittivity.

Near-Field and Plane-Wave Electromagnetic Coupling into a Slotted Circular Cylinder: Hard or TE Polarization

An analytically tractable model is proposed in this initial study of the electromagnetic phenomena that control our ability to synthesize, by using a near-field source, the effect of plane-wave coupling through an aperture into the interior of a vehicle under test. An integral equation for the tangential electric field in the slot aperture of a perfectly conducting, infinitesimally thin-walled circular cylinder is solved using a basis set of Chebyshev polynomials that are properly weighted according to the static edge condition. The resulting matrix elements from a Galerkin procedure are computed to high precision upon extracting the logarithmic singularity of the kernel of the integral operator. Exact expressions for the matrix elements, in the form of rapidly convergent series of elementary terms, are constructed by isolating another logarithmic function of the aperture width. A minimization of the mean-square error between the true plane-wave response and that due to a near-field line-source establishes the optimal complex source strength of the near-field source

Measured Spectral Amplitude of Lightning Sferics in the HF, VHF, and UHF Bands

An experimental study was carried out to measure the spectral amplitude of lightning sferics at 22.5 MHz, 225 MHz, and 2.25 GHz. This effort included the detection, storage, and analysis of RF emission data to determine accurately the relative electric-field strength produced by the lightning associated with a typical local thunderstorm. These measured spectral amplitudes are normalized and plotted relative to similar data from other investigators. These data support a l/f2 to 11f3 slope for sferics at frequencies above the HF range.

Natural resonances of conducting bodies of revolution

The complex plane natural resonances for several perfectly conducting bodies of revolution (sphere, right circular cylinder, prolate spheroid, and circular disk) are calculated using electric, magnetic, and combined field integral equation formulations (EFIE, HFIE, and CFIE, respectively). These results are compared with some recently published values, and numerical discrepancies are noted and discussed. >

Finite length cylindrical scatterer very near a perfectly conducting ground (A transmission line mode approximation)

A Pocklington type integro-differential equation, possessing an exact kernel, is formulated in terms of a complex frequency for the current induced on a thin finite-length cylindrical scatterer which is above, near, and parallel to a perfectly conducting ground plane. The circumferential variation of the axial current is assumed to be described by a transmission line mode approximation when the scatterer is near the ground plane. The integro-differential equation is reduced to a system of algebraic matrix equations through application of the method of moments. The singularity expansion method is utilized to determine the transient current response of the cylindrical scatterer to a unit step incident plane wave. Complex natural frequencies, natural mode vectors, normalization coefficients, and induced currents are compared to those found through a similar procedure with an approximate kernel, which assumes uniform circumferential variation of the axial current. The exact kernel with an assumed circumferential variation of the axial current is shown to be necessary when the thin cylindrical scatterer is near the ground plane.

SEM formulation of the fields scattered from arbitrary wire structures

The late-time field scattered from an arbitrary wire structure is formulated in terms of the singularity expansion method (SEM), and the contribution of each mode is shown to be representable as the product of two coupling coefficients. One coefficient governs how much of the incident field couples to each natural mode, and the other governs how much of each natural mode couples to the reradiated field. Numerical results are presented for the fields scattered from both straight and L-shaped wire structures and are compared to fields calculated using frequency-domain techniques. The fields calculated using these two different techniques are shown to agree very well after an appropriate time interval has elapsed. >

A modal radar cross section of thin-wire targets via the singularity expansion method

A modal radar cross section (RCS) of arbitrary wire scatterers is constructed in terms of singularity expansion method parameters. Numerical results are presented for both straight and L-shaped wire targets and are compared to computations performed in the frequency domain using the method of moments. >

Capacitance bounds and equivalent radius

The isolated capacitance of conducting ellipsoids is calculated, and the resulting values are presented in the form of equivalent radii. These data are used to establish bounds for the capacitance of other conducting objects, namely, the right circular cylinder and the rectangular parallelopiped.