Engineering topics

Burkholder, R. J.

Publications and source records attributed to Burkholder, R. J..

4 records

NASA NTRS1989

High-frequency asymptotic methods for analyzing the EM scattering by open-ended waveguide cavities

Four high-frequency methods are described for analyzing the electromagnetic (EM) scattering by electrically large open-ended cavities. They are: (1) a hybrid combination of waveguide modal analysis and high-frequency asymptotics, (2) geometrical optics (GO) ray shooting, (3) Gaussian beam (GB) shooting, and (4) the generalized ray expansion (GRE) method. The hybrid modal method gives very accurate results but is limited to cavities which are made up of sections of uniform waveguides for which the modal fields are known. The GO ray shooting method can be applied to much more arbitrary cavity geometries and can handle absorber treated interior walls, but it generally only predicts the major trends of the RCS pattern and not the details. Also, a very large number of rays need to be tracked for each new incidence angle. Like the GO ray shooting method, the GB shooting method can handle more arbitrary cavities, but it is much more efficient and generally more accurate than the GO method because it includes the fields diffracted by the rim at the open end which enter the cavity. However, due to beam divergence effects the GB method is limited to cavities which are not very long compared to their width. The GRE method overcomes the length-to-width limitation of the GB method by replacing the GB's with GO ray tubes which are launched in the same manner as the GB's to include the interior rim diffracted field. This method gives good accuracy and is generally more efficient than the GO method, but a large number of ray tubes needs to be tracked.

Burkholder, R. J.↗

NASA NTRS1988

Analysis of the EM scattering from arbitrary open-ended waveguide cavities using axial Gaussian Beam tracking

The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.

Burkholder, R. J.↗

NASA NTRS1988

A hybrid asymptotic-modal analysis of the EM scattering by an open-ended S-shaped rectangular waveguide cavity

The electromagnetic fields (EM) backscatter from a 3-dimensional perfectly conducting S-shaped open-ended cavity with a planar interior termination is analyzed when it is illuminated by an external plane wave. The analysis is based on a self-consistent multiple scattering method which accounts for the multiple wave interactions between the open end and the interior termination. The scattering matrices which described the reflection and transmission coefficients of the waveguide modes reflected and transmitted at each junction between the different waveguide sections, as well at the scattering from the edges at the open end are found via asymptotic high frequency methods such as the geometrical and physical theories of diffraction used in conjunction with the equivalent current method. The numerical results for an S-shaped inlet cavity are compared with the backscatter from a straight inlet cavity; the backscattered patterns are different because the curvature of an S-shaped inlet cavity redistributes the energy reflected from the interior termination in a way that is different from a straight inlet cavity.

Law, P. H.↗

NASA NTRS1987

Electromagnetic fields backscattered from an s-shaped inlet cavity with an absorber coating on its inner walls

The EM backscatter from a two-dimensional S-shaped inlet cavity is analyzed using three different techniques, namely a hybrid combination of asymptotic high frequency and modal methods, an integral equation method, and the geometrical optics ray method, respectively. This inlet has a thin absorber coating on its perfectly conducting inner walls and the planar interior termination is made perfectly conducting. The effect of the absorber on the inner wall is treated via a perturbation scheme in the hybrid approach where it is assumed that the loss is sufficiently small for the method to be valid. The results are compared with the backscatter from a straight inlet cavity to evaluate the effect of offsetting the termination in the S-bend configuration such that it is not visible from the open end of the inlet. The envelope of the backscatter pattern for the straight inlet is always seen to peak around the forward axis due to the large return from the directly visible termination, and the pattern envelope tapers off away from the forward axis. Offsetting the termination causes the envelope of the backscatter pattern to flatten out, thereby reducing the return near the forward axis by several dB. The absorber coating reduces the pattern level of the straight inlet in directions away from the forward axis but has little effect on the peak near the axis; furthermore, the absorber coating is seen to consistently reduce the backscatter from the S-bend inlet for almost all incidence angles. The hybrid method gives excellent agreement with experimental data and with the integral equation solution, whereas, the geometrical optics ray tracing method is able to generally predict the average of the bachscatter pattern but not the pattern details.

Burkholder, R. J.↗