Roy E. Jorgenson

Efficient calculation of the free-space periodic Green's function

Electromagnetic scattering from periodic structures can be formulated in terms of an integral equation that has as its kernel a periodic Greens function. The periodic Greens function can be derived as a response to an array of line/point sources (spatial domain) or as a response to series of current sheets (spectral domain). These responses are a Fourier transform pair and are slowly convergent summations. The convergence problems in each domain arise from unavoidable singularities in the reciprocal domain. A method is discussed to overcome the slow convergence by using the Poisson summation formula and summing in a combination of spectral and spatial domains. A parameter study is performed to determine an optimum way to weigh the combination of domains. simple examples of scattering from a one-dimensional array of strips and two-dimensional array of plates are used to illustrate the concepts. >

Variational nature of Galerkin and non-Galerkin moment method solutions

There is renewed interest in the use of variational methods in conjunction with numerical solutions of electromagnetic radiation and scattering problems. The variational aspects of secondary calculations based on a method of moments (MoM) solution are investigated. These calculations exhibit a type of second-order accuracy, regardless of whether or not the operator being discretized is self-adjoint, and regardless of whether or not testing functions are identical to the basis functions (Galerkins method). Numerical results support these conclusions and suggest that the advantage of Galerkins method in actual calculations is grossly overstated.

Statistical properties of linear antenna impedance in an electrically large cavity

The paper presents models and measurements of linear antenna input impedance in resonant cavities at high frequencies. Results are presented for both the case where the cavity is undermoded (modes with separate and discrete spectra) as well as the overmoded case (modes with overlapping spectra). A modal series is constructed and analyzed to determine the impedance statistical distribution. Both electrically small as well as electrically longer resonant and wall mounted antennas are analyzed. Measurements in a large mode stirred chamber cavity are compared with calculations. Finally, a method based on power arguments is given, yielding simple formulas for the impedance distribution.

EIGER: Electromagnetic Interactions GEneRalized

EIGER (Electromagnetic Interactions GEneRalized), a single integrated software tool set, brings together a variety of spectral domain analysis methods. These include moment method solutions of integral equation formulations and finite elements solutions of partial differential equations. New software engineering methods, specifically, object oriented design, are being used to implement abstractions of key components of spectral analysis methods so that the tools can be easily modified and extended to treat new classes of problems. The key components of the numerical analysis tool, and their roles, are: elements-to describe the geometry, basis functions-to interpolate the unknowns (e.g., fields) locally, and operators-to express the underlying physics formulations used to propagate the energy or enforce fundamental principals. The development of EMPACK by Yesantharao (1989) provided the fundamental impetus for these abstractions which are discussed.

EIGER ™ : An open-source frequency-domain electromagnetics code

EIGERtrade is a general-purpose, 3D frequency-domain electromagnetics code suite consisting of a pre-processor (Jungfrau), the physics code (EIGER), and post processor (Moench). In order to better enable collaborative development, EIGERtrade version 2.0 has been approved for release as open source software under a GNU Public License. EIGERtrade is primarily an integral-equation code for both frequency-domain electromagnetics and electrostatics. This version includes the following Greens functions: 2D and 3D free space, symmetry-planes, periodic and layered media. There is a thin-wire algorithm as well as junction basis functions for attachment of a wire to a conducting surface, and also thin-slot models for coupling into cavities. The code is written in Fortran 90 using object-oriented design and has the capability to run both in parallel and serial.

Scattering from structured slabs having two-dimensional periodicity

The problem of a plane wave incident on a structured slab is examined. To analyze the problem, an electric field integral equation (EFIE) is derived that has as its unknown the equivalent surface currents on the plates in the unit cell. The integral equation is discretized and solved approximately using the method of moments with subdomain basis and testing functions. The periodic Greens function is efficiently calculated using the Poisson summation formula. The interaction of the structure with the surrounding environment is described in terms of a generalized scattering matrix. Results are presented showing the reflection coefficient as a function of frequency for arrays of zigzagging strips and honeycomb slabs. >

Effect of Dielectric Photoemission on Surface Breakdown: An LDRD Report

The research discussed in this report was conceived during our earlier attempts to simulate breakdown across a dielectric surface using a Monte Carlo approach. While cataloguing the various ways that a dielectric surface could affect the breakdown process, we found that one obvious effect--photoemission from the surface--had been ignored. Initially, we felt that inclusion of this effect could have a major impact on how an ionization front propagates across a surface because of the following argument chain: (1) The photon energy required to release electrons from a surface via photoemission is less than the photon energy required to ionize gas molecules directly. (2) The mean free path of a photon in gas is longer for low-energy photons than for high-energy photons. (3) Photoionization is a major effect in advancing the ionization front for breakdown in gas without a surface, therefore, we know that even high-energy photons can be released from the head of a streamer and propagate some distance through the gas. Our hypothesis, therefore, was that photons with energies near the threshold of photoemission could travel further in front of the streamer before being absorbed than higher-energy photons needed for photoionization, yet the lower-energy photons, with the help of the surface, could still create seed electrons for new avalanches. Thus, the streamer would advance more rapidly next to a surface than in gas alone. Additionally, the photoemission from the surface would add to the electrons in the avalanche and cause the avalanche to grow faster. After some study, however, we are forced to conclude that although photoemission does contribute to avalanche growth at fields near breakdown threshold, secondary electron emission causes electrons to stick to the surface and cancels out the growth due to photoemission. This conclusion assumes a discharge that occurs over a short period of time so that charging of the surface, which could alter its secondary electron emission characteristics, does not occur. This report documents the numerical work we did on investigating this effect and the experimental work we did on pre-breakdown phenomena in gas.

Oblique scattering from lossy strip structures with one-dimensional periodicity

The intentional addition of loss to a periodic structure can be used as a technique to alter its scattering characteristics. The problem of an oblique plane wave incident on an array with one-dimensional periodicity is examined. The unit cell of the array is composed of a number of thin resistive strips. The obliqueness of the incident plane wave combined with the lossy nature of the structure causes the transverse electric (TE) to z and the transverse magnetic (TM) to z fields to couple. To analyze the described problem, two coupled electric field integral equations that have as unknowns the equivalent surface currents on the strips in the unit cell are derived. The integral equations are discretized and solved approximately using the method of moments with subdomain basis and testing functions. The periodic Greens function is efficiently calculated using the Poisson summation formula. The interaction of the structure with the surrounding environment is described in terms of a generalized scattering matrix. Results are presented showing the TE/TM coupling behavior as strip resistance is increased for representative structures. >

Ionization coefficient approach to modeling breakdown in nonuniform geometries.

This report summarizes the work on breakdown modeling in nonuniform geometries by the ionization coefficient approach. Included are: (1) fits to primary and secondary ionization coefficients used in the modeling; (2) analytical test cases for sphere-to-sphere, wire-to-wire, corner, coaxial, and rod-to-plane geometries; a compilation of experimental data with source references; comparisons between code results, test case results, and experimental data. A simple criterion is proposed to differentiate between corona and spark. The effect of a dielectric surface on avalanche growth is examined by means of Monte Carlo simulations. The presence of a clean dry surface does not appear to enhance growth.

Experimental verification of an integral equation solution for a thin-walled dichroic plate with cross-shaped holes

In order to add the capability of an X-band up-link onto the NASA/JPL Deep Space Network (DSN) 70-m antenna, a new dichroic plate is needed to replace the Pyle-guide shaped dichroic plate currently in use. The replacement dichroic plate must exhibit an additional pass band at the new up-link frequency of 7.165 GHz, while maintaining a pass band at the existing down-link frequency of 8.425 GHz. Because of the wide frequency separation of these two pass bands, conventionally designed air-filled dichroic plates exhibit grating lobe problems. A new method of solving this problem using a dichroic plate with cross-shaped holes is presented and verified experimentally. Two checks of the integral equation solution are described here. One is the comparison to a modal analysis for the limiting cross shape of a square hole. As a final check a prototype dichroic plate with cross-shaped holes was built and measured. >