Monograph records
https://feeds.library.caltech.edu/people/Papas-C-H/monograph.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 18:22:03 +0000Diffraction by a Strip
https://resolver.caltech.edu/CaltechAUTHORS:20190906-135712159
Authors: Erdélyi, A.; Papas, C. H.
Year: 2019
DOI: 10.7907/T5HY-3105
The problem of diffraction by an infinite strip or slit has been the subject of several investigations. There are at least two "exact" methods for attacking this problem. One of these is the integral equation method, the other the Fourier-Lamé method. The integral equation obtained for this problem cannot be solved in closed form; expansion of the solution in powers of the ratio (strip width/wavelength) leads to useful formulas for low frequencies. In the Fourier-Lamé method the wave equation is separated in coordinates of the elliptic cylinder, the solution appears as an infinite series of Mathieu functions, and the usefulness of the result is limited by the convergence of these infinite series, and by the available tabulation of Mathieu functions.
The variational technique developed by Levine and Schwinger avoids some of the difficulties of the above-mentioned methods and, at least in principle, is capable of furnishing good approximations for all frequency-ranges. The scattered field may be represented as the effect of the current induced in the strip, and it has been proved by Levine and Schwinger that it is possible to represent the amplitude of the far-zone scattered field in terms of the induced current in a form which is stationary with respect to small variations of the current about the true current. Substitution, in this representation, of a rough approximation for the current may give a remarkably good approximation of the far-zone scattered field amplitude. In this note we assume a normally incident field polarized parallel to the generators of the strip. As a rough approximation, we take a uniform density of the current induced in the strip. Since the incident magnetic field is constant over the strip, Fock's theory may be cited in support of the uniformity of the current distribution, except near the edges where the behaviour of the field indicates an infinite current density. A more detailed analysis of the current, by Moullin and Phillips, is available but was not used here.
Once the (approximate) amplitude of the far-zone field has been obtained, the scattering cross-section may be found by the application of the scattering theorem which relates this cross-section to the imaginary part of the amplitude of the far-zone scattered field along the central line of the umbral region. In spite of the crude approximation adopted for the induced current, the scattering cross-section shows a fair agreement with other available results.https://authors.library.caltech.edu/records/9f7yz-n0z83An Application of Sommerfeld's Complex Order Wave Functions to Antenna Theory
https://resolver.caltech.edu/CaltechAUTHORS:20190909-152146587
Authors: Papas, C. H.
Year: 2019
DOI: 10.7907/DDVZ-XC57
In the past wave functions of integral order have been used quite advantageously in the solution of certain antenna and boundary-value problems. However, in some instances these wave functions are completely alien to the problem and introduce difficulties which, indeed, can be resolved but only at the expense of logical simplicity. To place in evidence the usefulness and "naturalness" of complex order wave functions for the solution of certain problems, we examine theoretically the input admittance of a boss antenna with the aid of these functions.https://authors.library.caltech.edu/records/547n1-g5781On Perturbation Theory of Electromagnetic Cavity Resonators
https://resolver.caltech.edu/CaltechAUTHORS:20190910-100627820
Authors: Papas, C. H.
Year: 2019
DOI: 10.7907/0AYQ-NK07
In this note the Lagrangian function for the electromagnetic field of a cavity resonator is found. And from this Lagrangian is deduced a perturbation formula which includes Müller's celebrated result as a special case. The same perturbation formula is derived also from the Boltzmann-Ehrenfest adiabatic theorem in a most simple manner.https://authors.library.caltech.edu/records/64rr1-q2b80A Note Concerning a Gyroelectric Medium
https://resolver.caltech.edu/CaltechAUTHORS:20190910-154055354
Authors: Papas, Charles H.
Year: 2019
DOI: 10.7907/S6QJ-RS64
The fact that a homogeneous electron gas when immersed in a uniform magnetostatic field becomes electrically anisotropic, i.e., gyroelectric, is placed in evidence. The permeability of the gas remains equal to that of free space, but its dielectric constant is transformed to a dyadic or tensor upon application of the magnetostatic field. The properties of the dielectric tensor are such that a plane electromagnetic wave propagating through such a medium under- goes a Faraday rotation. This rotation is the dual of the Faraday rotation produced by gyromagnetic media.
The dielectric tensor of the electron gas is deduced and the Faraday rotation constant is calculated.https://authors.library.caltech.edu/records/qkxzp-g7p39On the Application of a Variational Principle to Antenna Theory
https://resolver.caltech.edu/CaltechAUTHORS:20190926-173654623
Authors: Papas, Charles H.
Year: 2019
DOI: 10.7907/T5ZR-NF60
The strong limitations on the applicability of exact methods of analysis to electromagnetic boundary-value problems have encouraged the development of certain approximation techniques. Among the most practical of these techniques is Schwinger's variational method. In this paper Schwinger's variational principle is derived from first principles and its application to antenna theory is critically examined.
La limitation de l'application des méthodes exactes d'analyses aux problèmes électromagnétiques comportant des conditions aux limites a encouragé le développement de certaines méthodes d'approximation. La plus pratique de ces méthodes est la méthode variationelle de Schwinger. Dans cette communication le principe variationnel de Schwinger sera dérivé de principes fondamentaux et on examinera de facon critique son application à la théorie des antennes.https://authors.library.caltech.edu/records/wskpy-nrb63On the High-Frequency Oscillations of the Electronic Plasma
https://resolver.caltech.edu/CaltechAUTHORS:20191001-125537405
Authors: Papas, Charles H.
Year: 2019
DOI: 10.7907/RHS9-WC14
For the purpose of this note an electronic plasma is defined as a gas of classical, non-relativistic electrons immersed in a constant charge-neutralizing background. The plasma is assumed to be spatially limitless and free of externally applied fields.
An exact analysis of the general oscillatory behavior of the plasma is forbiddingly difficult because it requires a detailed knowledge of the collision mechanism and ultimately leads to an intractable integro-differential equation. However, there are two extreme cases that are simple enough to be handled mathematically.
One of these limiting cases occurs when the collisions are so frequent that the electronic distribution is Maxwellian in every volume element and local equilibrium is established. Then the behavior of the plasma is determined by macroscopic hydrodynamical equations which lead to the dispersion relation
ω^2 = ω_(p)^(2) + (5/3)((ℋT)/m) k^2
where ω_p is the plasma frequency given by
ω_(p)^(2) = (ne^2)/(mε_o)
with T denoting the equilibrium temperature, ℋ Boltzmann's constant, k the wave number, m and e the electronic mass and charge respectively, and ε_o the dielectric constant of free space (M.K.S. system). This dispersion relation does not agree with the dispersion relation derived by the Thomsons, by Bailey, by Borgnis, and others. The reasons for this discrepancy have been reported by Van Kampen. In the other limiting case the collisions of the electrons with the ions and with each other are negligible and the collision term of Boltzmann's equation can be set equal to zero. This state is physically approximated when the frequency of oscillation is sufficiently high. Under special circumstances the dispersion relation in this case is approximately given by
ω^2 = ω_(p)^(2) + 3((ℋT)/m) k^2.
In this lecture we shall critically examine the theory of the high-frequency case, placing in evidence the tacit assumptions and hypotheses upon which the theory is based.https://authors.library.caltech.edu/records/9pres-v6038On the Attenuation of Guided Waves in the Limit of High Frequencies
https://resolver.caltech.edu/CaltechAUTHORS:20191001-161617326
Authors: Papas, Charles H.
Year: 2019
DOI: 10.7907/TSY9-2J11
The conventional formulas for the attenuation of waves due to the wall losses in uniform waveguides are based on the two assumptions that the wall currents are the same as the loss-free currents and that the surface resistance of the highly conductive walls is isotropic. In the limit of high frequencies the former assumption remains valid whereas the latter assumption breaks down. As the frequency is increased the surface resistance becomes anisotropic in the sense that it assumes different values depending on whether the wall current is longitudinal or transverse. In this paper new attenuation formulas are derived, which take into account the high-frequency anisotropy of the surface resistance and hence yield accurate results for all frequencies.https://authors.library.caltech.edu/records/8d40j-jwa63The Incoherent Scattering of Electromagnetic Waves by Free Electrons
https://resolver.caltech.edu/CaltechAUTHORS:20200220-111337349
Authors: Papas, C. H.; Lee, K. S. H.
Year: 2020
DOI: 10.7907/2R2B-5P77
In this paper the incoherent scattering of an electromagnetic wave by free electrons is examined theoretically. Under the assumption that the electrons have a Maxwellian velocity distribution, the scattered power and its frequency spectrum are calculated. The applicability of these results to ionospheric and laboratory plasmas is discussed.https://authors.library.caltech.edu/records/njnr4-n0755On the Index of Refraction of Spatially Periodic Plasma
https://resolver.caltech.edu/CaltechAUTHORS:20200219-164336165
Authors: Papas, C. H.
Year: 2020
DOI: 10.7907/YN3X-4B88
A knowledge of the change produced in the index of refraction of a uniform plasma by the spontaneous generation of coagula or inhomogeneities is essential to the use of electromagnetic waves as a diagnostic tool. The general problem is a difficult one to handle, but certain non-trivial cases are mathematically tractable. One of these, which is also of some practical import, occurs when the inhomogeneities are periodically distributed throughout the plasma. Here this special case is analyzed within the framework of the theory of periodic structures. The problem is reduced by virtue of Floquet's theorem to an equivalent problem for the domain of a unit cell with periodic boundary conditions. An approximate solution is obtained by a simplified theory. As a specific application the calculation for a plasma with periodically spaced spherical inhomogeneities is worked out in detail.https://authors.library.caltech.edu/records/2rcsv-40451