Electric Dipole Radiation in Isotropic and Uniaxial Plasmas

Citation

Kenny, John Joseph (1968) Electric Dipole Radiation in Isotropic and Uniaxial Plasmas. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2Q1Z-GS04. https://resolver.caltech.edu/CaltechETD:etd-09242002-082113

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This paper describes an investigation of radiation from an electric point dipole situated in a cold, collisionless, homogeneous, electronic plasma medium. Two limiting cases of a gyroelectric medium are studied. The magnetostatic biasing field [...] is first taken to be equal to zero, making the medium isotropic, and then it is taken to be infinite, causing a uniaxial anisotropy. The retarded electromagnetic fields and the instantaneous and averaged values of irreversibly radiated power [...] are calculated. In each medium, the partial differential equations resulting from the two-sided Laplace transformation of Maxwell's equations with an oscillating electric dipole source and the constitutive equations (derived from the appropriate form of the Lorentz force equation) are solved. A particular path deformation of the Laplace inversion integral reveals that the electromagnetic fields and [...] are exactly expressible in terms of circular, cylindrical, and two-variabled Lommel functions. Asymptotic expressions and graphical results of numerical calculations of these quantities are presented. For the isotropic case, it is shown that the retarded fields are well behaved for all space and time (excluding the origin, of course). [...] eventually settles down to the result derived from the conventional time-harmonic analysis when the dipole oscillation frequency [...] is greater than the plasma frequency [...] . When the value of [...] is less than that of [...], [...] eventually oscillates at a frequency [.....] with zero average value. When the medium is uniaxial, the fields are finite everywhere except at the dipole. The amplitude of the fields does, however, increase with increasing time. This is quite different from the ordinary time-harmonic solution which ignores all time variations different from [...] and which is singular on a conical surface defined by [...] for [...]. The value of [...] in a uniaxial medium is found to be equal to the value of [.....] of a dipole in vacuum. It is also shown that the so-called conventional expression for time-averaged radiated power will not give a sensible result since it contains the retarded electric field which never settles down to a steady-state variation with time. The quantity [...], on the other hand, does not increase with time, oscillates only at the source frequency, and has a well-defined time average.

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