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Maxwell's equations establish that patterns of electric charges and currents can be animated to travel faster than the speed of light in vacuo and that these superluminal distribution patterns emit tightly focused packets of electromagnetic radiation that are fundamentally different from the emissions by previously known terrestrial radiation sources. Novel antennae that employ extended distributions of polarization currents moving faster than light have proven to be effective emitters of electromagnetic radiation and are currently tested for applications in radar and low-power, secure communications technologies. Here, we we study the emission of a localized charge in constant superluminal rotation. We set out by applying basic methods introduced by Huyghens and Fresnel to gain phase information and find that radiation sources that travel not only faster than light, but are also subject to acceleration, possess a two-sheeted envelope and a cusp -- a region of intense concentration of energy. Moreover, careful analysis of the relationship between emission and observation time reveals that this need not be monotonic and one-to-one, as multiple retarded times -- or even extended periods of source time -- can contribute to a single instant of reception. Finding solutions to this unusual temporal relation enables us to "measure" the intriguing electromagnetic effects that occur on the cusp and within the envelope of the emitted wave fronts quantitatively. Finally, we proceed to calculate the more sophisticated electromagnetic potentials and fields for these locations, thereby introducing amplitude in addition to phase information. Since integral solutions to Maxwell's equations, traditionally used in the context of stationary or subluminally moving sources, may be problematic when applied to faster-than-light charges due to the presence of multiple or extended retarded times, we will derive and visualize what constitutes the main, substantive part of the present work: The correct formulae for the Liénard-Wiechert potentials and fields of a point charge travelling arbitrarily fast along a given trajectory. Numerical evaluation of these expressions shows that this radiation field has the following intrinsic characteristics: (i) it is sharply focused along a rigidly rotating spiral-shaped beam that embodies the cusp of the envelope of the emitted wave fronts, (ii) it consists of either one or three concurrent polarization modes (depending on the relative positions of the observer and the cusp) that constitute contributions to the field from differing retarded times, (iii) it is highly elliptically polarized, (iv) the position angle of each of its linearly polarized modes swings across the beam by as much as 180 degrees, and (v) the position angles of two of its modes remain approximately orthogonal throughout their excursion across the beam. In an appendix, we compare these findings to the radiation emitted by pulsars, rapidly rotating, highly magnetized neutron stars, and find that virtually all of the enigmatic features of pulsar radiation -— the polarization properties, image structure, apparent radiation temperature and peak spectral frequencies —- can be explained using a single, elegant model with few input parameters and no external assumptions. Hence, superluminal emission is almost certainly not only a human artifact, but an important and likely ubiquitous process in the observable universe that may represent significant amendments to standard models of many astronomical objects. Most calculations in Chapters 4, 5 and the Appendix are of a formal nature only. Rigor can, however, be achieved rather easily in future studies by means of the theory of distributions as outlined in the final part of Chapter 5.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Terry A. Loring

Second Committee Member

Jens Lorenz

Third Committee Member

Klaus Heinemann

Project Sponsors

Los Alamos National Laboratory




Light--Speed, Electromagnetic waves, Superluminal radio sources (Astronomy)

Document Type