## Terrestrial and extraterrestrial radiation sources that move faster than light

Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/22017

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Title

Terrestrial and extraterrestrial radiation sources that move faster than light

Author(s)

Schmidt Zweifel, Andrea Caroline

Advisor(s)

Singleton, John

Loring, Terry

Loring, Terry

Committee Member(s)

Loring, Terry

Lorenz, Jens

Heinemann, Klaus

Lorenz, Jens

Heinemann, Klaus

Department

University of New Mexico. Dept. of Mathematics and Statistics

LC Subject(s)

Light--Speed.

Electromagnetic waves.

Superluminal radio sources (Astronomy)

Electromagnetic waves.

Superluminal radio sources (Astronomy)

Degree Level

Masters

Abstract

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.

Date

December 2012

Subject(s)

superluminal

electromagnetic radiation

faster-than-light

point charge

Maxwell's equations

Liénard-Wiechert fields

Liénard-Wiechert potentials

scalar wave equation

sonic "boom"

Mach cone

Čerenkov radiation

pulsar emission

electromagnetic fields

electromagnetic potentials

fundamental causal solution

pulsar emission

pulsar frequency spectrum

pulsar polarization

Kepler's Equation

nonspherical decay

retarded Green's function

Stokes parameters

temporal focusing

electromagnetic radiation

faster-than-light

point charge

Maxwell's equations

Liénard-Wiechert fields

Liénard-Wiechert potentials

scalar wave equation

sonic "boom"

Mach cone

Čerenkov radiation

pulsar emission

electromagnetic fields

electromagnetic potentials

fundamental causal solution

pulsar emission

pulsar frequency spectrum

pulsar polarization

Kepler's Equation

nonspherical decay

retarded Green's function

Stokes parameters

temporal focusing

##### Collections

- Mathematics [34]
- Mathematics Theses [11]