  We consider the nonspherically decaying radiation field that is generated by
a polarization current with a superluminally rotating distribution pattern in
vacuum, a field that decays with the distance $\subP{R}$ from its source as
$\subP{R}^{-1/2}$, instead of $\subP{R}^{-1}$. It is shown (i) that the
nonspherical decay of this emission remains in force at all distances from its
source independently of the frequency of the radiation, (ii) that the part of
the source that makes the main contribution toward the value of the
nonspherically decaying field has a filamentary structure whose radial and
azimuthal widths become narrower (as $\subP{R}^{-2}$ and $\subP{R}^{-3}$,
respectively), the farther the observer is from the source, (iii) that the loci
on which the waves emanating from this filament interfere constructively
delineate a radiation `subbeam' that is nondiffracting in the polar direction,
(iv) that the cross-sectional area of each nondiffracting subbeam increases as
$\subP{R}$, instead of $\subP{R}^2$, so that the requirements of conservation
of energy are met by the nonspherically decaying radiation automatically, and
(v) that the overall radiation beam within which the field decays
nonspherically consists, in general, of the incoherent superposition of such
coherent nondiffracting subbeams. These findings are related to the recent
construction and use of superluminal sources in the laboratory and numerical
models of the emission from them. We also briefly discuss the relevance of
these results to the giant pulses received from pulsars.
