  The spectrum of electromagnetic fields satisfying perfectly conducting
boundary conditions in a segment of a straight beam pipe with a circular
cross-section is discussed as a function of various source models. These
include charged bunches that move along the axis of the pipe with constant
speed for which an exact solution to the initial-boundary value problem for
Maxwell's equations in the beam pipe is derived. In the ultra-relativistic
limit all longitudinal components of the fields tend to zero and the spectral
content of the transverse fields and average total electromagnetic energy
crossing any section of the beam pipe are directly related to the properties of
the ultra-relativistic source. It is shown that for axially symmetric
ultra-relativistic bunches interference effects occur that show a striking
resemblance to those that occur due to CSR in cyclic machines despite the fact
that in this limit the source is no longer accelerating. The results offer an
analytic description showing how such enhanced spectral behaviour depends on
the geometry of the source and the details of the stochastic distribution of
structure within the source. They offer a viable experimental means for
inferring properties of the longitudinal charge distribution of bunches with
micro-structure in ultra-relativistic motion in straight segments of a beam
pipe from observation of the associated electromagnetic energy spectra. They
are also of relevance to design criteria where the coherence effects of such
fields play a significant role.
