The spatial and spectral content of electromagnetic …fields produced by charged sources in prescribed motion, moving in an infinitely long cylindrical beam pipe with perfect electrically conducting boundary conditions, is investigated in order to understand dynamic …field effects.

In the ultra-relativistic limit analytic field solutions to Maxwell’s equations are determined in both the time and frequency domains, where the fields are explored for various non-stochastic and stochastic multiple pulse source configurations. Their frequency behaviour is shown to be bounded by envelopes and various features are directly related to the source configuration structure. The spectral energy density and spectral transverse field strength are found to have similar frequency response characteristics which differ from those of spectral power.

The …fields are found numerically for single pulse sources, which are not necessarily ultra-relativistic, for both constant velocity and hyperbolic accelerating sources. The equations are expressed in a dimensionless form to aid numerical efficiency. In the ultra-relativistic limit it is seen that the longitudinal …fields are negligible, in contrast with the large slug of transverse field which is co-moving with the source and exists over its entire longitudinal spatial extent. Away from the ultra-relativistic limit all the fields spread out longitudinally beyond the spatial extent of the source and also the longitudinal …field is no longer insignificant; all these …fields exhibit complicated oscillatory dynamics.

The model is based on theory derived from Maxwell’s equations, expressed as a differential system on Minkowski spacetime using the language of differential forms. Along with boundary conditions, the mode structure of the linear system of …field equations is developed, culminating in a telegraph-type equation with source, whose solution enables the system of equations for the transverse and
longitudinal magnetic and electric …fields in the beam pipe to be found for a source with a general charge pro…file.