G. Miano et al., TIME-DOMAIN ANALYSIS OF A CHARGED-PARTICLE TRAVELING ALONG THE AXIS OF A CIRCULAR WAVE-GUIDE, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 111(5), 1996, pp. 659-664
The aim of this note is to demonstrate that the electromagnetic field,
in the time domain, sustained by a point charge moving at a constant
velocity along the axis of a circular waveguide can be expanded by mea
ns of a Fourier-Bessel series. This expansion is rapidly convergent in
the complementary range of the classical integral representations, na
mely for large values of \z' - vt'\. Quickly convergent expansions are
necessary for tracking codes to simulate beam dynamics in accelerator
s.