  Fast magnetoacoustic waves guided along the magnetic field by plasma
non-uniformities, in particular coronal loops, fibrils and plumes, are known to
be highly dispersive, which leads to the formation of quasi-periodic wave
trains excited by a broadband impulsive driver, e.g. a solar flare. We
investigated effects of cylindrical geometry on the fast sausage wave train
formation. We performed magnetohydrodynamic numerical simulations of fast
magnetoacoustic perturbations of a sausage symmetry, propagating from a
localised impulsive source along a field-aligned plasma cylinder with a smooth
radial profile of the fast speed. The wave trains are found to have pronounced
period modulation, with the longer instant period seen in the beginning of the
wave train. The wave trains have also a pronounced amplitude modulation.
Wavelet spectra of the wave trains have characteristic tadpole features, with
the broadband large-amplitude heads preceding low-amplitude quasi-monochromatic
tails. The mean period of the wave train is about the transverse fast
magnetoacoustic transit time across the cylinder. The mean parallel wavelength
is about the diameter of the waveguiding plasma cylinder. Instant periods are
longer than the sausage wave cutoff period. The wave train characteristics
depend on the fast magnetoacoustic speed in both the internal and external
media, and the smoothness of the transverse profile of the equilibrium
quantities, and also the spatial size of the initial perturbation. If the
initial perturbation is localised at the axis of the cylinder, the wave trains
contain higher radial harmonics that have shorter periods.
