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Fast magnetoacoustic waves guided along the magnetic field by plasmanon-uniformities, in particular coronal loops, fibrils and plumes, are known tobe highly dispersive, which leads to the formation of quasi-periodic wavetrains excited by a broadband impulsive driver, e.g. a solar flare. Weinvestigated effects of cylindrical geometry on the fast sausage wave trainformation. We performed magnetohydrodynamic numerical simulations of fastmagnetoacoustic perturbations of a sausage symmetry, propagating from alocalised impulsive source along a field-aligned plasma cylinder with a smoothradial profile of the fast speed. The wave trains are found to have pronouncedperiod modulation, with the longer instant period seen in the beginning of thewave train. The wave trains have also a pronounced amplitude modulation.Wavelet spectra of the wave trains have characteristic tadpole features, withthe broadband large-amplitude heads preceding low-amplitude quasi-monochromatictails. The mean period of the wave train is about the transverse fastmagnetoacoustic transit time across the cylinder. The mean parallel wavelengthis about the diameter of the waveguiding plasma cylinder. Instant periods arelonger than the sausage wave cutoff period. The wave train characteristicsdepend on the fast magnetoacoustic speed in both the internal and externalmedia, and the smoothness of the transverse profile of the equilibriumquantities, and also the spatial size of the initial perturbation. If theinitial perturbation is localised at the axis of the cylinder, the wave trainscontain higher radial harmonics that have shorter periods.

Fast magnetoacoustic wave trains of sausage symmetry in cylindrical waveguides of the solar corona