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Context. Rapidly propagating coronal EUV disturbances recently discovered in the solar corona are interpreted in terms of guided fast magnetoacoustic waves. Fast magnetoacoustic waves experience geometric dispersion in waveguides, which causes localised, impulsive perturbations to develop into quasi-periodic wave trains.Aims. We consider the formation of fast wave trains in a super-radially expanding coronal hole modelled by a magnetic funnel with a field-aligned density profile that is rarefied in comparison to the surrounding plasma. This kind of structure is typical of coronal holes, and it forms a fast magnetoacoustic anti-waveguide as a local maximum in the Alfven speed.Methods. We performed 2D MHD numerical simulations for impulsively generated perturbations to the system. Both sausage and kink perturbations are considered and the role of the density contrast ratio investigated.Results. The anti-waveguide funnel geometry refracts wave energy away from the structure. However, in this geometry the quasi-periodic fast wave trains are found to appear, too, and so can be associated with the observed rapidly propagating coronal EUV disturbances. The wave trains propagate along the external edge of the coronal hole. The fast wave trains generated in coronal holes exhibit less dispersive evolution than in the case of a dense waveguide.Conclusions. We conclude that an impulsive energy release localised in a coronal plasma inhomogeneity develops into a fast wave train for both kink and sausage disturbances and for both waveguide and anti-waveguide transverse plasma profiles.

Fast magnetoacoustic wave trains in coronal holes