Aims . We aim to study the presence of superoscillations in coronal magnetoacoustic (MHD) waves and their possible role in heating coronal loops through the strong and localised gradients that they generate on the wave. Methods . An analytic model is built for the transition between sausage and kink wave modes propagating along field lines in the corona. We compute in this model the local frequencies, the wave gradients, and the associated heating rates due to compressive viscosity. Results . We find superoscillations associated with the transition between wave modes accompanying the wave dislocation that shifts through the wave domain. Frequencies ten times higher than the normal frequency are found. This means that a typical three-minute coronal wave will oscillate locally in 10 to 20 s. Such high frequencies bring up strong gradients that efficiently dissipate the wave through compressive viscosity. We compute the associated heating rates; locally, they are very strong, largely compensating typical radiative losses. Conclusions . We find a new heating mechanism associated to magnetoacoustic waves in the corona. Heating due to superoscillations only happens along particular field lines with small cross sections, comparable in size to coronal loops, inside the much larger magnetic flux tubes and wave propagation domain.
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