Fast magnetoacoustic waves in curved coronal loops - I. Trapped and leaky modes

A study of vertically polarised fast magnetoacoustic waves in a curved coronal loop is presented. The loop is modeled as a semi-circular magnetic slab in the zero plasma-beta limit. The governing equations for linear waves are derived. We show that the wave mode behaviour depends on the slope of the equilibrium density profile, which is modeled as a piece-wise continuous power law curve of index a. For all profiles, except for alpha = -4, wave modes are not trapped in the loop and leak out into the external medium through wave tunneling. The particular case of alpha = -4, which corresponds to a linearly increasing Alfven speed profile, is examined in more detail as this is the only model that can support trapped wave modes. We compare the results with a straight slab model and find similar behaviour. Coupling between sausage and kink wave modes has not been found in the model.