Fast magnetohydrodynamic waves in a solar coronal arcade

Aims. Our aim is to investigate detailed properties of fast magnetohydrodynamic (MHD) modes of a three-dimensional waveguide for a cylindrical magnetic arcade. Methods. We derive governing equations and dispersion relations for different density profiles and numerically solve them to obtain discrete eigenvalues for fast modes and the corresponding eigenfunctions. Results. We find that small changes in the density structure in the vicinity of the field lines can lead to drastic effects on propagating solutions and, under certain conditions, two evanescent waves arise. Conclusions. We investigate coronal loop oscillations in an arcade as fast MHD modes of oscillations. We find that coronal loops with slightly different density structures can exhibit different oscillatory behaviour and some eigenmodes can be present or absent depending on this density structure. Though the model has a simple potential field, the role of a cylindrical waveguide in conjunction with differing density structures is demonstrated clearly. Multiple-wavelength observations at several points in the coronal loop arcades is suggested for correct mode identification; this is crucial for unraveling the plasma properties of the oscillating loops.