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Three-Dimensional Propagation of Magnetohydrodynamic Waves in Solar Coronal Arcades

We numerically investigate the excitation and temporal evolution of oscillations in a two-dimensional coronal arcade by including the three-dimensional propagation of perturbations. The time evolution of impulsively generated perturbations is studied by solving the linear, ideal magnetohydrodynamic (MHD) equations in the zero-beta approximation. As we neglect gas pressure the slow mode is absent and therefore only coupled MHD fast and Alfven modes remain. Two types of numerical experiments are performed. First, the resonant wave energy transfer between a fast normal mode of the system and local Alfven waves is analyzed. It is seen how, because of resonant coupling, the fast wave with global character transfers its energy to Alfvenic oscillations localized around a particular magnetic surface within the arcade, thus producing the damping of the initial fast MHD mode. Second, the time evolution of a localized impulsive excitation, trying to mimic a nearby coronal disturbance, is considered. In this case, the generated fast wavefront leaves its energy on several magnetic surfaces within the arcade. The system is therefore able to trap energy in the form of Alfvenic oscillations, even in the absence of a density enhancement such as that of a coronal loop. These local oscillations are subsequently phase-mixed to smaller spatial scales. The amount of wave energy trapped by the system via wave energy conversion strongly depends on the wavelength of perturbations in the perpendicular direction, but is almost independent from the ratio of the magnetic to density scale heights.