Magnetohydrodynamic Waves in Solar Coronal Arcades

The propagation of magnetohydrodynamic (MRD) disturbances in a solar coronal arcade is investigated. The equations of magnetoacoustic fast and slow waves are presented in a very general form: a pair of second-order, two-dimensional partial differential equations in which the two dependent variables are the components of the velocity perturbation parallel and normal to the magnetic field. In deriving these equations, a general two-dimensional equilibrium structure with no longitudinal magnetic field component has been assumed. Thus, the equations are valid for rather general configurations. Alfvén waves are decoupled from the magnetoacoustic modes and give rise to an Alfvén continuous spectrum. The solutions to the wave equations have been obtained numerically, and the perturbed restoring forces (plasma pressure gradient, magnetic pressure gradient, and magnetic tension), responsible for the oscillatory modes, have also been computed. These forces give rise to the propagation of MRD waves, and their interaction determines the physical properties of the various modes. Therefore, the spatial structure of the forces and their interplay are basic in characterizing fast and slow modes. Pure fast and pure slow waves do not exist in the present configuration, although for the considered parameter values, all modes possess either fast-mode or slow-mode properties. "Slow" modes in these two-dimensional equilibria can propagate across the magnetic field only with difficulty and so display a structure of bands, centred about certain field lines, of alternate positive and negative parallel velocity component. On the other hand, "fast" modes are isotropic in nature, and their spatial structure is not so intimately linked to the shape of field lines. In addition, as a consequence of the distinct characteristic propagation speeds of fast and slow modes, their frequencies typically differ by an order of magnitude.