MAGNETOHYDRODYNAMIC WAVES IN SOLAR CORONAL ARCADES

The propagation of magnetohydrodynamic (MHD) disturbances in a solar c oronal arcade is investigated. The equations of magnetoacoustic fast a nd slow waves are presented in a very general form: a pair of second-o rder, two-dimensional partial differential equations in which the two dependent variables are the components of the velocity perturbation pa rallel and normal to the magnetic field. In deriving these equations, a general two-dimensional equilibrium structure with no longitudinal m agnetic field component has been assumed. Thus, the equations are vali d for rather general configurations. Alfven waves are decoupled from t he magnetoacoustic modes and give rise to an Alfven continuous spectru m.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 oscilla tory modes, have also been computed. These forces give rise to the pro pagation of MHD waves, and their interaction determines the physical p roperties of the various modes. Therefore, the spatial structure of th e forces and their interplay are basic in characterizing fast and slow modes. Pure fast and pure slow waves do not exist in the present conf iguration, although for the considered parameter values, all modes pos sess either fast-mode or slow-mode properties. ''Slow'' modes in these two-dimensional equilibria can propagate across the magnetic field on ly with difficulty and so display a structure of bands, centred about certain field lines, of alternate positive and negative parallel veloc ity component. On the other hand, ''fast'' modes are isotropic in natu re, and their spatial structure is not so intimately linked to the sha pe of field lines. In addition, as a consequence of the distinct chara cteristic propagation speeds of fast and slow modes, their frequencies typically differ by an order of magnitude.