MHD waves in coronal magnetic arcades

We analyze the eigenmodes of the solar coronal magnetic arcade that describes the magnetic field of a bipolar active region using the eikonal method for ideal magnetohydrodynamic equations. We write out the eikonal equations for Alfvèn and magnetoacoustic waves and derive the equations for the amplitudes of the zeroth approximation. We construct the wave fields for Alfvèn and fast magnetoacoustic modes and derive the expressions for the eigenfrequencies. We show that Alfvèn modes of a given frequency are near a number of magnetic surfaces, while fast magnetoacoustic eigenmodes are near nonmagnetic surfaces. A discrete set of eigenfrequencies that continuously change from one surface to another corresponds to each such surface.