Propagation of a fast magnetoacoustic shock wave in the magnetosphere of an active region

The propagation of a fast magnetoacoustic shock wave the magnetosphere of a solar active region is considered the nonlinear geometrical acoustics approximation. The magnetic field is modeled as a subphotospheric magnetic dipole embedded in the radial field of the quiet corona. The initial parameters of the wave are specified at a spherical surface in the depths of the active region. The wave propagates asymmetrically and is reflected from regions of the strong magnetic field, which results in the radiation of the wave energy predominantly upwards. Substantial gradients in the Alfvén speed facilitate appreciable growth in the wave intensity. Non-linear damping of the wave and divergence of the wave front lead to the opposite effect. Analysis of the joint action of these factors shows that a fast magnetoacoustic perturbation outgoing from an active region can correspond to a shock wave of moderate intensity. This supports the scenario in which the primary source of the coronal wave is an eruptive filament that impulsively expands in the magnetosphere of an active region.