Amplification of fast magnetosonic waves and the cut-off spectrum

The propagation of fast magnetosonic waves in an inhomogeneous medium with planar flow in investigated. The equations describing the rays along which the waves propagate are derived, as well as the equations for the variations of the wave amplitude along the rays. These equations are solved for the case of steady flow that depends only on the radius. In addition, it is shown that a spectrum of eigenmodes may exist if the steady flow contains a shock. For that purpose, the reflection coefficient of a fast magnetosonic wave form a shock is derived, and it is shown that the waves can be localized in a region bounded by a shock and a critical surface. A criterion for stability of the spectrum is derived.