Magnetosonic wave propagation in a weakly diffusive plasma

The evolution of fast magnetosonic waves in a Hartmann type magnetohydrodynamic equilibrium is studied with geometric optics methods. Rays are shown either to oscillate a round a fixed line parallel to the wall, go to infinity or hit the wall at a finite time. Perturbations of the equilibrium whose frequency has the same order as the inverse of the kinetic and magnetic diffusivities of the plasma are shown to satisfy a transport equation along the rays which may be converted into a viscous Burgers one. This allows us to describe the later evolution of these perturbations, which for periodic rays decay exponentially.