Waves and instabilities in a stratified isothermal atmosphere with constant Alfven speed - revisited

Harmonic perturbations are studied for a plane parallel model for the solar magnetic atmosphere, In the present model, the magnetic field lines are ho rizontal, the sound speed and the Alfven speed are constants. It is known t hat in this: model, analytical solutions can be obtained for linearized per turbations. The harmonic perturbations can either propagate as MHD modes mo dified by the action of gravity or be unstable due to magnetic buoyancy, Di spersion properties and stability limits of these waves as well as the grow thrates of the instability are displayed for various combinations of parame ters: directional angles phi and theta of wave propagation, wave number k a nd the plasma parameter beta. There are three modes propagating in the considered atmosphere: the fast, t he slow and the Alfven mode, all modified by gravity. Only the modified slo w MHD mode can become unstable; the modified Alfven and fast MHD modes are always stable. In the limit of a vanishing magnetic field the modified fast mode becomes an acoustic gravity mode, the modified Alfven mode becomes a mode oscillating with the Brunt-Vaisala frequency at large k, while the mod ified slow mode disappears.