Resonant Alfven wave excitation in two-dimensional systems

The resonant excitation of shear Alfven waves due to coupling with pressure perturbations is studied for an ideal MHD plasma with density varying both along and perpendicular to the constant magnetic field direction. For the case of infinite azimuthal wavelength it is noted that the MHD equations split into two sets describing the ordinary Alfven wave and the Alfven wave modified by pressure waves. Studying the latter set of equations analytically, we find that the pressure waves can resonantly excite the Alfven waves propagating along the z-direction, parallel to the magnetic field, in the neighborhood of the resonant layer $x=x_0$ with local Alfven wave frequency $\omega=\omega_A(x_0)$, with intensity varying in the z-direction. The intensity of the wave becomes maximum near the cutoff layer across which the wave changes from oscillatory to decaying. It is concluded that if the Alfven wave propagates along the magnetic field for considerable distance before reaching the cutoff layer, the Alfven waves in a two-dimensional system will retain the property of phase mixing and consequently resonant absorption similar to the case of a one-dimensional syste