Alfven waves in non-stationary and non-uniform media: An exactly solvable model

The modulation of Alfven waves interacting with a non-uniform and non-stationary plasma is considered. The waveforms are allowed to change rapidly. We examine our phenomena by means of exact analytical solutions of the MHD equations in the presence of large amplitude disturbances of the magnetic field and plasma density. In contrast to the WKB approach, we do not have to use limiting assumptions regarding the variations of the background medium, We show that the large amplitude time and space disturbances lead to a new cut-off frequency for Alfven wave propagation. A rapid reshaping of the Alfven waveform can also obstruct the resonant interactions between the waves and the plasma particles.