Nonlinear Alfven waves

Some important nonlinear effects involving Alfven waves in plasmas are presented. For illustrative purposes, we start with small amplitude Alfven waves and their relation with other low-frequency plasma modes. We then show that Alfven and magnetosonic waves can be nonlinearly excited by a high-frequency external pump wave. Finite-amplitude Alfven waves can either interact with the background plasma or with themselves, giving rise to a number of nonlinear phenomena such as wave- amplitude modulation or filamentation, density profile modification, as well as self-organization in vortical structures. The nonlinear effects that are described here are of relevance to the large-amplitude disturbances which are frequently observed in laboratory and space plasmas.