Nonlinear three-wave interaction of kinetic Alfvén waves (KAW) and particle acceleration in the earth's magnetosphere

In the kinetic approximation, the resonant nonlinear three-wave interaction of Alfvén waves in the Earth's plasmasphere is considered. The nonlinear equations describing evolution of amplitudes of kinetic Alfvén wave packets are obtained. The parametric decay of one KAW into two others is considered. It is shown that such an interaction is very effective, when the kinetic effects exert an essential influence on kinetic Alfvén waves dispersion, and can considerably exceed similar interaction occurring in other areas of the magnetosphere. The nonlinear interaction of a KAW can lead to the generation of a KAW with small enough transverse wave lengths. At an exit from the plasmasphere in an area remoter from the surface of the Earth, such waves will effectively interact with electrons, that will lead to their acceleration and injection into polar areas of the ionosphere.