The nonlinear mechanism of the transformation of magnetohydrodynamic (MHD) Alfvén waves to kinetic Alfvén waves (KAWs) in the homogeneous magnetized plasma with small plasma parameter $\beta\,{\ll}\,1$ is investigated. As the generation mechanism, the parametric instability where the MHD Alfvén wave is the pumping wave is considered. On the basis of the two-fluid MHD and Vlasov equation, the nonlinear dispersion relation describing three-waves interaction, the instability growth rate and the threshold of the instability are found. The theoretical results are used for the interpretation of plasma heating in the solar corona.

The parametric interaction of an upper-hybrid pump wave with kinetic Alfvén and electromagnetic waves that propagate in parallel and perpendicular directions to the ambient magnetic field is investigated on the basis of two-fluid magnetohydrodynamics. A nonlinear dispersion relation describing three-wave interaction and instability growth rates are found. The theoretical results are used for the interpretation of satellite observations in the magnetospheric plasma. It is shown that as a result of the decay of an upper-hybrid wave, electromagnetic waves propagating in both parallel and perpendicular directions to the ambient magnetic field are generated. The instability growth rate is much higher in the case of left-polarized electromagnetic wave generation than in the case of ordinary electromagnetic wave generation. The nonlinear parametric processes studied here could also take place during powerful bursts on the Sun, and in the magnetosphere of Jupiter.

The nonlinear mechanism for kinetic-Alfvén-wave (KAW) excitation by upper-hybrid waves (UHWs) is discussed. Taking into account perpendicular dispersion of KAWs, caused by effects of finite ion Larmor radius and electron inertia, we examine a new channel for UHW decay, in which a pump UHW decays into another UHW and an ultralow-frequency wave, KAW: UHW→KAW+UHW. A nonlinear dispersion relation is derived, and the growth rate of the parametric decay instability is calculated for a pump UHW propagating at an arbitrary angle to the background magnetic field. We find that the resulting KAWs often have a two-peaked spectrum with different perpendicular dispersions. Using satellite observations, the analytical results are applied to show that the considered process represents an effective mechanism for KAW generation and the consequent spreading of the UHW spectrum in the Earth's magnetosphere and solar corona.