Transformation of the Alfvén Waves in the Low Beta Plasma

The nonlinear mechanism of the transformation of magnetohydrodynamic (MHD) Alfvén waves to kinetic Alfvén waves (KAW) in the homogeneous magnetized plasma with small plasma parameter beta << 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-wave 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.