The transformation of MHD Alfven waves in space plasma

The nonlinear mechanism of the transformation of magnetohydrodynamic (MHD) Alfven waves to kinetic Alfven waves (KAWs) in the homogeneous magnetized plasma with small plasma parameter beta much less than 1 is investigated. As the generation mechanism, the parametric instability where the MHD Alfven 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.