Resonant decay of kinetic Alfvén waves and implication on spectral cascading

A general equation describing the resonant nonlinear mode-coupling among kinetic Alfv & eacute;n waves (KAWs) is derived using nonlinear gyrokinetic theory, which can be applied to study the potentially strong spectral energy transfer of KAWs. As a first application, the parametric decay of a pump KAW into two sideband KAWs is studied, with particular emphasis on cascading in the perpendicular wavenumber. It is found that, for the "co-propagating" cases with all three KAWs propagating in the same direction along the equilibrium magnetic field line, it exhibits a dual cascading character in the perpendicular wavenumber space; while for the "counter-propagating" cases with one sideband propagating in the opposite direction with respect to the pump wave, it instead, can exhibit both dual and inverse cascading behaviors. Furthermore, the implications of these findings on shear Alfv & eacute;n waves regarding instability, nonlinear saturation, and charged particle transport in fusion plasmas are also discussed.