Stationary Power-Law Solutions of Kinetic-Alfv\'enic Turbulence
Abstract
The wave-kinetic description of weak kinetic-Alfv\'enic turbulence based on the gyrokinetic theoretical framework is proposed. The wave kinetic equation describing kinetic Alfv\'en wave spectral cascading via resonant three-wave interactions is derived, and the stationary spectra are analytically obtained using the Zakharov transformation in both the long-wavelength limit and the short-wavelength limit, for both counter-propagating and co-propagating cases. The cascade directions of stationary solutions are identified and their existence is further verified by numerical solution of the wave kinetic equation. A brief discussion on the relevance of such predictions to the solar wind turbulence and helical kinetic-Alfv\'enic turbulence is presented.
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