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arXiv · 2508.03478

Stationary Power-Law Solutions of Kinetic-Alfv\'{e}nic Turbulence

Kexun Shen·Zhiwen Cheng·Zhiyong Qiu
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Abstract

The wave-kinetic description of weak kinetic-Alfv\'{e}nic turbulence based on the gyrokinetic theoretical framework is proposed. The wave kinetic equation describing kinetic Alfv\'{e}n 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\'{e}nic turbulence is presented.

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Kexun Shen, Zhiwen Cheng, Zhiyong Qiu. 2025-08-05. Stationary Power-Law Solutions of Kinetic-Alfv\'{e}nic Turbulence. https://arxiv.org/abs/2508.03478

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