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

TL;DR

This paper derives and analyzes stationary power-law spectra of kinetic-Alfvénic turbulence using wave-kinetic equations within gyrokinetic theory, with implications for solar wind turbulence.

Contribution

It introduces a wave-kinetic framework for kinetic-Alfvénic turbulence and analytically derives stationary spectra in different regimes, verified by numerical solutions.

Findings

Stationary spectra are analytically obtained for long and short wavelengths.

Cascade directions of turbulence are identified and confirmed numerically.

Relevance to solar wind turbulence is discussed.

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.