Three-wave coupling and weak turbulence of kinetic Alfvén waves

Abstract

The nonlinear dynamics of kinetic-Alfvén–wave (KAW) turbulence is studied. Weak KAW turbulence induced by three-wave interaction among parallel-propagating KAWs has a direct energy cascade in the wavenumber domain k_s⊥>ρ⁻¹_i and an inverse cascade in the domain k_s⊥<ρ⁻¹_i, resulting in Kolmogorov-type spectra, W_k∼(k_z) ^−1/2(k_⊥)^−p, with exponents p=4 and p=3.5 respectively. The interaction including antiparallel-propagating KAWs, usually most effective, results in an inverse energy cascade over the whole k_⊥ range and p=2 (at k_⊥<ρ⁻¹_i) and p=3.5 (for k_⊥>ρ⁻¹_i) spectra. Three applications concerning KAW turbulence in flaring loops, in the Earth's magnetosphere and in tokamaks are considered. It is suggested that turbulent KAW spectra are common in space plasmas.