Three Dimensional Anisotropic k Spectra of Turbulence at Subproton Scales in the Solar Wind

Abstract

We show the first three dimensional (3D) dispersion relations and k spectra of magnetic turbulence in the solar wind at subproton scales. We used the Cluster data with short separations and applied the k-filtering technique to the frequency range where the transition to subproton scales occurs. We show that the cascade is carried by highly oblique kinetic Alfvén waves with ωₚₗₐₛ≤ 0.1 ωcᵢ down to k⊥ρᵢ∼ 2. Each k spectrum in the direction perpendicular to B₀ shows two scaling ranges separated by a breakpoint (in the interval [0.4,1]k⊥ρᵢ): a Kolmogorov scaling k⊥⁻¹.⁷ followed by a steeper scaling ∼k⊥⁻⁴.⁵. We conjecture that the turbulence undergoes a transition range, where part of the energy is dissipated into proton heating via Landau damping and the remaining energy cascades down to electron scales where electron Landau damping may predominate.