Three dimensional anisotropic κ spectra of turbulence at subproton scales in the solar wind

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 ω(plas) ≤ 0.1ω(ci) down to k(⊥) ρ(i)∼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(⊥)ρ(i): a Kolmogorov scaling k(⊥)⁻¹ⁱ⁷ followed by a steeper scaling ∼k(⊥)⁻⁴ⁱ⁵. 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.