In situ observation of three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales

The energy distribution at wave number space is known to be anisotropic in space plasmas. At kinetic scales, the standard Kinetic Alfven Wave model predicts anisotropy scaling of k_par ∝ k_perp^(1/3), whereas the latest models considering the intermittency, or tearing instabilities, predict scalings such as k_par ∝ k_perp^(2/3) and k_par ∝ k_perp^(3/3). Recent numerical simulations also payed considerable attention to this issue. Based on a unified analysis of five-point structure functions of the turbulence in three kinetic simulations, Cerri et al. 2019 obtained a converging result of l_par ∝ l_perp^(3/3). To enrich our knowledge of the anisotropic scaling relation from an observational point of view, we conducted a statistical survey for the turbulence measured by MMS in the magnetosheath. For the 349 intervals with burst mode data, abundant evidence of 3D anisotropy at the sub-proton scale (1-100 km) is revealed by five-point second order structure functions. In particular, the eddies are mostly elongated along background magnetic field B₀ and shortened in the two perpendicular directions. The ratio between eddies’ parallel and perpendicular lengths features a trend of rise then fall toward small scales, whereas the anisotropy in the perpendicular plane appears scale invariant. Moreover, over 30% of the events exhibit scaling relations close to l_par ∝ l_perp^(2/3). In order to explain such signature, additional factors such as intermittency caused by different coherent structures may be required in addition to the critical balance premise.