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

<p>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 &#8733; k_perp^(1/3), whereas the latest models considering the intermittency, or tearing instabilities, predict scalings such as k_par &#8733; k_perp^(2/3) and k_par &#8733; 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 &#8733; 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 <strong>B₀</strong> and shortened in the two perpendicular directions. The ratio between eddies&#8217; 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 &#8733; 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.</p>